TSTP Solution File: GRP665-10 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP665-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n006.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 10:57:35 EDT 2022
% Result : Unsatisfiable 59.46s 59.49s
% Output : Proof 59.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP665-10 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 14:39:42 EDT 2022
% 0.12/0.35 % CPUTime :
% 59.46/59.49 % SZS status Unsatisfiable
% 59.46/59.49 % SZS output start Proof
% 59.46/59.49 The input problem is unsatisfiable because
% 59.46/59.49
% 59.46/59.49 [1] the following set of Horn clauses is unsatisfiable:
% 59.46/59.49
% 59.46/59.49 mult(A, ld(A, B)) = B
% 59.46/59.49 ld(A, mult(A, B)) = B
% 59.46/59.49 mult(rd(A, B), B) = A
% 59.46/59.49 rd(mult(A, B), B) = A
% 59.46/59.49 mult(A, unit) = A
% 59.46/59.49 mult(unit, A) = A
% 59.46/59.49 mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C))
% 59.46/59.49 mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C)))
% 59.46/59.49 mult(op_c, A) = mult(A, op_c)
% 59.46/59.49 mult(op_c, mult(x0, x1)) = mult(mult(op_c, x0), x1) ==> \bottom
% 59.46/59.49
% 59.46/59.49 This holds because
% 59.46/59.49
% 59.46/59.49 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 59.46/59.49
% 59.46/59.49 E:
% 59.46/59.49 f1(mult(mult(op_c, x0), x1)) = false__
% 59.46/59.49 f1(mult(op_c, mult(x0, x1))) = true__
% 59.46/59.49 ld(A, mult(A, B)) = B
% 59.46/59.49 mult(A, ld(A, B)) = B
% 59.46/59.49 mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C))
% 59.46/59.49 mult(A, unit) = A
% 59.46/59.49 mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C)))
% 59.46/59.49 mult(op_c, A) = mult(A, op_c)
% 59.46/59.49 mult(rd(A, B), B) = A
% 59.46/59.49 mult(unit, A) = A
% 59.46/59.49 rd(mult(A, B), B) = A
% 59.46/59.49 G:
% 59.46/59.49 true__ = false__
% 59.46/59.49
% 59.46/59.49 This holds because
% 59.46/59.49
% 59.46/59.49 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 59.46/59.49
% 59.46/59.49 ld(X0, X0) = ld(Y0, Y0)
% 59.46/59.49 ld(X0, X0) = rd(Y0, Y0)
% 59.46/59.49 ld(X1, X1) = mult(op_c, ld(mult(op_c, Y1), Y1))
% 59.46/59.49 ld(Y0, Y0) = rd(false__, false__)
% 59.46/59.49 ld(Y0, Y0) = unit
% 59.46/59.49 ld(Y0, mult(mult(rd(Y0, X1), X2), X1)) = ld(X1, mult(X2, X1))
% 59.46/59.49 ld(Y1, mult(Y2, Y1)) = mult(mult(rd(rd(false__, false__), Y1), Y2), Y1)
% 59.46/59.49 ld(mult(Y0, Y1), mult(Y0, Y1)) = rd(false__, false__)
% 59.46/59.49 ld(op_c, mult(X0, mult(X1, ld(X0, op_c)))) = rd(mult(X0, X1), X0)
% 59.46/59.49 mult(X0, ld(Y1, mult(Y2, Y1))) = mult(mult(rd(X0, Y1), Y2), Y1)
% 59.46/59.49 mult(X1, op_c) = mult(mult(Y0, op_c), ld(Y0, X1))
% 59.46/59.49 mult(Y0, mult(X0, mult(X1, op_c))) = mult(op_c, mult(Y0, mult(X0, X1)))
% 59.46/59.49 mult(Y0, mult(X0, mult(op_c, X1))) = mult(op_c, mult(Y0, mult(X0, X1)))
% 59.46/59.49 mult(Y0, mult(X0, mult(op_c, op_c))) = mult(op_c, mult(Y0, mult(op_c, X0)))
