TSTP Solution File: GRP190-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP190-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:53:59 EDT 2022
% Result : Unsatisfiable 174.22s 173.70s
% Output : Proof 174.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP190-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 12:55:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 174.22/173.70 % SZS status Unsatisfiable
% 174.22/173.70 % SZS output start Proof
% 174.22/173.70 The input problem is unsatisfiable because
% 174.22/173.70
% 174.22/173.70 [1] the following set of Horn clauses is unsatisfiable:
% 174.22/173.70
% 174.22/173.70 multiply(identity, X) = X
% 174.22/173.70 multiply(inverse(X), X) = identity
% 174.22/173.70 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 174.22/173.70 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 174.22/173.70 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 174.22/173.70 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 174.22/173.70 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 174.22/173.70 least_upper_bound(X, X) = X
% 174.22/173.70 greatest_lower_bound(X, X) = X
% 174.22/173.70 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 174.22/173.70 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 174.22/173.70 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 174.22/173.70 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 174.22/173.70 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 174.22/173.70 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 174.22/173.70 least_upper_bound(a, b) = a
% 174.22/173.70 least_upper_bound(inverse(a), inverse(b)) = inverse(b) ==> \bottom
% 174.22/173.70
% 174.22/173.70 This holds because
% 174.22/173.70
% 174.22/173.70 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 174.22/173.70
% 174.22/173.70 E:
% 174.22/173.70 f1(inverse(b)) = false__
% 174.22/173.70 f1(least_upper_bound(inverse(a), inverse(b))) = true__
% 174.22/173.70 greatest_lower_bound(X, X) = X
% 174.22/173.70 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 174.22/173.70 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 174.22/173.70 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 174.22/173.70 least_upper_bound(X, X) = X
% 174.22/173.70 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 174.22/173.70 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 174.22/173.70 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 174.22/173.70 least_upper_bound(a, b) = a
% 174.22/173.70 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 174.22/173.70 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 174.22/173.70 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 174.22/173.70 multiply(identity, X) = X
% 174.22/173.70 multiply(inverse(X), X) = identity
% 174.22/173.70 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 174.22/173.70 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 174.22/173.70 G:
% 174.22/173.70 true__ = false__
% 174.22/173.70
% 174.22/173.70 This holds because
% 174.22/173.70
% 174.22/173.70 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 174.22/173.70
% 174.22/173.70 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 174.22/173.70 greatest_lower_bound(X0, greatest_lower_bound(b, Y2)) = greatest_lower_bound(Y2, greatest_lower_bound(b, X0))
% 174.22/173.70 greatest_lower_bound(X1, multiply(X0, X1)) = multiply(greatest_lower_bound(identity, inverse(X0)), multiply(X0, X1))
% 174.22/173.70 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, Y1), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(X2, Y1)), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(Y1, X2)), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, Y1) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(least_upper_bound(X1, identity), Y1), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X0, a), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X0, least_upper_bound(X1, a)), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X0, least_upper_bound(a, X1)), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(a, X0), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(multiply(least_upper_bound(X0, identity), a), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, b) = greatest_lower_bound(b, greatest_lower_bound(multiply(least_upper_bound(identity, X0), a), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, greatest_lower_bound(X0, a)) = greatest_lower_bound(a, greatest_lower_bound(X0, greatest_lower_bound(a, Y0)))
% 174.22/173.70 greatest_lower_bound(Y0, greatest_lower_bound(X0, b)) = greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(a, Y0)))
% 174.22/173.70 greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(b, Y0))) = greatest_lower_bound(Y0, greatest_lower_bound(b, X1))
% 174.22/173.70 greatest_lower_bound(Y0, greatest_lower_bound(a, X0)) = greatest_lower_bound(a, greatest_lower_bound(X0, greatest_lower_bound(a, Y0)))
% 174.22/173.70 greatest_lower_bound(Y0, greatest_lower_bound(a, X0)) = greatest_lower_bound(a, greatest_lower_bound(Y0, greatest_lower_bound(X0, a)))
% 174.22/173.70 greatest_lower_bound(Y0, greatest_lower_bound(b, X0)) = greatest_lower_bound(b, greatest_lower_bound(Y0, greatest_lower_bound(X0, a)))
% 174.22/173.70 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(a, inverse(b)), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, identity) = greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(b), a), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, inverse(a)) = greatest_lower_bound(inverse(b), greatest_lower_bound(inverse(a), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), Y0)
% 174.22/173.70 greatest_lower_bound(Y0, multiply(X0, Y0)) = multiply(greatest_lower_bound(identity, inverse(inverse(X0))), Y0)
% 174.22/173.70 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(identity, multiply(X0, X1)), Y0)
% 174.22/173.70 greatest_lower_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(greatest_lower_bound(multiply(X0, X1), identity), Y0)
% 174.22/173.70 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1)))
% 174.22/173.70 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0))
% 174.22/173.70 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(X1, Y1)))
% 174.22/173.70 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1)) = greatest_lower_bound(Y1, greatest_lower_bound(multiply(X1, Y1), Y0))
% 174.22/173.70 greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y2)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2))
% 174.22/173.70 greatest_lower_bound(Y1, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, identity), Y1)
% 174.22/173.70 greatest_lower_bound(Y1, multiply(Y2, Y1)) = multiply(greatest_lower_bound(identity, Y2), Y1)
% 174.22/173.70 greatest_lower_bound(Y1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), X1), Y1)) = multiply(greatest_lower_bound(X1, identity), Y1)
% 174.22/173.70 greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2))
% 174.22/173.70 greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(Y1, a))) = greatest_lower_bound(Y1, greatest_lower_bound(b, X0))
% 174.22/173.70 greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(a, Y2))) = greatest_lower_bound(Y2, greatest_lower_bound(b, X0))
% 174.22/173.70 greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(identity, Y2))) = greatest_lower_bound(Y2, greatest_lower_bound(X0, identity))
% 174.22/173.70 greatest_lower_bound(identity, greatest_lower_bound(multiply(b, inverse(a)), Y2)) = greatest_lower_bound(Y2, multiply(b, inverse(a)))
% 174.22/173.70 greatest_lower_bound(identity, multiply(X0, inverse(X1))) = multiply(greatest_lower_bound(X0, X1), inverse(X1))
% 174.22/173.70 greatest_lower_bound(identity, multiply(X1, inverse(X0))) = multiply(greatest_lower_bound(X0, X1), inverse(X0))
% 174.22/173.70 greatest_lower_bound(identity, multiply(Y0, Y1)) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1)
% 174.22/173.70 greatest_lower_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), greatest_lower_bound(Y1, Y2))
% 174.22/173.70 greatest_lower_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), greatest_lower_bound(Y1, Y2))
% 174.22/173.70 greatest_lower_bound(least_upper_bound(X0, a), greatest_lower_bound(least_upper_bound(a, X0), Y2)) = greatest_lower_bound(Y2, least_upper_bound(X0, a))
% 174.22/173.70 greatest_lower_bound(least_upper_bound(a, X0), greatest_lower_bound(least_upper_bound(X0, a), Y2)) = greatest_lower_bound(Y2, least_upper_bound(a, X0))
% 174.22/173.70 greatest_lower_bound(least_upper_bound(b, X0), greatest_lower_bound(least_upper_bound(a, X0), Y2)) = greatest_lower_bound(Y2, least_upper_bound(b, X0))
% 174.22/173.70 greatest_lower_bound(multiply(X0, X1), identity) = multiply(X0, greatest_lower_bound(X1, inverse(X0)))
% 174.22/173.70 greatest_lower_bound(multiply(X0, X1), identity) = multiply(X0, greatest_lower_bound(inverse(X0), X1))
% 174.22/173.70 greatest_lower_bound(multiply(Y0, Y1), identity) = multiply(greatest_lower_bound(Y0, inverse(Y1)), Y1)
% 174.22/173.70 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 174.22/173.70 least_upper_bound(X0, a) = least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(false__, identity), a), X0))
% 174.22/173.70 least_upper_bound(X1, least_upper_bound(X2, least_upper_bound(X1, least_upper_bound(X2, a)))) = least_upper_bound(a, least_upper_bound(X1, X2))
% 174.22/173.70 least_upper_bound(X1, multiply(X0, X1)) = multiply(least_upper_bound(identity, inverse(X0)), multiply(X0, X1))
% 174.22/173.70 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, Y1), Y0))
% 174.22/173.70 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)), Y0))
% 174.22/173.70 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)), Y0))
% 174.22/173.70 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(multiply(greatest_lower_bound(X1, identity), Y1), Y0))
% 174.22/173.70 least_upper_bound(Y0, Y1) = least_upper_bound(Y1, least_upper_bound(multiply(greatest_lower_bound(identity, X1), Y1), Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(X0, b)))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(X0, greatest_lower_bound(X1, b))))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(X0, greatest_lower_bound(b, X1))))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(b, X0)))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, multiply(greatest_lower_bound(X0, identity), b)))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X0), b)))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(greatest_lower_bound(X0, b), Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(X1, b)), Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(b, X1)), Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(X2, a)), Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(a, X2)), Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(X0, identity), b), Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(X1, identity), a), Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(identity, X0), b), Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(b, least_upper_bound(a, Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(greatest_lower_bound(X0, b), least_upper_bound(a, Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(X1, b)), least_upper_bound(a, Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(b, X1)), least_upper_bound(a, Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(greatest_lower_bound(b, X0), least_upper_bound(a, Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(multiply(greatest_lower_bound(X0, identity), b), least_upper_bound(a, Y0))