% 59.46/59.49 mult(Y0, mult(Y1, op_c)) = mult(op_c, mult(Y0, Y1))
% 59.46/59.49 mult(Y0, mult(ld(Y0, Y2), op_c)) = mult(op_c, Y2)
% 59.46/59.49 mult(Y0, mult(op_c, mult(X0, op_c))) = mult(op_c, mult(Y0, mult(op_c, X0)))
% 59.46/59.49 mult(Y0, mult(op_c, mult(op_c, X0))) = mult(op_c, mult(Y0, mult(X0, op_c)))
% 59.46/59.49 mult(Y0, mult(rd(Y1, X1), mult(op_c, X1))) = mult(op_c, mult(Y0, Y1))
% 59.46/59.49 mult(Y1, mult(op_c, Y2)) = mult(op_c, mult(Y1, Y2))
% 59.46/59.49 mult(ld(Y1, mult(Y2, Y1)), op_c) = mult(mult(rd(op_c, Y1), Y2), Y1)
% 59.46/59.49 mult(ld(op_c, X0), X1) = mult(X0, ld(op_c, X1))
% 59.46/59.49 mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C)))
% 59.46/59.49 mult(mult(X0, X1), op_c) = mult(mult(rd(X0, X0), op_c), mult(X0, X1))
% 59.46/59.49 mult(mult(X0, mult(X1, X2)), Y2) = mult(mult(rd(mult(X0, X1), X0), Y2), ld(Y2, mult(mult(X0, X2), Y2)))
% 59.46/59.49 mult(mult(X0, mult(X1, X2)), ld(mult(X0, X2), mult(Y2, mult(X0, X2)))) = mult(mult(rd(mult(X0, X1), X0), Y2), mult(X0, X2))
% 59.46/59.49 mult(mult(X0, mult(X1, op_c)), Y1) = mult(mult(X0, X1), mult(Y1, op_c))
% 59.46/59.49 mult(mult(X0, mult(X1, op_c)), Y1) = mult(mult(mult(X0, X1), Y1), op_c)
% 59.46/59.49 mult(mult(X0, mult(X1, op_c)), ld(mult(X0, X1), Y1)) = mult(Y1, op_c)
% 59.46/59.49 mult(mult(X0, mult(op_c, X1)), Y1) = mult(mult(X0, X1), mult(Y1, op_c))
% 59.46/59.49 mult(mult(X0, mult(op_c, X1)), Y1) = mult(mult(mult(X0, X1), Y1), op_c)
% 59.46/59.49 mult(mult(X0, mult(op_c, X1)), ld(mult(X0, X1), Y1)) = mult(Y1, op_c)
% 59.46/59.49 mult(mult(Y0, Y1), ld(Y1, mult(mult(X0, Y1), ld(Y1, mult(X1, Y1))))) = mult(mult(Y0, mult(X0, X1)), Y1)
% 59.46/59.49 mult(mult(Y0, Y1), op_c) = mult(Y0, mult(op_c, Y1))
% 59.46/59.49 mult(mult(Y0, Y1), op_c) = mult(mult(Y0, op_c), Y1)
% 59.46/59.49 mult(mult(Y0, ld(X1, mult(X2, X1))), ld(ld(X1, mult(X2, X1)), mult(mult(X0, X2), X1))) = mult(mult(Y0, mult(X0, X1)), ld(X1, mult(X2, X1)))
% 59.46/59.49 mult(mult(Y0, mult(X0, X2)), ld(mult(X0, X2), mult(X0, mult(X1, X2)))) = mult(mult(Y0, rd(mult(X0, X1), X0)), mult(X0, X2))
% 59.46/59.49 mult(mult(Y0, op_c), ld(Y0, mult(Y1, Y0))) = mult(mult(Y1, op_c), Y0)
% 59.46/59.49 mult(mult(Y1, op_c), Y2) = mult(mult(op_c, Y2), ld(Y2, mult(Y1, Y2)))
% 59.46/59.49 mult(mult(Y1, op_c), ld(Y1, mult(Y2, Y1))) = mult(mult(op_c, Y2), Y1)
% 59.46/59.49 mult(mult(ld(Y1, X1), op_c), ld(ld(Y1, X1), X1)) = mult(mult(op_c, Y1), ld(Y1, X1))
% 59.46/59.49 mult(mult(mult(X0, X2), X1), Y2) = mult(mult(mult(X0, X1), Y2), ld(Y2, mult(ld(X1, mult(X2, X1)), Y2)))
% 59.46/59.49 mult(mult(mult(X0, X2), X1), ld(ld(X1, mult(X2, X1)), mult(Y2, ld(X1, mult(X2, X1))))) = mult(mult(mult(X0, X1), Y2), ld(X1, mult(X2, X1)))
% 59.46/59.49 mult(mult(mult(X0, Y1), ld(Y1, mult(X1, Y1))), Y2) = mult(mult(mult(X0, X1), Y2), ld(Y2, mult(Y1, Y2)))
% 59.46/59.49 mult(mult(mult(X0, Y1), ld(Y1, mult(X1, Y1))), ld(Y1, mult(Y2, Y1))) = mult(mult(mult(X0, X1), Y2), Y1)