% 174.22/173.70 least_upper_bound(Y0, a) = least_upper_bound(multiply(greatest_lower_bound(identity, X0), b), least_upper_bound(a, Y0))
% 174.22/173.70 least_upper_bound(Y0, identity) = least_upper_bound(identity, least_upper_bound(multiply(b, inverse(a)), Y0))
% 174.22/173.70 least_upper_bound(Y0, inverse(b)) = least_upper_bound(inverse(b), least_upper_bound(inverse(a), Y0))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(X0, a)) = least_upper_bound(b, least_upper_bound(X0, least_upper_bound(a, Y0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(X0, a)) = least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(a, X0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(X0, b)) = least_upper_bound(b, least_upper_bound(X0, least_upper_bound(b, Y0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(X1, least_upper_bound(a, Y0))) = least_upper_bound(Y0, least_upper_bound(a, X1))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(Y1, a)) = least_upper_bound(Y1, least_upper_bound(Y0, least_upper_bound(a, Y1)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(Y1, a)) = least_upper_bound(Y1, least_upper_bound(a, least_upper_bound(Y1, Y0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(Y2, a)) = least_upper_bound(a, least_upper_bound(Y2, Y0))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, X0)) = least_upper_bound(a, least_upper_bound(X0, least_upper_bound(a, Y0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, X0)) = least_upper_bound(a, least_upper_bound(Y0, least_upper_bound(X0, a)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, X0)) = least_upper_bound(a, least_upper_bound(Y0, least_upper_bound(b, X0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, X0)) = least_upper_bound(b, least_upper_bound(X0, least_upper_bound(Y0, a)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, X0)) = least_upper_bound(b, least_upper_bound(X0, least_upper_bound(a, Y0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, X0)) = least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(X0, a)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, X0)) = least_upper_bound(b, least_upper_bound(a, least_upper_bound(X0, Y0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, Y1)) = least_upper_bound(Y1, least_upper_bound(a, Y0))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, Y1)) = least_upper_bound(Y1, least_upper_bound(a, least_upper_bound(Y1, Y0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(a, least_upper_bound(X1, Y0))) = least_upper_bound(Y0, least_upper_bound(X1, a))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(b, X0)) = least_upper_bound(b, least_upper_bound(X0, least_upper_bound(b, Y0)))
% 174.22/173.70 least_upper_bound(Y0, least_upper_bound(b, X0)) = least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(X0, b)))
% 174.22/173.70 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, inverse(inverse(X0))), Y0)
% 174.22/173.70 least_upper_bound(Y0, multiply(X0, Y0)) = multiply(least_upper_bound(identity, least_upper_bound(X0, identity)), Y0)
% 174.22/173.70 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(identity, multiply(X0, X1)), Y0)
% 174.22/173.70 least_upper_bound(Y0, multiply(X0, multiply(X1, Y0))) = multiply(least_upper_bound(multiply(X0, X1), identity), Y0)
% 174.22/173.70 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1)))
% 174.22/173.70 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0))
% 174.22/173.70 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(Y0, multiply(X1, Y1)))
% 174.22/173.70 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y1)) = least_upper_bound(Y1, least_upper_bound(multiply(X1, Y1), Y0))
% 174.22/173.70 least_upper_bound(Y1, least_upper_bound(Y0, Y2)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2))
% 174.22/173.70 least_upper_bound(Y1, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, identity), Y1)
% 174.22/173.70 least_upper_bound(Y1, multiply(Y2, Y1)) = multiply(least_upper_bound(identity, Y2), Y1)
% 174.22/173.70 least_upper_bound(Y2, least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, Y2))
% 174.22/173.70 least_upper_bound(a, Y1) = least_upper_bound(Y1, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), a))
% 174.30/173.73 least_upper_bound(a, least_upper_bound(X1, least_upper_bound(X0, a))) = least_upper_bound(a, least_upper_bound(X0, X1))
% 174.30/173.73 least_upper_bound(a, least_upper_bound(X2, least_upper_bound(b, X1))) = least_upper_bound(a, least_upper_bound(X1, X2))
% 174.30/173.73 least_upper_bound(b, greatest_lower_bound(least_upper_bound(X1, b), a)) = greatest_lower_bound(a, least_upper_bound(X1, b))
% 174.30/173.73 least_upper_bound(b, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(X2, b)), a)) = greatest_lower_bound(a, least_upper_bound(X1, least_upper_bound(X2, b)))
% 174.30/173.73 least_upper_bound(b, greatest_lower_bound(least_upper_bound(X1, least_upper_bound(b, X2)), a)) = greatest_lower_bound(a, least_upper_bound(X1, least_upper_bound(b, X2)))
% 174.30/173.73 least_upper_bound(b, greatest_lower_bound(least_upper_bound(b, X1), a)) = greatest_lower_bound(a, least_upper_bound(b, X1))
% 174.30/173.73 least_upper_bound(b, greatest_lower_bound(multiply(least_upper_bound(X1, identity), b), a)) = greatest_lower_bound(a, multiply(least_upper_bound(X1, identity), b))
% 174.30/173.73 least_upper_bound(b, greatest_lower_bound(multiply(least_upper_bound(identity, X1), b), a)) = greatest_lower_bound(a, multiply(least_upper_bound(identity, X1), b))
% 174.30/173.73 least_upper_bound(b, least_upper_bound(X0, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), least_upper_bound(X0, least_upper_bound(multiply(greatest_lower_bound(false__, identity), X0), a))))) = least_upper_bound(a, X0)
% 174.30/173.73 least_upper_bound(b, least_upper_bound(X1, least_upper_bound(X2, a))) = least_upper_bound(a, least_upper_bound(X1, X2))
% 174.30/173.73 least_upper_bound(b, least_upper_bound(X1, least_upper_bound(a, X2))) = least_upper_bound(a, least_upper_bound(X1, X2))
% 174.30/173.73 least_upper_bound(b, least_upper_bound(Y0, a)) = least_upper_bound(a, Y0)
% 174.30/173.73 least_upper_bound(greatest_lower_bound(X0, a), least_upper_bound(greatest_lower_bound(b, X0), Y2)) = least_upper_bound(Y2, greatest_lower_bound(X0, a))
% 174.30/173.73 least_upper_bound(greatest_lower_bound(Y0, b), greatest_lower_bound(Y0, a)) = greatest_lower_bound(a, Y0)
% 174.30/173.73 least_upper_bound(greatest_lower_bound(b, X0), least_upper_bound(greatest_lower_bound(a, X0), Y2)) = least_upper_bound(Y2, greatest_lower_bound(a, X0))
% 174.30/173.73 least_upper_bound(greatest_lower_bound(b, Y0), greatest_lower_bound(Y0, a)) = greatest_lower_bound(a, Y0)
% 174.30/173.73 least_upper_bound(identity, least_upper_bound(X0, least_upper_bound(identity, Y2))) = least_upper_bound(Y2, least_upper_bound(X0, identity))
% 174.30/173.73 least_upper_bound(identity, least_upper_bound(multiply(a, inverse(b)), Y2)) = least_upper_bound(Y2, multiply(a, inverse(b)))
% 174.30/173.73 least_upper_bound(identity, least_upper_bound(multiply(inverse(b), a), Y2)) = least_upper_bound(Y2, multiply(inverse(b), a))
% 174.30/173.73 least_upper_bound(identity, multiply(X0, inverse(X1))) = multiply(least_upper_bound(X0, X1), inverse(X1))
% 174.30/173.73 least_upper_bound(identity, multiply(X0, inverse(a))) = multiply(least_upper_bound(a, X0), inverse(a))
% 174.30/173.73 least_upper_bound(identity, multiply(X1, inverse(X0))) = multiply(least_upper_bound(X0, X1), inverse(X0))
% 174.30/173.73 least_upper_bound(identity, multiply(Y0, Y1)) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1)
% 174.30/173.73 least_upper_bound(identity, multiply(a, inverse(X0))) = multiply(least_upper_bound(X0, a), inverse(X0))
% 174.30/173.73 least_upper_bound(identity, multiply(inverse(Y1), Y2)) = multiply(inverse(Y1), least_upper_bound(Y1, Y2))
% 174.30/173.73 least_upper_bound(identity, multiply(inverse(Y2), Y1)) = multiply(inverse(Y2), least_upper_bound(Y1, Y2))
% 174.30/173.73 least_upper_bound(multiply(X0, X1), identity) = multiply(X0, least_upper_bound(X1, inverse(X0)))
% 174.30/173.73 least_upper_bound(multiply(X0, X1), identity) = multiply(X0, least_upper_bound(inverse(X0), X1))
% 174.30/173.73 least_upper_bound(multiply(Y0, Y1), identity) = multiply(least_upper_bound(Y0, inverse(Y1)), Y1)
% 174.30/173.73 multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1))
% 174.30/173.73 multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1) = greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, X2), Y1))
% 174.30/173.73 multiply(greatest_lower_bound(X1, identity), greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(X1, greatest_lower_bound(Y0, Y1))))
% 174.30/173.73 multiply(greatest_lower_bound(identity, X1), greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, multiply(X1, greatest_lower_bound(Y0, Y1))))
% 174.30/173.73 multiply(least_upper_bound(X1, identity), a) = least_upper_bound(greatest_lower_bound(false__, b), multiply(least_upper_bound(identity, X1), a))
% 174.30/173.73 multiply(least_upper_bound(X1, identity), least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, multiply(X1, least_upper_bound(Y0, Y1))))
% 174.30/173.73 multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1))
% 174.30/173.73 multiply(least_upper_bound(X1, least_upper_bound(identity, X1)), a) = least_upper_bound(greatest_lower_bound(false__, b), multiply(least_upper_bound(identity, X1), a))
% 174.30/173.73 multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1) = least_upper_bound(Y1, multiply(least_upper_bound(X1, X2), Y1))
% 174.30/173.73 multiply(least_upper_bound(identity, X1), least_upper_bound(Y0, Y1)) = least_upper_bound(Y0, least_upper_bound(Y1, multiply(X1, least_upper_bound(Y0, Y1))))
% 174.30/173.73 f1(inverse(b)) -> false__
% 174.30/173.73 f1(least_upper_bound(inverse(a), inverse(b))) -> true__
% 174.30/173.73 f1(least_upper_bound(inverse(b), inverse(a))) -> true__
% 174.30/173.73 greatest_lower_bound(X, X) -> X
% 174.30/173.73 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X
% 174.30/173.73 greatest_lower_bound(X0, greatest_lower_bound(a, least_upper_bound(Y1, greatest_lower_bound(a, X0)))) -> greatest_lower_bound(X0, a)
% 174.30/173.73 greatest_lower_bound(X0, greatest_lower_bound(b, least_upper_bound(Y1, a))) -> greatest_lower_bound(X0, b)
% 174.30/173.73 greatest_lower_bound(X0, greatest_lower_bound(b, least_upper_bound(Y1, greatest_lower_bound(a, X0)))) -> greatest_lower_bound(X0, b)
% 174.30/173.73 greatest_lower_bound(X0, greatest_lower_bound(inverse(a), least_upper_bound(Y1, inverse(b)))) -> greatest_lower_bound(X0, inverse(a))
% 174.30/173.73 greatest_lower_bound(X1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(X1, false__)), inverse(multiply(inverse(X1), least_upper_bound(Y1, identity))))) -> inverse(multiply(inverse(X1), least_upper_bound(Y1, identity)))
% 174.30/173.73 greatest_lower_bound(X1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(X1, false__)), inverse(multiply(inverse(X1), least_upper_bound(identity, Y1))))) -> inverse(multiply(inverse(X1), least_upper_bound(identity, Y1)))
% 174.30/173.73 greatest_lower_bound(X1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), inverse(Y1)), X1)) -> multiply(greatest_lower_bound(Y1, identity), multiply(inverse(Y1), X1))
% 174.30/173.73 greatest_lower_bound(X1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), inverse(Y1)), X1)) -> multiply(greatest_lower_bound(identity, Y1), multiply(inverse(Y1), X1))
% 174.30/173.73 greatest_lower_bound(X1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), inverse(least_upper_bound(Y1, identity))), X1)) -> multiply(inverse(least_upper_bound(Y1, identity)), X1)