% 59.46/59.49 mult(mult(mult(X0, op_c), X1), Y1) = mult(mult(mult(X0, X1), Y1), op_c)
% 59.46/59.49 mult(mult(op_c, Y0), Y1) = mult(mult(Y0, Y1), op_c)
% 59.46/59.49 mult(mult(op_c, Y0), Y2) = mult(mult(Y0, Y2), ld(Y2, mult(op_c, Y2)))
% 59.46/59.49 mult(mult(op_c, Y0), ld(Y0, X0)) = mult(mult(rd(X0, Y0), op_c), Y0)
% 59.46/59.49 mult(mult(op_c, Y0), ld(op_c, mult(Y2, op_c))) = mult(mult(Y0, Y2), op_c)
% 59.46/59.49 mult(mult(op_c, Y1), ld(Y1, Y0)) = mult(Y0, op_c)
% 59.46/59.49 mult(mult(rd(Y0, X1), mult(op_c, X1)), Y1) = mult(mult(Y0, Y1), op_c)
% 59.46/59.49 mult(mult(rd(Y0, X1), mult(op_c, X1)), ld(Y0, Y1)) = mult(Y1, op_c)
% 59.46/59.49 mult(op_c, A) = mult(A, op_c)
% 59.46/59.49 mult(op_c, X0) = mult(rd(X0, Y1), mult(op_c, Y1))
% 59.46/59.49 mult(op_c, mult(X0, mult(X1, op_c))) = mult(mult(X0, X1), mult(op_c, op_c))
% 59.46/59.49 mult(op_c, mult(X0, mult(op_c, X1))) = mult(mult(X0, X1), mult(op_c, op_c))
% 59.46/59.50 mult(op_c, mult(X1, mult(ld(mult(op_c, X1), X0), ld(mult(op_c, X1), op_c)))) = rd(X0, X1)
% 59.46/59.50 mult(op_c, mult(Y1, op_c)) = mult(mult(op_c, op_c), Y1)
% 59.46/59.50 mult(op_c, mult(mult(X0, Y1), op_c)) = mult(mult(op_c, mult(X0, op_c)), Y1)
% 59.46/59.50 mult(op_c, mult(mult(X0, op_c), X1)) = mult(mult(X0, X1), mult(op_c, op_c))
% 59.46/59.50 mult(op_c, mult(mult(X0, op_c), X1)) = mult(mult(op_c, op_c), mult(X0, X1))
% 59.46/59.50 mult(op_c, mult(op_c, X0)) = mult(rd(X0, X1), mult(op_c, mult(op_c, X1)))
% 59.46/59.50 mult(op_c, mult(op_c, X1)) = mult(Y0, mult(op_c, mult(ld(Y0, X1), op_c)))
% 59.46/59.50 mult(op_c, mult(op_c, Y0)) = mult(Y0, mult(op_c, op_c))
% 59.46/59.50 mult(op_c, mult(op_c, mult(Y0, X1))) = mult(Y0, mult(op_c, mult(X1, op_c)))
% 59.46/59.50 mult(op_c, mult(op_c, mult(Y0, X1))) = mult(Y0, mult(op_c, mult(op_c, X1)))
% 59.46/59.50 mult(op_c, mult(op_c, mult(op_c, Y0))) = mult(Y0, mult(op_c, mult(op_c, op_c)))
% 59.46/59.50 mult(op_c, mult(rd(Y0, X1), mult(op_c, X1))) = mult(Y0, mult(op_c, op_c))
% 59.46/59.50 mult(op_c, rd(mult(Y0, Y1), Y0)) = mult(Y0, mult(Y1, ld(Y0, op_c)))
% 59.46/59.50 mult(rd(X0, rd(X0, Y1)), Y2) = mult(Y1, mult(ld(Y1, X0), ld(rd(X0, Y1), Y2)))
% 59.46/59.50 mult(rd(X1, Y0), Y2) = mult(Y0, mult(ld(Y0, X1), ld(Y0, Y2)))
% 59.46/59.50 mult(rd(Y0, X1), mult(op_c, X1)) = mult(rd(Y0, Y1), mult(op_c, Y1))
% 59.46/59.50 mult(rd(Y0, mult(X0, X1)), mult(X0, mult(X1, op_c))) = mult(op_c, Y0)
% 59.46/59.50 mult(rd(Y0, mult(X0, X1)), mult(X0, mult(op_c, X1))) = mult(op_c, Y0)
% 59.46/59.50 mult(rd(mult(Y0, Y1), X1), mult(op_c, X1)) = mult(Y0, mult(op_c, Y1))
% 59.46/59.50 mult(rd(mult(Y0, Y1), Y0), X1) = mult(Y0, mult(Y1, ld(Y0, X1)))
% 59.46/59.50 mult(rd(mult(mult(X0, X1), Y1), mult(X0, X1)), mult(mult(X0, X2), X1)) = mult(mult(X0, X1), mult(Y1, ld(X1, mult(X2, X1))))
% 59.46/59.50 rd(X0, X0) = rd(Y0, Y0)
% 59.46/59.50 rd(Y1, Y1) = rd(false__, false__)