% 174.30/173.73 greatest_lower_bound(X1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), inverse(least_upper_bound(identity, Y1))), X1)) -> multiply(inverse(least_upper_bound(identity, Y1)), X1)
% 174.30/173.73 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1)
% 174.30/173.73 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(X1, greatest_lower_bound(Y0, Y1)))) -> greatest_lower_bound(Y0, Y1)
% 174.30/173.73 greatest_lower_bound(Y0, greatest_lower_bound(Y1, least_upper_bound(greatest_lower_bound(Y0, Y1), X1))) -> greatest_lower_bound(Y0, Y1)
% 174.30/173.73 greatest_lower_bound(Y0, greatest_lower_bound(Y2, least_upper_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y2)
% 174.30/173.73 greatest_lower_bound(Y0, greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(X1, a), Y0))) -> greatest_lower_bound(Y0, b)
% 174.30/173.73 greatest_lower_bound(Y0, greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(a, X1), Y0))) -> greatest_lower_bound(Y0, b)
% 174.30/173.73 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(X1, Y0), Y2)) -> greatest_lower_bound(Y0, Y2)
% 174.30/173.73 greatest_lower_bound(Y0, greatest_lower_bound(least_upper_bound(Y0, X1), Y2)) -> greatest_lower_bound(Y0, Y2)
% 174.30/173.73 greatest_lower_bound(Y0, greatest_lower_bound(multiply(least_upper_bound(identity, X1), Y0), Y2)) -> greatest_lower_bound(Y0, Y2)
% 174.30/173.73 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y0))) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y0, X2))) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(X2, Y0)))) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(Y0, X2)))) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y0))) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y0))) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X1)), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0))
% 174.30/173.73 greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0))
% 174.30/173.73 greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> greatest_lower_bound(Y0, multiply(X1, Y0))
% 174.30/173.73 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y0)) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y0)) -> Y0
% 174.30/173.73 greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> Y0
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, Y1))) -> greatest_lower_bound(Y0, Y1)
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, Y1)))) -> greatest_lower_bound(Y0, Y1)
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(X1, least_upper_bound(Y1, X2)))) -> greatest_lower_bound(Y0, Y1)
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(Y0, least_upper_bound(Y1, X1))) -> greatest_lower_bound(Y0, Y1)
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(X1, identity), Y1))) -> greatest_lower_bound(Y0, Y1)
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X1), Y1))) -> greatest_lower_bound(Y0, Y1)
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2)
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(b, Y1)) -> greatest_lower_bound(b, Y1)
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), X1)) -> greatest_lower_bound(Y1, X1)
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)))) -> greatest_lower_bound(X1, greatest_lower_bound(X2, Y1))
% 174.30/173.73 greatest_lower_bound(Y1, greatest_lower_bound(least_upper_bound(false__, least_upper_bound(Y1, false__)), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)))) -> greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))
% 174.30/173.73 greatest_lower_bound(Y1, multiply(a, multiply(inverse(b), Y1))) -> Y1
% 174.30/173.73 greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1)
% 174.30/173.73 greatest_lower_bound(Y1, multiply(greatest_lower_bound(least_upper_bound(false__, identity), X1), Y1)) -> multiply(greatest_lower_bound(identity, X1), Y1)
% 174.30/173.73 greatest_lower_bound(Y1, multiply(inverse(b), multiply(a, Y1))) -> Y1
% 174.30/173.73 greatest_lower_bound(a, greatest_lower_bound(Y0, greatest_lower_bound(X0, a))) -> greatest_lower_bound(Y0, greatest_lower_bound(X0, a))
% 174.30/173.73 greatest_lower_bound(a, greatest_lower_bound(Y1, a)) -> greatest_lower_bound(Y1, a)
% 174.30/173.73 greatest_lower_bound(a, greatest_lower_bound(Y1, a)) -> greatest_lower_bound(a, Y1)
% 174.30/173.73 greatest_lower_bound(a, greatest_lower_bound(multiply(least_upper_bound(false__, identity), a), least_upper_bound(b, greatest_lower_bound(X1, a)))) -> least_upper_bound(b, greatest_lower_bound(X1, a))
% 174.30/173.73 greatest_lower_bound(a, greatest_lower_bound(multiply(least_upper_bound(false__, identity), a), least_upper_bound(b, greatest_lower_bound(a, X1)))) -> least_upper_bound(b, greatest_lower_bound(a, X1))
% 174.30/173.73 greatest_lower_bound(a, least_upper_bound(b, greatest_lower_bound(X1, a))) -> least_upper_bound(b, greatest_lower_bound(X1, a))
% 174.30/173.73 greatest_lower_bound(a, least_upper_bound(b, greatest_lower_bound(a, X1))) -> least_upper_bound(b, greatest_lower_bound(a, X1))
% 174.30/173.73 greatest_lower_bound(b, a) -> b
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(X0, a)) -> greatest_lower_bound(b, X0)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(X0, b)) -> greatest_lower_bound(X0, b)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(X0, greatest_lower_bound(a, Y2))) -> greatest_lower_bound(b, greatest_lower_bound(X0, Y2))
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(X0, least_upper_bound(Y1, a))) -> greatest_lower_bound(b, X0)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(X0, least_upper_bound(Y1, greatest_lower_bound(a, X0)))) -> greatest_lower_bound(b, X0)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(X1, greatest_lower_bound(X2, a))) -> greatest_lower_bound(b, greatest_lower_bound(X1, X2))
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, b)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(Y0, greatest_lower_bound(X0, a))) -> greatest_lower_bound(Y0, greatest_lower_bound(X0, b))
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(Y0, greatest_lower_bound(a, X0))) -> greatest_lower_bound(Y0, greatest_lower_bound(b, X0))
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(X0, least_upper_bound(X1, a)))) -> greatest_lower_bound(Y0, b)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(X0, least_upper_bound(a, X1)))) -> greatest_lower_bound(Y0, b)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(Y0, least_upper_bound(a, X0))) -> greatest_lower_bound(Y0, b)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(Y0, multiply(least_upper_bound(X0, identity), a))) -> greatest_lower_bound(Y0, b)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(Y0, multiply(least_upper_bound(identity, X0), a))) -> greatest_lower_bound(Y0, b)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(a, Y2)) -> greatest_lower_bound(b, Y2)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(Y1, a), Y0)) -> greatest_lower_bound(b, Y0)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(least_upper_bound(a, Y1), Y0)) -> greatest_lower_bound(b, Y0)
% 174.30/173.73 greatest_lower_bound(b, greatest_lower_bound(multiply(least_upper_bound(false__, identity), a), multiply(inverse(b), multiply(a, b)))) -> b
% 174.30/173.73 greatest_lower_bound(b, least_upper_bound(X0, a)) -> b
% 174.30/173.73 greatest_lower_bound(b, least_upper_bound(Y0, least_upper_bound(X1, least_upper_bound(X2, a)))) -> b
% 174.30/173.73 greatest_lower_bound(b, least_upper_bound(Y0, least_upper_bound(X1, least_upper_bound(a, X2)))) -> b
% 174.30/173.73 greatest_lower_bound(b, least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), a))) -> b
% 174.30/173.73 greatest_lower_bound(b, least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), a))) -> b
% 174.30/173.73 greatest_lower_bound(b, least_upper_bound(Y1, least_upper_bound(X0, a))) -> b
% 174.30/173.73 greatest_lower_bound(b, least_upper_bound(Y1, least_upper_bound(a, X0))) -> b
% 174.30/173.73 greatest_lower_bound(b, least_upper_bound(a, X0)) -> b
% 174.30/173.73 greatest_lower_bound(b, multiply(a, multiply(inverse(b), a))) -> b
% 174.30/173.73 greatest_lower_bound(b, multiply(greatest_lower_bound(X1, identity), a)) -> greatest_lower_bound(b, multiply(X1, a))
% 174.30/173.73 greatest_lower_bound(b, multiply(greatest_lower_bound(identity, X1), a)) -> greatest_lower_bound(b, multiply(X1, a))
% 174.30/173.73 greatest_lower_bound(b, multiply(greatest_lower_bound(least_upper_bound(false__, identity), multiply(inverse(b), a)), a)) -> b
% 174.30/173.73 greatest_lower_bound(b, multiply(inverse(b), multiply(a, a))) -> b
% 174.30/173.73 greatest_lower_bound(b, multiply(least_upper_bound(X1, identity), a)) -> b
% 174.30/173.73 greatest_lower_bound(b, multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), a)) -> b
% 174.30/173.73 greatest_lower_bound(b, multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), a)) -> b
% 174.30/173.73 greatest_lower_bound(b, multiply(least_upper_bound(identity, X1), a)) -> b
% 174.30/173.73 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 174.30/173.73 greatest_lower_bound(identity, greatest_lower_bound(X0, greatest_lower_bound(identity, Y2))) -> greatest_lower_bound(X0, greatest_lower_bound(identity, Y2))
% 174.30/173.73 greatest_lower_bound(identity, greatest_lower_bound(X0, identity)) -> greatest_lower_bound(X0, identity)
% 174.30/173.73 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(a, inverse(b)))) -> greatest_lower_bound(Y0, identity)
% 174.30/173.73 greatest_lower_bound(identity, greatest_lower_bound(Y0, multiply(inverse(b), a))) -> greatest_lower_bound(Y0, identity)
% 174.30/173.73 greatest_lower_bound(identity, greatest_lower_bound(Y1, identity)) -> greatest_lower_bound(identity, Y1)
% 174.30/173.73 greatest_lower_bound(identity, greatest_lower_bound(multiply(a, inverse(b)), Y2)) -> greatest_lower_bound(identity, Y2)
% 174.30/173.73 greatest_lower_bound(identity, greatest_lower_bound(multiply(inverse(b), a), Y2)) -> greatest_lower_bound(identity, Y2)
% 174.30/173.73 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(Y1, identity), inverse(Y1))
% 174.30/173.73 greatest_lower_bound(identity, inverse(Y1)) -> multiply(greatest_lower_bound(identity, Y1), inverse(Y1))
% 174.30/173.73 greatest_lower_bound(identity, inverse(identity)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, inverse(least_upper_bound(Y1, identity))) -> inverse(least_upper_bound(Y1, identity))
% 174.30/173.73 greatest_lower_bound(identity, inverse(least_upper_bound(identity, Y1))) -> inverse(least_upper_bound(identity, Y1))
% 174.30/173.73 greatest_lower_bound(identity, least_upper_bound(Y0, inverse(identity))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(greatest_lower_bound(identity, inverse(identity))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(inverse(identity)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, least_upper_bound(Y1, inverse(least_upper_bound(identity, inverse(identity))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, least_upper_bound(inverse(greatest_lower_bound(identity, inverse(identity))), Y1)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, least_upper_bound(inverse(identity), Y1)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, least_upper_bound(inverse(inverse(identity)), Y1)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, least_upper_bound(inverse(least_upper_bound(identity, inverse(identity))), Y1)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(X0, greatest_lower_bound(X1, inverse(X0)))) -> multiply(X0, greatest_lower_bound(X1, inverse(X0)))
% 174.30/173.73 greatest_lower_bound(identity, multiply(X0, greatest_lower_bound(inverse(X0), X1))) -> multiply(X0, greatest_lower_bound(inverse(X0), X1))
% 174.30/173.73 greatest_lower_bound(identity, multiply(X0, least_upper_bound(Y1, inverse(X0)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(X0, least_upper_bound(Y1, inverse(inverse(inverse(X0)))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(X0, least_upper_bound(inverse(X0), Y1))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(X0, least_upper_bound(inverse(inverse(inverse(X0))), Y1))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(X1, inverse(multiply(least_upper_bound(Y1, identity), X1)))) -> multiply(X1, inverse(multiply(least_upper_bound(Y1, identity), X1)))
% 174.30/173.73 greatest_lower_bound(identity, multiply(X1, inverse(multiply(least_upper_bound(identity, Y1), X1)))) -> multiply(X1, inverse(multiply(least_upper_bound(identity, Y1), X1)))
% 174.30/173.73 greatest_lower_bound(identity, multiply(X1, multiply(X0, least_upper_bound(Y1, multiply(inverse(X0), inverse(X1)))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(X1, multiply(X0, least_upper_bound(multiply(inverse(X0), inverse(X1)), Y1)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(X1, multiply(inverse(X0), least_upper_bound(Y1, multiply(X0, inverse(X1)))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(X1, multiply(inverse(X0), least_upper_bound(multiply(X0, inverse(X1)), Y1)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, Y0)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(Y0, inverse(greatest_lower_bound(Y0, X1)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(a, inverse(b))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(a, inverse(greatest_lower_bound(X0, b)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(a, inverse(greatest_lower_bound(X0, greatest_lower_bound(X1, b))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(a, inverse(greatest_lower_bound(X0, greatest_lower_bound(b, X1))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(a, inverse(greatest_lower_bound(b, X0)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(a, inverse(multiply(greatest_lower_bound(X0, identity), b)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(a, inverse(multiply(greatest_lower_bound(identity, X0), b)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, X1), inverse(X0))) -> multiply(greatest_lower_bound(X0, X1), inverse(X0))
% 174.30/173.73 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, X1), inverse(X1))) -> multiply(greatest_lower_bound(X0, X1), inverse(X1))
% 174.30/173.73 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, a), inverse(greatest_lower_bound(X0, b)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, a), inverse(greatest_lower_bound(b, X0)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, b), inverse(a))) -> multiply(greatest_lower_bound(X0, b), inverse(a))
% 174.30/173.73 greatest_lower_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> multiply(greatest_lower_bound(X0, inverse(X1)), X1)
% 174.30/173.73 greatest_lower_bound(identity, multiply(greatest_lower_bound(a, X0), inverse(greatest_lower_bound(b, X0)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(a))) -> multiply(greatest_lower_bound(b, X0), inverse(a))
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(X0), greatest_lower_bound(X0, X1))) -> multiply(inverse(X0), greatest_lower_bound(X0, X1))
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(X0), least_upper_bound(X0, X1))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(X0), least_upper_bound(X1, X0))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(X1), multiply(X0, least_upper_bound(Y1, multiply(inverse(X0), X1))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(X1), multiply(X0, least_upper_bound(multiply(inverse(X0), X1), Y1)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(X1), multiply(inverse(X0), least_upper_bound(Y1, multiply(X0, X1))))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(X1), multiply(inverse(X0), least_upper_bound(multiply(X0, X1), Y1)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(a), greatest_lower_bound(X0, a))) -> multiply(inverse(a), greatest_lower_bound(X0, a))
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(b), a)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(b), greatest_lower_bound(X0, b))) -> multiply(inverse(b), greatest_lower_bound(X0, b))
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(b), least_upper_bound(X0, a))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(b), least_upper_bound(a, X0))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X0, b)), a)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X0, greatest_lower_bound(X1, b))), a)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(X0, greatest_lower_bound(b, X1))), a)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(greatest_lower_bound(b, X0)), a)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(least_upper_bound(b, X0)), least_upper_bound(a, X0))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(multiply(greatest_lower_bound(X0, identity), b)), a)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(multiply(greatest_lower_bound(false__, identity), b)), a)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(inverse(multiply(greatest_lower_bound(identity, X0), b)), a)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(X0, a), inverse(b))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(X0, a), inverse(least_upper_bound(a, X0)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(X0, identity), multiply(a, inverse(b)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(X0, least_upper_bound(X1, a)), inverse(b))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(X0, least_upper_bound(a, X1)), inverse(b))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(X1, least_upper_bound(Y1, X2)), inverse(Y1))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, X0), inverse(X0))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, multiply(X1, X0)), multiply(inverse(X0), inverse(X1)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, multiply(X1, inverse(X0))), multiply(X0, inverse(X1)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, multiply(inverse(X1), X0)), multiply(inverse(X0), X1))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(Y0, multiply(inverse(X1), inverse(X0))), multiply(X0, X1))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(Y1, Y0), inverse(Y1))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(Y1, a), inverse(Y1))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(a, X0), inverse(b))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(a, X0), inverse(least_upper_bound(X0, a)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(a, X0), inverse(least_upper_bound(b, X0)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(a, Y0), inverse(a))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(b, X0), inverse(least_upper_bound(X0, b)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(identity, X0), multiply(a, inverse(b)))) -> identity
% 174.30/173.73 greatest_lower_bound(identity, multiply(least_upper_bound(multiply(X0, X1), Y1), multiply(inverse(X1), inverse(X0)))) -> identity
% 174.30/173.73 greatest_lower_bound(inverse(X1), inverse(multiply(X1, least_upper_bound(Y1, identity)))) -> inverse(multiply(X1, least_upper_bound(Y1, identity)))
% 174.30/173.73 greatest_lower_bound(inverse(X1), inverse(multiply(X1, least_upper_bound(identity, Y1)))) -> inverse(multiply(X1, least_upper_bound(identity, Y1)))
% 174.30/173.73 greatest_lower_bound(inverse(a), least_upper_bound(Y1, inverse(b))) -> inverse(a)
% 174.30/173.73 greatest_lower_bound(inverse(b), greatest_lower_bound(Y0, inverse(a))) -> greatest_lower_bound(Y0, inverse(a))
% 174.30/173.73 greatest_lower_bound(inverse(b), greatest_lower_bound(Y1, inverse(b))) -> greatest_lower_bound(Y1, inverse(b))
% 174.30/173.73 greatest_lower_bound(inverse(b), greatest_lower_bound(inverse(a), Y2)) -> greatest_lower_bound(inverse(a), Y2)
% 174.30/173.73 greatest_lower_bound(inverse(b), inverse(a)) -> inverse(a)
% 174.30/173.73 greatest_lower_bound(inverse(least_upper_bound(Y2, identity)), least_upper_bound(Y1, identity)) -> inverse(least_upper_bound(Y2, identity))
% 174.30/173.73 greatest_lower_bound(inverse(least_upper_bound(identity, Y2)), least_upper_bound(Y1, identity)) -> inverse(least_upper_bound(identity, Y2))
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, X1), least_upper_bound(X0, least_upper_bound(X1, Y1))) -> least_upper_bound(X0, X1)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(Y1, least_upper_bound(a, X0))) -> least_upper_bound(X0, a)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(a, X0)) -> least_upper_bound(X0, a)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(Y1, least_upper_bound(b, X0))) -> least_upper_bound(X0, b)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(b, X0)) -> least_upper_bound(X0, b)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, greatest_lower_bound(X1, b)), least_upper_bound(X0, a)) -> least_upper_bound(X0, greatest_lower_bound(X1, b))
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, greatest_lower_bound(X1, b)), least_upper_bound(Y1, least_upper_bound(X0, a))) -> least_upper_bound(X0, greatest_lower_bound(X1, b))
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, greatest_lower_bound(b, X1)), least_upper_bound(X0, a)) -> least_upper_bound(X0, greatest_lower_bound(b, X1))
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, greatest_lower_bound(b, X1)), least_upper_bound(Y1, least_upper_bound(X0, a))) -> least_upper_bound(X0, greatest_lower_bound(b, X1))
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, identity), least_upper_bound(Y1, least_upper_bound(identity, X0))) -> least_upper_bound(X0, identity)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X0, identity), least_upper_bound(identity, X0)) -> least_upper_bound(X0, identity)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X1, least_upper_bound(Y1, X2))) -> least_upper_bound(X1, X2)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(X2, least_upper_bound(Y1, X1))) -> least_upper_bound(X1, X2)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(X2, Y2)))) -> least_upper_bound(X1, X2)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(Y2, X2)))) -> least_upper_bound(X1, X2)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, X2), least_upper_bound(Y1, least_upper_bound(X2, least_upper_bound(Y2, X1)))) -> least_upper_bound(X1, X2)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, Y1), least_upper_bound(X1, greatest_lower_bound(X2, Y1))) -> least_upper_bound(X1, greatest_lower_bound(X2, Y1))
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, Y1), least_upper_bound(X1, greatest_lower_bound(Y1, X2))) -> least_upper_bound(X1, greatest_lower_bound(Y1, X2))
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, a), least_upper_bound(Y1, least_upper_bound(a, least_upper_bound(X1, Y2)))) -> least_upper_bound(X1, a)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, a), least_upper_bound(a, least_upper_bound(X1, Y1))) -> least_upper_bound(X1, a)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(X1, greatest_lower_bound(Y1, X2)), least_upper_bound(Y1, X1)) -> least_upper_bound(X1, greatest_lower_bound(Y1, X2))