% 59.46/59.50 rd(Y1, Y1) = unit
% 59.46/59.50 f1(mult(mult(op_c, x0), x1)) -> false__
% 59.46/59.50 f1(mult(op_c, mult(x0, x1))) -> true__
% 59.46/59.50 ld(A, mult(A, B)) -> B
% 59.46/59.50 ld(Y0, mult(X1, mult(ld(X1, Y0), op_c))) -> op_c
% 59.46/59.50 ld(Y0, mult(Y1, op_c)) -> mult(ld(Y0, Y1), op_c)
% 59.46/59.50 ld(Y0, mult(mult(Y0, X1), op_c)) -> mult(op_c, X1)
% 59.46/59.50 ld(Y0, mult(op_c, X1)) -> mult(ld(Y0, X1), op_c)
% 59.46/59.50 ld(Y0, mult(op_c, X1)) -> mult(op_c, ld(Y0, X1))
% 59.46/59.50 ld(Y0, mult(op_c, Y0)) -> op_c
% 59.46/59.50 ld(Y0, mult(op_c, mult(Y0, X1))) -> mult(op_c, X1)
% 59.46/59.50 ld(Y0, mult(op_c, mult(op_c, Y0))) -> mult(op_c, op_c)
% 59.46/59.50 ld(Y0, mult(rd(Y0, X1), mult(op_c, X1))) -> op_c
% 59.46/59.50 ld(Y0, mult(rd(mult(Y0, X1), Y0), X2)) -> mult(X1, ld(Y0, X2))
% 59.46/59.50 ld(Y0, op_c) -> mult(ld(Y0, ld(false__, false__)), op_c)
% 59.46/59.50 ld(ld(X0, X0), Y0) -> Y0
% 59.46/59.50 ld(ld(X1, mult(X2, X1)), mult(mult(rd(op_c, X1), X2), X1)) -> op_c
% 59.46/59.50 ld(ld(op_c, X1), X1) -> op_c
% 59.46/59.50 ld(ld(op_c, Y0), X1) -> ld(Y0, mult(X1, op_c))
% 59.46/59.50 ld(ld(op_c, ld(false__, false__)), Y1) -> mult(Y1, op_c)
% 59.46/59.50 ld(mult(X0, X1), mult(X0, X1)) -> ld(X1, X1)
% 59.46/59.50 ld(mult(X0, X1), mult(X0, mult(X1, op_c))) -> op_c
% 59.46/59.50 ld(mult(X0, X1), mult(X0, mult(op_c, X1))) -> op_c
% 59.46/59.50 ld(mult(X0, X1), mult(mult(X0, X2), X1)) -> ld(X1, mult(X2, X1))
% 59.46/59.50 ld(mult(X0, X1), mult(mult(X0, Y1), ld(Y1, mult(X1, Y1)))) -> Y1
% 59.46/59.50 ld(mult(X0, X1), mult(mult(op_c, X0), X1)) -> op_c
% 59.46/59.50 ld(mult(X0, ld(op_c, X1)), mult(X0, X1)) -> op_c
% 59.46/59.50 ld(mult(X0, mult(op_c, X1)), mult(mult(X0, X1), mult(op_c, op_c))) -> op_c
% 59.46/59.50 ld(mult(X0, mult(op_c, X1)), mult(mult(X0, X1), op_c)) -> ld(false__, false__)
% 59.46/59.50 ld(mult(X0, mult(op_c, op_c)), mult(op_c, mult(op_c, X0))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(X0, op_c), mult(X1, op_c)) -> ld(X0, X1)
% 59.46/59.50 ld(mult(X0, op_c), mult(mult(op_c, X1), X0)) -> ld(X0, mult(X1, X0))
% 59.46/59.50 ld(mult(X0, op_c), mult(mult(op_c, Y1), ld(Y1, mult(X0, Y1)))) -> Y1
% 59.46/59.50 ld(mult(X0, op_c), mult(op_c, X0)) -> ld(X0, X0)
% 59.46/59.50 ld(mult(X0, op_c), mult(op_c, mult(X0, Y1))) -> Y1
% 59.46/59.50 ld(mult(X1, op_c), mult(op_c, mult(op_c, X1))) -> op_c
% 59.46/59.50 ld(mult(Y0, ld(mult(op_c, Y0), X1)), X1) -> op_c
% 59.46/59.50 ld(mult(Y0, mult(X0, op_c)), mult(Y0, mult(op_c, mult(op_c, X0)))) -> op_c
% 59.46/59.50 ld(mult(Y0, mult(X1, op_c)), mult(op_c, mult(Y0, X1))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(Y0, mult(ld(Y0, X1), op_c)), mult(op_c, X1)) -> ld(false__, false__)
% 59.46/59.50 ld(mult(Y0, mult(op_c, X1)), mult(op_c, mult(Y0, X1))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(Y0, op_c), op_c) -> ld(Y0, ld(false__, false__))
% 59.46/59.50 ld(mult(Y1, op_c), mult(op_c, Y1)) -> ld(false__, false__)
% 59.46/59.50 ld(mult(ld(op_c, X0), X1), mult(X0, X1)) -> op_c
% 59.46/59.50 ld(mult(mult(X0, X1), op_c), mult(X0, mult(op_c, X1))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(mult(X0, X1), op_c), mult(op_c, mult(X0, X1))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, X0), mult(X0, mult(op_c, op_c))) -> op_c
% 59.46/59.50 ld(mult(op_c, X0), mult(X1, op_c)) -> ld(X0, X1)
% 59.46/59.50 ld(mult(op_c, X0), mult(mult(X0, Y1), op_c)) -> Y1
% 59.46/59.50 ld(mult(op_c, X0), mult(mult(X1, op_c), X0)) -> ld(X0, mult(X1, X0))
% 59.46/59.50 ld(mult(op_c, X0), mult(mult(Y1, op_c), ld(Y1, mult(X0, Y1)))) -> Y1
% 59.46/59.50 ld(mult(op_c, X1), mult(Y0, mult(ld(Y0, X1), op_c))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, Y0), X0) -> ld(Y0, ld(op_c, X0))
% 59.46/59.50 ld(mult(op_c, Y0), op_c) -> ld(Y0, ld(false__, false__))
% 59.46/59.50 ld(mult(op_c, Y1), mult(Y1, op_c)) -> ld(Y1, Y1)
% 59.46/59.50 ld(mult(op_c, Y1), mult(Y1, op_c)) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, Y1), mult(rd(Y1, X1), mult(op_c, X1))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, mult(X0, X1)), mult(mult(X0, X1), op_c)) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, mult(X0, op_c)), mult(op_c, mult(op_c, X0))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, mult(X1, mult(ld(mult(op_c, X1), X0), ld(mult(op_c, X1), X1)))), X0) -> op_c
% 59.46/59.50 ld(mult(op_c, mult(Y0, X1)), mult(Y0, mult(X1, op_c))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, mult(Y0, X1)), mult(Y0, mult(op_c, X1))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, mult(Y0, X1)), mult(Y0, mult(op_c, mult(X1, op_c)))) -> op_c
% 59.46/59.50 ld(mult(op_c, mult(Y0, X1)), mult(Y0, mult(op_c, mult(op_c, X1)))) -> op_c
% 59.46/59.50 ld(mult(op_c, mult(op_c, X0)), mult(X0, mult(op_c, op_c))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, mult(op_c, X0)), mult(op_c, mult(X0, op_c))) -> ld(false__, false__)
% 59.46/59.50 ld(mult(op_c, op_c), mult(op_c, mult(Y1, op_c))) -> Y1
% 59.46/59.50 ld(mult(op_c, op_c), mult(op_c, mult(op_c, Y1))) -> Y1
% 59.46/59.50 ld(mult(op_c, rd(X0, mult(op_c, op_c))), X0) -> op_c
% 59.46/59.50 ld(mult(rd(X0, Y1), op_c), mult(X0, op_c)) -> Y1
% 59.46/59.50 ld(mult(rd(Y1, X1), mult(op_c, X1)), mult(op_c, Y1)) -> ld(false__, false__)
% 59.46/59.50 ld(op_c, mult(X0, X1)) -> mult(X0, ld(op_c, X1))
% 59.46/59.50 ld(op_c, mult(X0, Y1)) -> mult(ld(op_c, X0), Y1)
% 59.46/59.50 ld(op_c, mult(X0, mult(X1, op_c))) -> mult(X0, X1)
% 59.46/59.50 ld(op_c, mult(X0, mult(op_c, X1))) -> mult(X0, X1)
% 59.46/59.50 ld(op_c, mult(X1, mult(ld(X1, Y1), op_c))) -> Y1
% 59.46/59.50 ld(op_c, mult(Y1, op_c)) -> Y1
% 59.46/59.50 ld(op_c, mult(mult(X0, op_c), X1)) -> mult(X0, X1)
% 59.46/59.50 ld(rd(X0, X0), Y0) -> Y0
% 59.46/59.50 ld(rd(X0, X0), mult(X0, X1)) -> mult(X0, X1)