% 174.30/173.73 greatest_lower_bound(least_upper_bound(Y0, a), least_upper_bound(b, Y0)) -> least_upper_bound(b, Y0)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(Y0, b), least_upper_bound(Y0, a)) -> least_upper_bound(b, Y0)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(Y0, b), least_upper_bound(a, Y0)) -> least_upper_bound(b, Y0)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(Y1, X2), least_upper_bound(greatest_lower_bound(X1, Y1), X2)) -> least_upper_bound(greatest_lower_bound(X1, Y1), X2)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(Y1, X2), least_upper_bound(greatest_lower_bound(Y1, X1), X2)) -> least_upper_bound(greatest_lower_bound(Y1, X1), X2)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(a, X0), least_upper_bound(X0, a)) -> least_upper_bound(a, X0)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(a, X0), least_upper_bound(Y1, least_upper_bound(X0, a))) -> least_upper_bound(a, X0)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(a, X1), least_upper_bound(X1, least_upper_bound(a, Y1))) -> least_upper_bound(a, X1)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(a, X1), least_upper_bound(Y1, least_upper_bound(X1, least_upper_bound(a, Y2)))) -> least_upper_bound(a, X1)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(a, Y0), least_upper_bound(Y0, b)) -> least_upper_bound(b, Y0)
% 174.30/173.73 greatest_lower_bound(least_upper_bound(b, X0), least_upper_bound(Y1, least_upper_bound(a, X0))) -> least_upper_bound(b, X0)
% 174.30/173.74 greatest_lower_bound(least_upper_bound(b, X0), least_upper_bound(a, X0)) -> least_upper_bound(b, X0)
% 174.30/173.74 greatest_lower_bound(least_upper_bound(b, Y0), least_upper_bound(Y0, a)) -> least_upper_bound(b, Y0)
% 174.30/173.74 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X0, b), X1), least_upper_bound(X1, a)) -> least_upper_bound(greatest_lower_bound(X0, b), X1)
% 174.30/173.74 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X0, b), X1), least_upper_bound(Y1, least_upper_bound(X1, a))) -> least_upper_bound(greatest_lower_bound(X0, b), X1)
% 174.30/173.74 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X0, b), X1), least_upper_bound(a, X1)) -> least_upper_bound(greatest_lower_bound(X0, b), X1)
% 174.30/173.74 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1, Y1), X2), least_upper_bound(X2, Y1)) -> least_upper_bound(greatest_lower_bound(X1, Y1), X2)
% 174.30/173.74 greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1, Y2), X2), least_upper_bound(Y1, least_upper_bound(X2, Y2))) -> least_upper_bound(greatest_lower_bound(X1, Y2), X2)
% 174.30/173.74 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z))
% 174.30/173.74 greatest_lower_bound(multiply(X0, greatest_lower_bound(X1, X2)), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X0, X2), Y2))
% 174.30/173.74 greatest_lower_bound(multiply(X0, inverse(least_upper_bound(X0, X1))), least_upper_bound(Y1, identity)) -> multiply(X0, inverse(least_upper_bound(X0, X1)))
% 174.30/173.74 greatest_lower_bound(multiply(X0, inverse(least_upper_bound(X1, X0))), least_upper_bound(Y1, identity)) -> multiply(X0, inverse(least_upper_bound(X1, X0)))
% 174.30/173.74 greatest_lower_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(greatest_lower_bound(multiply(X0, X1), Y2), Y1)
% 174.30/173.74 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(X1, identity), Y2))) -> multiply(X1, Y2)
% 174.30/173.74 greatest_lower_bound(multiply(X1, Y2), least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y2))) -> multiply(X1, Y2)
% 174.30/173.74 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X)
% 174.30/173.74 greatest_lower_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(greatest_lower_bound(Y0, multiply(X0, X1)), Y1)
% 174.30/173.74 greatest_lower_bound(multiply(b, inverse(a)), greatest_lower_bound(multiply(X0, inverse(a)), least_upper_bound(Y1, identity))) -> multiply(greatest_lower_bound(b, X0), inverse(a))
% 174.30/173.74 greatest_lower_bound(multiply(b, inverse(a)), least_upper_bound(Y1, identity)) -> multiply(b, inverse(a))
% 174.30/173.74 greatest_lower_bound(multiply(b, inverse(least_upper_bound(X0, a))), least_upper_bound(Y1, identity)) -> multiply(b, inverse(least_upper_bound(X0, a)))
% 174.30/173.74 greatest_lower_bound(multiply(b, inverse(least_upper_bound(a, X0))), least_upper_bound(Y1, identity)) -> multiply(b, inverse(least_upper_bound(a, X0)))
% 174.30/173.74 greatest_lower_bound(multiply(b, multiply(inverse(a), Y2)), least_upper_bound(Y1, Y2)) -> multiply(b, multiply(inverse(a), Y2))
% 174.30/173.74 greatest_lower_bound(multiply(greatest_lower_bound(X0, X2), X1), Y2) -> greatest_lower_bound(multiply(X0, X1), greatest_lower_bound(multiply(X2, X1), Y2))
% 174.30/173.74 inverse(greatest_lower_bound(identity, inverse(identity))) -> identity
% 174.30/173.74 inverse(identity) -> identity
% 174.30/173.74 inverse(inverse(Y0)) -> Y0
% 174.30/173.74 inverse(inverse(identity)) -> identity
% 174.30/173.74 inverse(least_upper_bound(identity, inverse(identity))) -> identity
% 174.30/173.74 inverse(multiply(X1, Y0)) -> multiply(inverse(Y0), inverse(X1))
% 174.30/173.74 inverse(multiply(X1, inverse(Y0))) -> multiply(Y0, inverse(X1))
% 174.30/173.74 inverse(multiply(inverse(X1), Y0)) -> multiply(inverse(Y0), X1)
% 174.30/173.74 inverse(multiply(inverse(X1), inverse(Y0))) -> multiply(Y0, X1)
% 174.30/173.74 least_upper_bound(X, X) -> X
% 174.30/173.74 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X
% 174.30/173.74 least_upper_bound(X0, least_upper_bound(a, X0)) -> least_upper_bound(a, X0)
% 174.30/173.74 least_upper_bound(X0, least_upper_bound(a, least_upper_bound(X1, greatest_lower_bound(Y1, b)))) -> least_upper_bound(X0, least_upper_bound(a, X1))
% 174.30/173.74 least_upper_bound(X1, least_upper_bound(greatest_lower_bound(false__, greatest_lower_bound(X1, false__)), inverse(multiply(inverse(X1), greatest_lower_bound(Y1, identity))))) -> inverse(multiply(inverse(X1), greatest_lower_bound(Y1, identity)))
% 174.30/173.74 least_upper_bound(X1, least_upper_bound(greatest_lower_bound(false__, greatest_lower_bound(X1, false__)), inverse(multiply(inverse(X1), greatest_lower_bound(identity, Y1))))) -> inverse(multiply(inverse(X1), greatest_lower_bound(identity, Y1)))
% 174.30/173.74 least_upper_bound(X1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), inverse(Y1)), X1)) -> multiply(least_upper_bound(Y1, identity), multiply(inverse(Y1), X1))
% 174.30/173.74 least_upper_bound(X1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), inverse(Y1)), X1)) -> multiply(least_upper_bound(identity, Y1), multiply(inverse(Y1), X1))
% 174.30/173.74 least_upper_bound(X1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), inverse(greatest_lower_bound(Y1, identity))), X1)) -> multiply(inverse(greatest_lower_bound(Y1, identity)), X1)
% 174.30/173.74 least_upper_bound(X1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), inverse(greatest_lower_bound(identity, Y1))), X1)) -> multiply(inverse(greatest_lower_bound(identity, Y1)), X1)
% 174.30/173.74 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0))) -> Y0
% 174.30/173.74 least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2))) -> Y0
% 174.30/173.74 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0
% 174.30/173.74 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(X2, Y0)))) -> Y0
% 174.30/173.74 least_upper_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(Y0, X2)))) -> Y0
% 174.30/173.74 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y0))) -> Y0
% 174.30/173.74 least_upper_bound(Y0, greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y0))) -> Y0
% 174.30/173.74 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(X1, least_upper_bound(Y0, Y1)))) -> least_upper_bound(Y0, Y1)
% 174.30/173.74 least_upper_bound(Y0, least_upper_bound(Y1, greatest_lower_bound(least_upper_bound(Y0, Y1), X1))) -> least_upper_bound(Y0, Y1)
% 174.30/173.74 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1)
% 174.30/173.74 least_upper_bound(Y0, least_upper_bound(Y2, greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, Y2)
% 174.30/173.74 least_upper_bound(Y0, least_upper_bound(a, Y0)) -> least_upper_bound(Y0, a)
% 174.30/173.74 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(X1, b), least_upper_bound(a, Y0))) -> least_upper_bound(Y0, a)
% 174.30/173.74 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y0, X1), Y2)) -> least_upper_bound(Y0, Y2)
% 174.30/173.74 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(Y1, Y0), Y2)) -> least_upper_bound(Y0, Y2)
% 174.30/173.74 least_upper_bound(Y0, least_upper_bound(greatest_lower_bound(b, X1), least_upper_bound(a, Y0))) -> least_upper_bound(Y0, a)
% 174.30/173.74 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y0)) -> Y0
% 174.30/173.74 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y0)) -> Y0
% 174.30/173.74 least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y0)) -> Y0
% 174.30/173.74 least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y0)) -> Y0
% 174.30/173.74 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0))
% 174.30/173.74 least_upper_bound(Y0, multiply(least_upper_bound(X1, identity), greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, multiply(X1, greatest_lower_bound(Y0, Y1)))
% 174.30/173.74 least_upper_bound(Y0, multiply(least_upper_bound(X1, least_upper_bound(identity, X1)), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0))
% 174.30/173.74 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), Y0)) -> least_upper_bound(Y0, multiply(X1, Y0))
% 174.30/173.74 least_upper_bound(Y0, multiply(least_upper_bound(identity, X1), greatest_lower_bound(Y0, Y1))) -> least_upper_bound(Y0, multiply(X1, greatest_lower_bound(Y0, Y1)))
% 174.30/173.74 least_upper_bound(Y1, least_upper_bound(X1, multiply(least_upper_bound(X2, identity), Y1))) -> least_upper_bound(X1, multiply(least_upper_bound(X2, identity), Y1))
% 174.30/173.74 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, Y1))) -> least_upper_bound(Y0, Y1)
% 174.30/173.74 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, Y1)))) -> least_upper_bound(Y0, Y1)
% 174.30/173.74 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)))) -> least_upper_bound(Y0, Y1)
% 174.30/173.74 least_upper_bound(Y1, least_upper_bound(Y0, greatest_lower_bound(Y1, X1))) -> least_upper_bound(Y0, Y1)
% 174.30/173.74 least_upper_bound(Y1, least_upper_bound(Y0, least_upper_bound(a, Y1))) -> least_upper_bound(Y0, least_upper_bound(a, Y1))
% 174.30/173.74 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(X1, identity), Y1))) -> least_upper_bound(Y0, Y1)
% 174.30/173.74 least_upper_bound(Y1, least_upper_bound(Y0, multiply(greatest_lower_bound(identity, X1), Y1))) -> least_upper_bound(Y0, Y1)
% 174.30/173.74 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2)
% 174.30/173.74 least_upper_bound(Y1, multiply(b, multiply(inverse(a), Y1))) -> Y1
% 174.30/173.74 least_upper_bound(Y1, multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1)) -> multiply(least_upper_bound(X1, least_upper_bound(X2, identity)), Y1)
% 174.30/173.74 least_upper_bound(Y1, multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1)) -> multiply(least_upper_bound(X1, least_upper_bound(identity, X2)), Y1)
% 174.30/173.74 least_upper_bound(Y1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), multiply(a, inverse(b))), Y1)) -> multiply(a, multiply(inverse(b), Y1))
% 174.30/173.74 least_upper_bound(Y1, multiply(least_upper_bound(greatest_lower_bound(false__, identity), multiply(inverse(b), a)), Y1)) -> multiply(inverse(b), multiply(a, Y1))
% 174.30/173.74 least_upper_bound(Y1, multiply(least_upper_bound(identity, X1), Y1)) -> multiply(least_upper_bound(identity, X1), Y1)
% 174.30/173.74 least_upper_bound(a, b) -> a
% 174.30/173.74 least_upper_bound(a, greatest_lower_bound(X1, b)) -> a
% 174.30/173.74 least_upper_bound(a, greatest_lower_bound(X1, greatest_lower_bound(X2, b))) -> a
% 174.30/173.74 least_upper_bound(a, greatest_lower_bound(X1, greatest_lower_bound(b, X2))) -> a
% 174.30/173.74 least_upper_bound(a, greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(X2, b)))) -> a