% 59.46/59.50 ld(rd(X0, X1), mult(X0, op_c)) -> mult(op_c, X1)
% 59.46/59.50 ld(rd(X0, X1), mult(op_c, X0)) -> mult(op_c, X1)
% 59.46/59.50 ld(rd(X0, Y1), X0) -> Y1
% 59.46/59.50 ld(rd(ld(false__, false__), X0), op_c) -> mult(op_c, X0)
% 59.46/59.50 ld(rd(mult(X0, X1), X0), mult(X0, mult(X1, X2))) -> mult(X0, X2)
% 59.46/59.50 ld(unit, Y1) -> Y1
% 59.46/59.50 mult(A, ld(A, B)) -> B
% 59.46/59.50 mult(A, unit) -> A
% 59.46/59.50 mult(X0, ld(rd(X0, op_c), mult(Y1, rd(X0, op_c)))) -> mult(mult(op_c, Y1), rd(X0, op_c))
% 59.46/59.50 mult(X0, mult(op_c, mult(op_c, ld(mult(op_c, X0), Y0)))) -> mult(op_c, Y0)
% 59.46/59.50 mult(X1, ld(ld(Y0, X1), ld(Y0, X1))) -> X1
% 59.46/59.50 mult(X1, ld(ld(Y0, X1), mult(Y2, ld(Y0, X1)))) -> mult(mult(Y0, Y2), ld(Y0, X1))
% 59.46/59.50 mult(X1, ld(ld(op_c, X1), Y1)) -> mult(Y1, op_c)
% 59.46/59.50 mult(X1, mult(op_c, mult(op_c, ld(mult(X1, op_c), Y0)))) -> mult(op_c, Y0)
% 59.46/59.50 mult(Y0, ld(X0, X0)) -> Y0
% 59.46/59.50 mult(Y0, ld(ld(X0, X0), Y1)) -> mult(Y0, Y1)
% 59.46/59.50 mult(Y0, ld(ld(op_c, Y0), X1)) -> mult(op_c, X1)
% 59.46/59.50 mult(Y0, ld(mult(Y0, op_c), X1)) -> ld(op_c, X1)
% 59.46/59.50 mult(Y0, ld(mult(op_c, Y0), X1)) -> ld(op_c, X1)
% 59.46/59.50 mult(Y0, ld(rd(X0, X0), Y1)) -> mult(Y0, Y1)
% 59.46/59.50 mult(Y0, ld(unit, Y1)) -> mult(Y0, Y1)
% 59.46/59.50 mult(Y0, mult(ld(Y0, Y0), Y2)) -> mult(Y0, Y2)
% 59.46/59.50 mult(Y0, mult(op_c, ld(Y0, X1))) -> mult(op_c, X1)
% 59.46/59.50 mult(Y0, mult(op_c, mult(op_c, ld(Y0, X1)))) -> mult(op_c, mult(op_c, X1))
% 59.46/59.50 mult(Y0, rd(X0, X0)) -> Y0
% 59.46/59.50 mult(Y1, mult(ld(Y1, Y0), op_c)) -> mult(Y0, op_c)
% 59.46/59.50 mult(Y1, mult(ld(Y1, ld(X1, X1)), op_c)) -> op_c
% 59.46/59.50 mult(Y1, mult(ld(Y1, ld(false__, false__)), op_c)) -> op_c
% 59.46/59.50 mult(Y1, mult(ld(Y1, mult(X0, mult(Y1, op_c))), ld(Y1, op_c))) -> mult(op_c, mult(X0, op_c))
% 59.46/59.50 mult(Y1, mult(ld(Y1, mult(X0, mult(Y1, op_c))), ld(Y1, op_c))) -> mult(op_c, mult(op_c, X0))
% 59.46/59.50 mult(Y2, mult(Y1, ld(Y2, Y2))) -> mult(Y2, Y1)
% 59.46/59.50 mult(false__, mult(ld(false__, ld(false__, false__)), mult(op_c, op_c))) -> mult(op_c, op_c)
% 59.46/59.50 mult(ld(X0, X0), Y0) -> Y0
% 59.46/59.50 mult(ld(X0, X1), mult(ld(ld(X0, X1), mult(X1, op_c)), ld(ld(X0, X1), op_c))) -> mult(op_c, mult(op_c, X0))
% 59.46/59.50 mult(ld(Y1, op_c), mult(ld(ld(Y1, op_c), op_c), ld(ld(Y1, op_c), op_c))) -> mult(Y1, op_c)
% 59.46/59.50 mult(ld(Y1, op_c), mult(ld(ld(Y1, op_c), op_c), ld(ld(Y1, op_c), op_c))) -> mult(op_c, Y1)
% 59.46/59.50 mult(ld(ld(op_c, Y0), X1), mult(ld(ld(ld(op_c, Y0), X1), X1), ld(ld(ld(op_c, Y0), X1), op_c))) -> Y0
% 59.46/59.50 mult(mult(X0, X1), ld(mult(X0, ld(op_c, X1)), Y1)) -> mult(Y1, op_c)
% 59.46/59.50 mult(mult(X0, X1), ld(mult(ld(op_c, X0), X1), Y1)) -> mult(Y1, op_c)
% 59.46/59.50 mult(mult(X0, mult(op_c, X1)), Y1) -> mult(op_c, mult(mult(X0, X1), Y1))