% 174.30/173.74 least_upper_bound(a, greatest_lower_bound(Y0, greatest_lower_bound(X1, greatest_lower_bound(b, X2)))) -> a
% 174.30/173.74 least_upper_bound(a, greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), b))) -> a
% 174.30/173.74 least_upper_bound(a, greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), b))) -> a
% 174.30/173.74 least_upper_bound(a, greatest_lower_bound(b, X1)) -> a
% 174.30/173.74 least_upper_bound(a, least_upper_bound(X0, a)) -> least_upper_bound(a, X0)
% 174.30/173.74 least_upper_bound(a, least_upper_bound(X0, greatest_lower_bound(Y1, b))) -> least_upper_bound(a, X0)
% 174.30/173.74 least_upper_bound(a, least_upper_bound(X0, least_upper_bound(b, least_upper_bound(X0, a)))) -> least_upper_bound(b, least_upper_bound(a, X0))
% 174.30/173.74 least_upper_bound(a, least_upper_bound(X1, least_upper_bound(X2, b))) -> least_upper_bound(a, least_upper_bound(X1, X2))
% 174.30/173.74 least_upper_bound(a, least_upper_bound(X1, least_upper_bound(b, X1))) -> least_upper_bound(b, least_upper_bound(a, X1))
% 174.30/173.74 least_upper_bound(a, least_upper_bound(X1, least_upper_bound(b, X2))) -> least_upper_bound(a, least_upper_bound(X1, X2))
% 174.30/173.74 least_upper_bound(a, least_upper_bound(Y0, greatest_lower_bound(b, Y1))) -> least_upper_bound(a, Y0)
% 174.30/173.74 least_upper_bound(a, least_upper_bound(b, Y2)) -> least_upper_bound(a, Y2)
% 174.30/173.74 least_upper_bound(a, least_upper_bound(greatest_lower_bound(X0, b), Y2)) -> least_upper_bound(a, Y2)
% 174.30/173.74 least_upper_bound(a, least_upper_bound(greatest_lower_bound(X0, b), a)) -> a
% 174.30/173.74 least_upper_bound(a, least_upper_bound(greatest_lower_bound(b, X1), X2)) -> least_upper_bound(b, least_upper_bound(a, X2))
% 174.30/173.74 least_upper_bound(a, least_upper_bound(multiply(X0, a), greatest_lower_bound(Y1, b))) -> multiply(least_upper_bound(X0, identity), a)
% 174.30/173.74 least_upper_bound(a, least_upper_bound(multiply(X0, a), greatest_lower_bound(Y1, b))) -> multiply(least_upper_bound(identity, X0), a)
% 174.30/173.74 least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(false__, identity), a), X1)) -> least_upper_bound(a, X1)
% 174.30/173.74 least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(false__, identity), a), greatest_lower_bound(X1, greatest_lower_bound(X2, a)))) -> a
% 174.30/173.74 least_upper_bound(a, least_upper_bound(multiply(greatest_lower_bound(false__, identity), a), greatest_lower_bound(X1, greatest_lower_bound(a, X2)))) -> a
% 174.30/173.74 least_upper_bound(a, multiply(b, multiply(inverse(a), b))) -> a
% 174.30/173.74 least_upper_bound(a, multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), b)) -> a
% 174.30/173.74 least_upper_bound(a, multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), b)) -> a
% 174.30/173.74 least_upper_bound(a, multiply(greatest_lower_bound(X1, identity), b)) -> a
% 174.30/173.74 least_upper_bound(a, multiply(greatest_lower_bound(identity, X1), b)) -> a
% 174.30/173.74 least_upper_bound(a, multiply(least_upper_bound(X1, identity), b)) -> least_upper_bound(a, multiply(X1, b))
% 174.30/173.74 least_upper_bound(a, multiply(least_upper_bound(identity, X1), b)) -> least_upper_bound(a, multiply(X1, b))
% 174.30/173.74 least_upper_bound(b, a) -> a
% 174.30/173.74 least_upper_bound(b, greatest_lower_bound(a, least_upper_bound(X1, b))) -> greatest_lower_bound(a, least_upper_bound(X1, b))
% 174.30/173.74 least_upper_bound(b, greatest_lower_bound(a, least_upper_bound(b, X1))) -> greatest_lower_bound(a, least_upper_bound(b, X1))
% 174.30/173.74 least_upper_bound(b, least_upper_bound(X1, least_upper_bound(X2, a))) -> least_upper_bound(X1, least_upper_bound(X2, a))
% 174.30/173.74 least_upper_bound(b, least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 174.30/173.74 least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(X0, b))) -> least_upper_bound(Y0, least_upper_bound(X0, b))
% 174.30/173.74 least_upper_bound(b, least_upper_bound(Y0, least_upper_bound(a, X0))) -> least_upper_bound(Y0, least_upper_bound(a, X0))
% 174.30/173.74 least_upper_bound(b, least_upper_bound(Y1, b)) -> least_upper_bound(Y1, b)
% 174.30/173.74 least_upper_bound(b, least_upper_bound(Y1, b)) -> least_upper_bound(b, Y1)
% 174.30/173.74 least_upper_bound(b, least_upper_bound(a, Y0)) -> least_upper_bound(a, Y0)
% 174.30/173.74 least_upper_bound(b, least_upper_bound(a, least_upper_bound(X0, Y2))) -> least_upper_bound(a, least_upper_bound(X0, Y2))
% 174.30/173.74 least_upper_bound(b, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), least_upper_bound(X0, least_upper_bound(X1, a)))) -> least_upper_bound(X0, least_upper_bound(X1, a))
% 174.30/173.74 least_upper_bound(b, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), least_upper_bound(X0, least_upper_bound(a, X1)))) -> least_upper_bound(X0, least_upper_bound(a, X1))
% 174.30/173.74 least_upper_bound(b, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), multiply(least_upper_bound(X0, identity), a))) -> multiply(least_upper_bound(X0, identity), a)
% 174.30/173.74 least_upper_bound(b, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), multiply(least_upper_bound(identity, X0), a))) -> multiply(least_upper_bound(identity, X0), a)
% 174.30/173.74 least_upper_bound(b, multiply(inverse(b), multiply(a, a))) -> multiply(inverse(b), multiply(a, a))
% 174.30/173.74 least_upper_bound(b, multiply(least_upper_bound(X1, identity), a)) -> multiply(least_upper_bound(identity, X1), a)
% 174.30/173.74 least_upper_bound(b, multiply(least_upper_bound(identity, X1), a)) -> multiply(least_upper_bound(identity, X1), a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, X1), greatest_lower_bound(X0, greatest_lower_bound(X1, Y1))) -> greatest_lower_bound(X0, X1)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(Y1, greatest_lower_bound(X0, b))) -> greatest_lower_bound(X0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(Y1, greatest_lower_bound(a, X0))) -> greatest_lower_bound(X0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(Y1, greatest_lower_bound(b, X0))) -> greatest_lower_bound(X0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(a, X0)) -> greatest_lower_bound(X0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(b, X0)) -> greatest_lower_bound(X0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, b), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, b), least_upper_bound(multiply(greatest_lower_bound(false__, identity), greatest_lower_bound(X0, b)), greatest_lower_bound(X0, a))) -> greatest_lower_bound(X0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, greatest_lower_bound(X1, b)), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, identity), greatest_lower_bound(Y1, greatest_lower_bound(identity, X0))) -> greatest_lower_bound(X0, identity)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, identity), greatest_lower_bound(identity, X0)) -> greatest_lower_bound(X0, identity)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X0, least_upper_bound(X1, a)), greatest_lower_bound(b, X0)) -> greatest_lower_bound(X0, least_upper_bound(X1, a))
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X1, greatest_lower_bound(Y1, X2))) -> greatest_lower_bound(X1, X2)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(X2, greatest_lower_bound(Y1, X1))) -> greatest_lower_bound(X1, X2)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(X2, Y2)))) -> greatest_lower_bound(X1, X2)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(Y2, X2)))) -> greatest_lower_bound(X1, X2)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, X2), greatest_lower_bound(Y1, greatest_lower_bound(X2, greatest_lower_bound(Y2, X1)))) -> greatest_lower_bound(X1, X2)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, Y1), greatest_lower_bound(X1, least_upper_bound(X2, Y1))) -> greatest_lower_bound(X1, least_upper_bound(X2, Y1))
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, Y1), greatest_lower_bound(X1, least_upper_bound(Y1, X2))) -> greatest_lower_bound(X1, least_upper_bound(Y1, X2))
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(X2, greatest_lower_bound(Y0, b))), a) -> a
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, greatest_lower_bound(Y0, greatest_lower_bound(b, X2))), a) -> a
% 174.30/173.74 least_upper_bound(greatest_lower_bound(X1, least_upper_bound(Y1, X2)), greatest_lower_bound(Y1, X1)) -> greatest_lower_bound(X1, least_upper_bound(Y1, X2))
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y0, b), a) -> a
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y0, b), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y0, b), greatest_lower_bound(a, Y0)) -> greatest_lower_bound(a, Y0)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y0, greatest_lower_bound(Y1, b)), a) -> a
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y0, greatest_lower_bound(b, Y1)), a) -> a
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y0, multiply(greatest_lower_bound(X1, identity), b)), a) -> a
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y0, multiply(greatest_lower_bound(identity, X1), b)), a) -> a
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y1, X2), greatest_lower_bound(least_upper_bound(X1, Y1), X2)) -> greatest_lower_bound(least_upper_bound(X1, Y1), X2)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y1, X2), greatest_lower_bound(least_upper_bound(Y1, X1), X2)) -> greatest_lower_bound(least_upper_bound(Y1, X1), X2)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(Y1, b), least_upper_bound(a, Y0)) -> least_upper_bound(a, Y0)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(a, X0), greatest_lower_bound(Y1, greatest_lower_bound(b, X0))) -> greatest_lower_bound(a, X0)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(a, X0)) -> greatest_lower_bound(a, X0)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(b, X0), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(b, X0), least_upper_bound(multiply(greatest_lower_bound(false__, identity), greatest_lower_bound(b, X0)), greatest_lower_bound(a, X0))) -> greatest_lower_bound(a, X0)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(b, X1), greatest_lower_bound(X1, greatest_lower_bound(b, Y1))) -> greatest_lower_bound(b, X1)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(b, X1), greatest_lower_bound(Y1, greatest_lower_bound(X1, greatest_lower_bound(b, Y2)))) -> greatest_lower_bound(b, X1)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(b, Y0), a) -> a
% 174.30/173.74 least_upper_bound(greatest_lower_bound(b, Y0), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(b, Y1), least_upper_bound(a, Y0)) -> least_upper_bound(a, Y0)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(false__, b), multiply(least_upper_bound(identity, X1), a)) -> multiply(least_upper_bound(identity, X1), a)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(false__, multiply(greatest_lower_bound(false__, identity), b)), a) -> a
% 174.30/173.74 least_upper_bound(greatest_lower_bound(least_upper_bound(X0, a), X1), greatest_lower_bound(X1, b)) -> greatest_lower_bound(least_upper_bound(X0, a), X1)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(least_upper_bound(X1, Y1), X2), greatest_lower_bound(X2, Y1)) -> greatest_lower_bound(least_upper_bound(X1, Y1), X2)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(least_upper_bound(X1, Y2), X2), greatest_lower_bound(Y1, greatest_lower_bound(X2, Y2))) -> greatest_lower_bound(least_upper_bound(X1, Y2), X2)
% 174.30/173.74 least_upper_bound(greatest_lower_bound(least_upper_bound(a, X0), X1), greatest_lower_bound(X1, b)) -> greatest_lower_bound(least_upper_bound(a, X0), X1)
% 174.30/173.74 least_upper_bound(identity, greatest_lower_bound(Y0, inverse(identity))) -> identity
% 174.30/173.74 least_upper_bound(identity, greatest_lower_bound(inverse(greatest_lower_bound(identity, inverse(identity))), Y1)) -> identity
% 174.30/173.74 least_upper_bound(identity, greatest_lower_bound(inverse(identity), Y1)) -> identity
% 174.30/173.74 least_upper_bound(identity, greatest_lower_bound(inverse(inverse(identity)), Y1)) -> identity
% 174.30/173.74 least_upper_bound(identity, greatest_lower_bound(inverse(least_upper_bound(identity, inverse(identity))), Y1)) -> identity
% 174.30/173.74 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(Y1, identity), inverse(Y1))
% 174.30/173.74 least_upper_bound(identity, inverse(Y1)) -> multiply(least_upper_bound(identity, Y1), inverse(Y1))
% 174.30/173.74 least_upper_bound(identity, inverse(greatest_lower_bound(Y1, identity))) -> inverse(greatest_lower_bound(Y1, identity))
% 174.30/173.74 least_upper_bound(identity, inverse(greatest_lower_bound(identity, Y1))) -> inverse(greatest_lower_bound(identity, Y1))
% 174.30/173.74 least_upper_bound(identity, inverse(identity)) -> identity
% 174.30/173.74 least_upper_bound(identity, least_upper_bound(X0, identity)) -> least_upper_bound(X0, identity)
% 174.30/173.74 least_upper_bound(identity, least_upper_bound(X0, least_upper_bound(identity, Y2))) -> least_upper_bound(X0, least_upper_bound(identity, Y2))
% 174.30/173.74 least_upper_bound(identity, least_upper_bound(Y0, multiply(b, inverse(a)))) -> least_upper_bound(Y0, identity)
% 174.30/173.74 least_upper_bound(identity, least_upper_bound(Y1, identity)) -> least_upper_bound(identity, Y1)
% 174.30/173.74 least_upper_bound(identity, least_upper_bound(multiply(a, inverse(b)), Y2)) -> least_upper_bound(multiply(a, inverse(b)), Y2)
% 174.30/173.74 least_upper_bound(identity, least_upper_bound(multiply(b, inverse(a)), Y2)) -> least_upper_bound(identity, Y2)
% 174.30/173.74 least_upper_bound(identity, least_upper_bound(multiply(inverse(b), a), Y2)) -> least_upper_bound(multiply(inverse(b), a), Y2)
% 174.30/173.74 least_upper_bound(identity, multiply(X0, greatest_lower_bound(inverse(X0), Y1))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(X0, greatest_lower_bound(inverse(inverse(inverse(X0))), Y1))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(X0, least_upper_bound(X1, inverse(X0)))) -> multiply(X0, least_upper_bound(X1, inverse(X0)))
% 174.30/173.74 least_upper_bound(identity, multiply(X0, least_upper_bound(inverse(X0), X1))) -> multiply(X0, least_upper_bound(inverse(X0), X1))
% 174.30/173.74 least_upper_bound(identity, multiply(X0, multiply(X1, greatest_lower_bound(Y1, multiply(inverse(X1), inverse(X0)))))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(X0, multiply(inverse(X1), greatest_lower_bound(Y1, multiply(X1, inverse(X0)))))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(X1, multiply(X0, greatest_lower_bound(multiply(inverse(X0), inverse(X1)), Y1)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(X1, multiply(inverse(X0), greatest_lower_bound(multiply(X0, inverse(X1)), Y1)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(Y0, greatest_lower_bound(Y1, inverse(Y0)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(X1, Y0)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(X1, least_upper_bound(X2, Y0))))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(X1, least_upper_bound(Y0, X2))))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(Y0, inverse(least_upper_bound(Y0, X1)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(a, inverse(b))) -> multiply(a, inverse(b))
% 174.30/173.74 least_upper_bound(identity, multiply(a, inverse(greatest_lower_bound(X0, b)))) -> multiply(a, inverse(greatest_lower_bound(X0, b)))
% 174.30/173.74 least_upper_bound(identity, multiply(a, inverse(greatest_lower_bound(b, X0)))) -> multiply(a, inverse(greatest_lower_bound(b, X0)))
% 174.30/173.74 least_upper_bound(identity, multiply(b, inverse(a))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(b, inverse(least_upper_bound(X0, a)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(b, inverse(least_upper_bound(X0, least_upper_bound(X1, a))))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(b, inverse(least_upper_bound(X0, least_upper_bound(a, X1))))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(b, inverse(least_upper_bound(a, X0)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(b, inverse(multiply(least_upper_bound(X0, identity), a)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(b, inverse(multiply(least_upper_bound(identity, X0), a)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(X0, b), inverse(a))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(X0, b), inverse(greatest_lower_bound(X0, a)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(X0, greatest_lower_bound(X1, b)), inverse(a))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(X0, greatest_lower_bound(b, X1)), inverse(a))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(X0, identity), multiply(b, inverse(a)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(X0, inverse(X1)), X1)) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(X1, greatest_lower_bound(Y1, X2)), inverse(Y1))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, X0), inverse(X0))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, multiply(X1, X0)), multiply(inverse(X0), inverse(X1)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, multiply(X1, inverse(X0))), multiply(X0, inverse(X1)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, multiply(inverse(X1), X0)), multiply(inverse(X0), X1))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(Y0, multiply(inverse(X1), inverse(X0))), multiply(X0, X1))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(Y1, Y0), inverse(Y1))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(a, X0), inverse(greatest_lower_bound(X0, a)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(a))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(greatest_lower_bound(X0, a)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(b, X0), inverse(greatest_lower_bound(a, X0)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(identity, X0), multiply(b, inverse(a)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(multiply(X0, X1), Y1), multiply(inverse(X1), inverse(X0)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(greatest_lower_bound(multiply(inverse(X0), X1), Y1), multiply(inverse(X1), X0))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(X0), greatest_lower_bound(X0, X1))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(X0), least_upper_bound(X0, X1))) -> multiply(inverse(X0), least_upper_bound(X0, X1))
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(X0), least_upper_bound(X1, X0))) -> multiply(inverse(X0), least_upper_bound(X1, X0))
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(X0), multiply(X1, greatest_lower_bound(Y1, multiply(inverse(X1), X0))))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(X0), multiply(inverse(X1), greatest_lower_bound(Y1, multiply(X1, X0))))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(X1), multiply(X0, greatest_lower_bound(multiply(inverse(X0), X1), Y1)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(X1), multiply(inverse(X0), greatest_lower_bound(multiply(X0, X1), Y1)))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(Y0), greatest_lower_bound(b, Y0))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(a), greatest_lower_bound(X0, a))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(b), a)) -> multiply(inverse(b), a)
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(b), greatest_lower_bound(X0, b))) -> identity
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(b), least_upper_bound(X0, a))) -> multiply(inverse(b), least_upper_bound(X0, a))
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(b), least_upper_bound(a, X0))) -> multiply(inverse(b), least_upper_bound(a, X0))
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(greatest_lower_bound(X0, b)), a)) -> multiply(inverse(greatest_lower_bound(X0, b)), a)
% 174.30/173.74 least_upper_bound(identity, multiply(inverse(greatest_lower_bound(b, X0)), a)) -> multiply(inverse(greatest_lower_bound(b, X0)), a)
% 174.30/173.74 least_upper_bound(identity, multiply(least_upper_bound(X0, X1), inverse(X0))) -> multiply(least_upper_bound(X0, X1), inverse(X0))
% 174.30/173.74 least_upper_bound(identity, multiply(least_upper_bound(X0, X1), inverse(X1))) -> multiply(least_upper_bound(X0, X1), inverse(X1))
% 174.30/173.74 least_upper_bound(identity, multiply(least_upper_bound(X0, a), inverse(X0))) -> multiply(least_upper_bound(X0, a), inverse(X0))
% 174.30/173.74 least_upper_bound(identity, multiply(least_upper_bound(X0, a), inverse(b))) -> multiply(least_upper_bound(X0, a), inverse(b))
% 174.30/173.74 least_upper_bound(identity, multiply(least_upper_bound(X0, inverse(X1)), X1)) -> multiply(least_upper_bound(X0, inverse(X1)), X1)
% 174.30/173.74 least_upper_bound(identity, multiply(least_upper_bound(a, X0), inverse(a))) -> multiply(least_upper_bound(a, X0), inverse(a))
% 174.30/173.74 least_upper_bound(identity, multiply(least_upper_bound(a, X0), inverse(b))) -> multiply(least_upper_bound(a, X0), inverse(b))
% 174.30/173.74 least_upper_bound(inverse(X1), inverse(multiply(X1, greatest_lower_bound(Y1, identity)))) -> inverse(multiply(X1, greatest_lower_bound(Y1, identity)))
% 174.30/173.74 least_upper_bound(inverse(X1), inverse(multiply(X1, greatest_lower_bound(identity, Y1)))) -> inverse(multiply(X1, greatest_lower_bound(identity, Y1)))
% 174.30/173.74 least_upper_bound(inverse(a), least_upper_bound(Y1, inverse(a))) -> least_upper_bound(Y1, inverse(a))
% 174.30/173.74 least_upper_bound(inverse(b), greatest_lower_bound(Y1, inverse(a))) -> inverse(b)
% 174.30/173.74 least_upper_bound(inverse(b), greatest_lower_bound(inverse(a), Y0)) -> inverse(b)
% 174.30/173.74 least_upper_bound(inverse(b), inverse(a)) -> inverse(b)
% 174.30/173.74 least_upper_bound(inverse(b), least_upper_bound(Y0, inverse(a))) -> least_upper_bound(Y0, inverse(b))
% 174.30/173.74 least_upper_bound(inverse(b), least_upper_bound(inverse(a), Y2)) -> least_upper_bound(inverse(b), Y2)
% 174.30/173.74 least_upper_bound(inverse(greatest_lower_bound(Y2, identity)), greatest_lower_bound(Y1, identity)) -> inverse(greatest_lower_bound(Y2, identity))
% 174.30/173.74 least_upper_bound(inverse(greatest_lower_bound(identity, Y2)), greatest_lower_bound(Y1, identity)) -> inverse(greatest_lower_bound(identity, Y2))
% 174.30/173.74 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z))
% 174.30/173.74 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z))
% 174.30/173.74 least_upper_bound(multiply(X0, inverse(greatest_lower_bound(X0, X1))), greatest_lower_bound(Y1, identity)) -> multiply(X0, inverse(greatest_lower_bound(X0, X1)))
% 174.30/173.74 least_upper_bound(multiply(X0, inverse(greatest_lower_bound(X1, X0))), greatest_lower_bound(Y1, identity)) -> multiply(X0, inverse(greatest_lower_bound(X1, X0)))
% 174.30/173.74 least_upper_bound(multiply(X0, least_upper_bound(X1, X2)), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X0, X2), Y2))
% 174.30/173.74 least_upper_bound(multiply(X0, multiply(X1, Y1)), multiply(Y2, Y1)) -> multiply(least_upper_bound(multiply(X0, X1), Y2), Y1)
% 174.30/173.74 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(X1, identity), Y2))) -> multiply(X1, Y2)
% 174.30/173.74 least_upper_bound(multiply(X1, Y2), greatest_lower_bound(Y1, multiply(greatest_lower_bound(identity, X1), Y2))) -> multiply(X1, Y2)
% 174.30/173.74 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X)