% 59.46/59.50 mult(mult(X0, mult(op_c, op_c)), ld(mult(op_c, X0), Y1)) -> mult(Y1, op_c)
% 59.46/59.50 mult(mult(Y0, Y1), op_c) -> mult(Y0, mult(Y1, op_c))
% 59.46/59.50 mult(mult(Y0, Y2), ld(Y2, Y2)) -> mult(Y0, Y2)
% 59.46/59.50 mult(mult(Y0, ld(Y2, X1)), ld(ld(Y2, X1), X1)) -> mult(mult(Y0, Y2), ld(Y2, X1))
% 59.46/59.50 mult(mult(Y0, op_c), Y1) -> mult(op_c, mult(Y0, Y1))
% 59.46/59.50 mult(mult(Y0, op_c), ld(op_c, mult(Y1, op_c))) -> mult(op_c, mult(Y0, Y1))
% 59.46/59.50 mult(mult(Y0, op_c), rd(X0, op_c)) -> mult(mult(Y0, op_c), ld(op_c, X0))
% 59.46/59.50 mult(mult(Y0, rd(X0, Y1)), Y1) -> mult(mult(Y0, Y1), ld(Y1, X0))
% 59.46/59.50 mult(mult(Y1, op_c), ld(Y1, Y1)) -> mult(op_c, Y1)
% 59.46/59.50 mult(mult(mult(X0, X1), op_c), ld(X1, X1)) -> mult(mult(X0, X1), op_c)
% 59.46/59.50 mult(mult(op_c, Y0), Y1) -> mult(op_c, mult(Y0, Y1))
% 59.46/59.50 mult(mult(op_c, mult(X0, op_c)), Y1) -> mult(op_c, mult(mult(X0, op_c), Y1))
% 59.46/59.50 mult(mult(op_c, op_c), Y1) -> mult(op_c, mult(op_c, Y1))
% 59.46/59.50 mult(mult(op_c, op_c), rd(X0, op_c)) -> mult(X0, op_c)
% 59.46/59.50 mult(mult(rd(X0, Y1), Y2), ld(Y2, mult(Y1, Y2))) -> mult(X0, Y2)
% 59.46/59.50 mult(mult(rd(X0, Y1), op_c), Y1) -> mult(X0, op_c)
% 59.46/59.50 mult(mult(rd(Y1, Y1), Y2), Y1) -> mult(Y2, Y1)
% 59.46/59.50 mult(op_c, ld(X0, ld(op_c, X0))) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, ld(X1, mult(ld(op_c, X1), Y1))) -> Y1
% 59.46/59.50 mult(op_c, ld(Y0, ld(op_c, X1))) -> ld(Y0, X1)
% 59.46/59.50 mult(op_c, ld(mult(X0, X1), mult(X0, ld(op_c, X1)))) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, ld(mult(X0, X1), mult(ld(op_c, X0), X1))) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, ld(mult(Y0, op_c), Y0)) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, ld(mult(Y0, op_c), Y1)) -> ld(Y0, Y1)
% 59.46/59.50 mult(op_c, ld(mult(op_c, X0), X0)) -> ld(X0, X0)
% 59.46/59.50 mult(op_c, ld(mult(op_c, X0), X0)) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, ld(mult(op_c, Y0), Y1)) -> ld(Y0, Y1)
% 59.46/59.50 mult(op_c, ld(mult(op_c, Y0), mult(Y0, Y1))) -> Y1
% 59.46/59.50 mult(op_c, ld(mult(op_c, mult(X0, Y1)), mult(X0, Y1))) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, mult(X0, ld(mult(op_c, X0), op_c))) -> op_c
% 59.46/59.50 mult(op_c, mult(X0, mult(op_c, ld(mult(X0, op_c), op_c)))) -> mult(op_c, op_c)
% 59.46/59.50 mult(op_c, mult(X0, mult(op_c, ld(mult(op_c, X0), op_c)))) -> mult(op_c, op_c)
% 59.46/59.50 mult(op_c, mult(X1, mult(ld(mult(op_c, X1), X0), ld(mult(op_c, X1), X1)))) -> ld(op_c, X0)
% 59.46/59.50 mult(op_c, mult(X1, mult(op_c, mult(ld(mult(X1, op_c), mult(Y0, X1)), ld(mult(X1, op_c), op_c))))) -> mult(Y0, op_c)
% 59.46/59.50 mult(op_c, mult(X1, mult(op_c, mult(ld(mult(op_c, X1), mult(Y0, X1)), ld(mult(op_c, X1), op_c))))) -> mult(Y0, op_c)
% 59.46/59.50 mult(op_c, mult(Y0, ld(mult(Y0, op_c), X1))) -> X1
% 59.46/59.50 mult(op_c, mult(Y0, ld(mult(op_c, Y0), X1))) -> X1