% 174.30/173.74 least_upper_bound(multiply(Y0, Y1), multiply(X0, multiply(X1, Y1))) -> multiply(least_upper_bound(Y0, multiply(X0, X1)), Y1)
% 174.30/173.74 least_upper_bound(multiply(a, inverse(b)), greatest_lower_bound(Y1, identity)) -> multiply(a, inverse(b))
% 174.30/173.74 least_upper_bound(multiply(a, inverse(b)), least_upper_bound(multiply(X0, inverse(b)), greatest_lower_bound(Y1, identity))) -> multiply(least_upper_bound(a, X0), inverse(b))
% 174.30/173.74 least_upper_bound(multiply(a, inverse(greatest_lower_bound(X0, b))), greatest_lower_bound(Y1, identity)) -> multiply(a, inverse(greatest_lower_bound(X0, b)))
% 174.30/173.74 least_upper_bound(multiply(a, inverse(greatest_lower_bound(b, X0))), greatest_lower_bound(Y1, identity)) -> multiply(a, inverse(greatest_lower_bound(b, X0)))
% 174.30/173.74 least_upper_bound(multiply(a, multiply(inverse(b), Y2)), greatest_lower_bound(Y1, Y2)) -> multiply(a, multiply(inverse(b), Y2))
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(X0, identity), b), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), b), a) -> a
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), b), a) -> a
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(X1, identity), greatest_lower_bound(Y0, b)), a) -> a
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(Y0, identity), b), a) -> a
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), a) -> a
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), least_upper_bound(X0, a)) -> least_upper_bound(X0, a)
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), least_upper_bound(a, X0)) -> least_upper_bound(a, X0)
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(false__, identity), multiply(greatest_lower_bound(false__, identity), b)), a) -> a
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(identity, X0), b), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a)
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(identity, X1), greatest_lower_bound(Y0, b)), a) -> a
% 174.30/173.74 least_upper_bound(multiply(greatest_lower_bound(identity, Y0), b), a) -> a
% 174.30/173.74 least_upper_bound(multiply(inverse(b), X0), least_upper_bound(multiply(inverse(b), a), greatest_lower_bound(Y1, identity))) -> multiply(inverse(b), least_upper_bound(X0, a))
% 174.30/173.74 least_upper_bound(multiply(inverse(b), a), greatest_lower_bound(Y1, identity)) -> multiply(inverse(b), a)
% 174.30/173.74 least_upper_bound(multiply(inverse(b), a), least_upper_bound(multiply(inverse(b), X0), greatest_lower_bound(Y1, identity))) -> multiply(inverse(b), least_upper_bound(a, X0))
% 174.30/173.74 least_upper_bound(multiply(inverse(b), multiply(a, Y2)), greatest_lower_bound(Y1, Y2)) -> multiply(inverse(b), multiply(a, Y2))
% 174.30/173.74 least_upper_bound(multiply(inverse(b), multiply(a, a)), greatest_lower_bound(Y1, b)) -> multiply(inverse(b), multiply(a, a))
% 174.30/173.74 least_upper_bound(multiply(inverse(greatest_lower_bound(X0, b)), a), greatest_lower_bound(Y1, identity)) -> multiply(inverse(greatest_lower_bound(X0, b)), a)
% 174.30/173.74 least_upper_bound(multiply(inverse(greatest_lower_bound(b, X0)), a), greatest_lower_bound(Y1, identity)) -> multiply(inverse(greatest_lower_bound(b, X0)), a)
% 174.30/173.74 least_upper_bound(multiply(least_upper_bound(X0, X2), X1), Y2) -> least_upper_bound(multiply(X0, X1), least_upper_bound(multiply(X2, X1), Y2))
% 174.30/173.74 multiply(X1, inverse(multiply(Y0, X1))) -> inverse(Y0)
% 174.30/173.74 multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0
% 174.30/173.74 multiply(X1, least_upper_bound(inverse(X1), inverse(multiply(greatest_lower_bound(Y1, identity), X1)))) -> multiply(X1, inverse(multiply(greatest_lower_bound(Y1, identity), X1)))
% 174.30/173.74 multiply(X1, least_upper_bound(inverse(X1), inverse(multiply(greatest_lower_bound(identity, Y1), X1)))) -> multiply(X1, inverse(multiply(greatest_lower_bound(identity, Y1), X1)))
% 174.30/173.74 multiply(Y0, inverse(Y0)) -> identity
% 174.30/173.74 multiply(Y0, inverse(inverse(inverse(Y0)))) -> identity
% 174.30/173.74 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 174.30/173.74 multiply(Y0, multiply(Y1, multiply(inverse(multiply(Y0, Y1)), X1))) -> X1
% 174.30/173.74 multiply(Y0, multiply(inverse(Y0), X1)) -> X1
% 174.30/173.74 multiply(Y1, identity) -> Y1
% 174.30/173.74 multiply(greatest_lower_bound(X0, a), inverse(greatest_lower_bound(a, X0))) -> identity
% 174.30/173.74 multiply(greatest_lower_bound(X0, identity), inverse(greatest_lower_bound(identity, X0))) -> identity
% 174.30/173.74 multiply(greatest_lower_bound(Y0, multiply(X1, Y0)), multiply(inverse(Y0), inverse(greatest_lower_bound(X1, identity)))) -> identity
% 174.30/173.74 multiply(greatest_lower_bound(a, X0), inverse(greatest_lower_bound(X0, a))) -> identity
% 174.30/173.74 multiply(greatest_lower_bound(identity, X0), inverse(greatest_lower_bound(X0, identity))) -> identity
% 174.30/173.74 multiply(greatest_lower_bound(identity, greatest_lower_bound(X0, identity)), inverse(greatest_lower_bound(X0, identity))) -> identity
% 174.30/173.74 multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, greatest_lower_bound(X2, identity))), Y1) -> multiply(greatest_lower_bound(X1, greatest_lower_bound(X2, identity)), Y1)
% 174.30/173.74 multiply(greatest_lower_bound(identity, greatest_lower_bound(X1, greatest_lower_bound(identity, X2))), Y1) -> multiply(greatest_lower_bound(X1, greatest_lower_bound(identity, X2)), Y1)
% 174.30/173.74 multiply(greatest_lower_bound(identity, inverse(identity)), Y0) -> Y0
% 174.30/173.74 multiply(greatest_lower_bound(identity, inverse(inverse(X0))), identity) -> greatest_lower_bound(identity, X0)
% 174.30/173.74 multiply(greatest_lower_bound(identity, inverse(multiply(greatest_lower_bound(X0, inverse(X1)), X1))), identity) -> identity
% 174.30/173.74 multiply(greatest_lower_bound(inverse(Y1), Y2), Y1) -> greatest_lower_bound(identity, multiply(Y2, Y1))
% 174.30/173.74 multiply(greatest_lower_bound(inverse(b), greatest_lower_bound(multiply(least_upper_bound(false__, identity), inverse(b)), inverse(a))), X1) -> multiply(inverse(a), X1)
% 174.30/173.74 multiply(greatest_lower_bound(least_upper_bound(identity, X0), least_upper_bound(X0, identity)), inverse(least_upper_bound(X0, identity))) -> identity
% 174.30/173.74 multiply(identity, X) -> X
% 174.30/173.74 multiply(inverse(X), X) -> identity
% 174.30/173.74 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 174.30/173.74 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1
% 174.30/173.74 multiply(inverse(greatest_lower_bound(X0, identity)), greatest_lower_bound(identity, X0)) -> identity
% 174.30/173.74 multiply(inverse(greatest_lower_bound(X0, inverse(Y1))), greatest_lower_bound(multiply(X0, Y1), identity)) -> Y1
% 174.30/173.74 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(X0, identity)) -> identity
% 174.30/173.74 multiply(inverse(greatest_lower_bound(identity, X0)), greatest_lower_bound(Y1, multiply(X0, Y1))) -> Y1
% 174.30/173.74 multiply(inverse(greatest_lower_bound(identity, inverse(identity))), Y1) -> Y1
% 174.30/173.74 multiply(inverse(identity), Y1) -> Y1
% 174.30/173.74 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 174.30/173.74 multiply(inverse(inverse(Y1)), identity) -> Y1
% 174.30/173.74 multiply(inverse(least_upper_bound(X0, a)), greatest_lower_bound(least_upper_bound(a, X0), least_upper_bound(X0, a))) -> identity
% 174.30/173.74 multiply(inverse(least_upper_bound(X0, b)), greatest_lower_bound(least_upper_bound(b, X0), least_upper_bound(X0, b))) -> identity
% 174.30/173.74 multiply(inverse(least_upper_bound(X0, identity)), greatest_lower_bound(least_upper_bound(identity, X0), least_upper_bound(X0, identity))) -> identity
% 174.30/173.74 multiply(inverse(least_upper_bound(X0, identity)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1
% 174.30/173.74 multiply(inverse(least_upper_bound(X0, identity)), least_upper_bound(identity, X0)) -> identity
% 174.30/173.74 multiply(inverse(least_upper_bound(X0, inverse(Y1))), least_upper_bound(multiply(X0, Y1), identity)) -> Y1
% 174.30/173.74 multiply(inverse(least_upper_bound(a, X0)), greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(a, X0))) -> identity
% 174.30/173.74 multiply(inverse(least_upper_bound(identity, X0)), least_upper_bound(Y1, multiply(X0, Y1))) -> Y1
% 174.30/173.74 multiply(inverse(least_upper_bound(identity, inverse(identity))), Y1) -> Y1
% 174.30/173.74 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1
% 174.30/173.74 multiply(inverse(multiply(X1, Y1)), X1) -> inverse(Y1)
% 174.30/173.74 multiply(inverse(multiply(X1, inverse(Y1))), X1) -> Y1
% 174.30/173.74 multiply(inverse(multiply(greatest_lower_bound(X1, identity), Y1)), greatest_lower_bound(Y1, multiply(X1, Y1))) -> identity
% 174.30/173.74 multiply(inverse(multiply(inverse(X1), Y1)), inverse(X1)) -> inverse(Y1)
% 174.30/173.74 multiply(inverse(multiply(inverse(X1), inverse(Y1))), inverse(X1)) -> Y1
% 174.30/173.74 multiply(least_upper_bound(X0, a), inverse(least_upper_bound(a, X0))) -> identity
% 174.30/173.74 multiply(least_upper_bound(X0, b), inverse(least_upper_bound(b, X0))) -> identity
% 174.30/173.74 multiply(least_upper_bound(X0, identity), inverse(least_upper_bound(identity, X0))) -> identity
% 174.30/173.74 multiply(least_upper_bound(X0, least_upper_bound(greatest_lower_bound(false__, greatest_lower_bound(X0, false__)), Y1)), inverse(least_upper_bound(X0, Y1))) -> identity
% 174.30/173.74 multiply(least_upper_bound(X0, least_upper_bound(greatest_lower_bound(false__, greatest_lower_bound(X0, false__)), Y1)), inverse(least_upper_bound(Y1, X0))) -> identity
% 174.30/173.74 multiply(least_upper_bound(X0, least_upper_bound(multiply(greatest_lower_bound(false__, identity), X0), a)), inverse(least_upper_bound(a, X0))) -> identity
% 174.30/173.74 multiply(least_upper_bound(X1, least_upper_bound(identity, X1)), a) -> multiply(least_upper_bound(identity, X1), a)
% 174.30/173.74 multiply(least_upper_bound(Y0, multiply(X1, Y0)), multiply(inverse(Y0), inverse(least_upper_bound(X1, identity)))) -> identity
% 174.30/173.74 multiply(least_upper_bound(a, X0), inverse(least_upper_bound(X0, a))) -> identity
% 174.30/173.74 multiply(least_upper_bound(b, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), X0)), inverse(least_upper_bound(X0, b))) -> identity
% 174.30/173.74 multiply(least_upper_bound(b, least_upper_bound(multiply(greatest_lower_bound(false__, identity), b), X1)), inverse(least_upper_bound(b, X1))) -> identity
% 174.30/173.74 multiply(least_upper_bound(greatest_lower_bound(identity, X0), greatest_lower_bound(X0, identity)), inverse(greatest_lower_bound(X0, identity))) -> identity
% 174.30/173.74 multiply(least_upper_bound(identity, X0), inverse(least_upper_bound(X0, identity))) -> identity
% 174.30/173.74 multiply(least_upper_bound(identity, inverse(identity)), Y0) -> Y0
% 174.30/173.74 multiply(least_upper_bound(identity, inverse(inverse(X0))), identity) -> least_upper_bound(identity, X0)
% 174.30/173.74 multiply(least_upper_bound(identity, multiply(a, inverse(b))), multiply(b, inverse(a))) -> identity
% 174.30/173.74 multiply(least_upper_bound(inverse(Y1), Y2), Y1) -> least_upper_bound(identity, multiply(Y2, Y1))
% 174.30/173.74 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 174.30/173.74 true__ -> false__
% 174.30/173.74 with the LPO induced by
% 174.30/173.74 a > f1 > b > inverse > identity > greatest_lower_bound > least_upper_bound > multiply > true__ > false__
% 174.30/173.74
% 174.30/173.74 % SZS output end Proof
% 174.30/173.74
%------------------------------------------------------------------------------