% 59.46/59.50 mult(op_c, mult(Y0, ld(op_c, X1))) -> mult(Y0, X1)
% 59.46/59.50 mult(op_c, mult(Y0, mult(X0, ld(op_c, X1)))) -> mult(Y0, mult(X0, X1))
% 59.46/59.50 mult(op_c, mult(Y0, mult(ld(mult(op_c, Y0), Y0), ld(mult(op_c, Y0), op_c)))) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, mult(Y0, mult(ld(op_c, X0), X1))) -> mult(Y0, mult(X0, X1))
% 59.46/59.50 mult(op_c, mult(Y0, rd(X0, op_c))) -> mult(Y0, X0)
% 59.46/59.50 mult(op_c, mult(Y1, mult(ld(mult(Y1, op_c), mult(Y0, Y1)), ld(mult(Y1, op_c), op_c)))) -> Y0
% 59.46/59.50 mult(op_c, mult(ld(Y0, X1), mult(op_c, mult(ld(mult(ld(Y0, X1), op_c), X1), ld(mult(ld(Y0, X1), op_c), op_c))))) -> mult(Y0, op_c)
% 59.46/59.50 mult(op_c, mult(ld(Y1, Y0), mult(ld(mult(ld(Y1, Y0), op_c), Y0), ld(mult(ld(Y1, Y0), op_c), op_c)))) -> Y1
% 59.46/59.50 mult(op_c, mult(ld(Y1, op_c), mult(ld(mult(op_c, ld(Y1, op_c)), op_c), ld(mult(op_c, ld(Y1, op_c)), op_c)))) -> Y1
% 59.46/59.50 mult(op_c, mult(ld(op_c, X1), Y1)) -> mult(X1, Y1)
% 59.46/59.50 mult(op_c, mult(mult(X0, X1), ld(mult(op_c, mult(X0, X1)), op_c))) -> op_c
% 59.46/59.50 mult(op_c, mult(mult(X0, X1), mult(ld(mult(op_c, mult(X0, X1)), mult(X0, X1)), ld(mult(op_c, mult(X0, X1)), op_c)))) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, mult(mult(X0, mult(X1, op_c)), mult(ld(mult(X0, mult(X1, op_c)), Y0), ld(mult(X0, mult(X1, op_c)), mult(X0, X1))))) -> Y0
% 59.46/59.50 mult(op_c, mult(mult(X0, mult(op_c, X1)), mult(ld(mult(X0, mult(op_c, X1)), Y0), ld(mult(X0, mult(op_c, X1)), mult(X0, X1))))) -> Y0
% 59.46/59.50 mult(op_c, mult(mult(Y0, op_c), X1)) -> mult(op_c, mult(op_c, mult(Y0, X1)))
% 59.46/59.50 mult(op_c, mult(mult(ld(op_c, X0), X1), Y1)) -> mult(mult(X0, X1), Y1)
% 59.46/59.50 mult(op_c, mult(mult(ld(op_c, X1), ld(X1, Y0)), Y1)) -> mult(Y0, Y1)
% 59.46/59.50 mult(op_c, mult(op_c, ld(X0, ld(op_c, X0)))) -> op_c
% 59.46/59.50 mult(op_c, mult(op_c, ld(X0, mult(X1, mult(ld(mult(op_c, X1), X0), ld(mult(op_c, X1), X1)))))) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, mult(op_c, ld(mult(op_c, X0), X0))) -> op_c
% 59.46/59.50 mult(op_c, mult(op_c, ld(mult(op_c, mult(op_c, Y1)), Y1))) -> ld(false__, false__)
% 59.46/59.50 mult(op_c, mult(op_c, ld(mult(op_c, op_c), X1))) -> X1
% 59.46/59.50 mult(op_c, mult(op_c, mult(X0, ld(mult(X0, op_c), Y1)))) -> mult(Y1, op_c)
% 59.46/59.50 mult(op_c, mult(op_c, mult(X1, ld(mult(op_c, X1), Y0)))) -> mult(op_c, Y0)
% 59.46/59.50 mult(op_c, mult(op_c, mult(Y1, mult(ld(mult(Y1, op_c), X0), ld(mult(Y1, op_c), Y1))))) -> X0
% 59.46/59.50 mult(op_c, mult(op_c, mult(mult(X0, mult(op_c, op_c)), mult(ld(mult(X0, mult(op_c, op_c)), Y0), ld(mult(X0, mult(op_c, op_c)), X0))))) -> Y0
% 59.46/59.50 mult(op_c, mult(op_c, mult(mult(X1, mult(ld(mult(op_c, X1), X0), ld(mult(op_c, X1), X1))), ld(ld(op_c, X0), Y0)))) -> mult(op_c, Y0)
% 59.46/59.50 mult(op_c, mult(op_c, mult(op_c, mult(X1, mult(ld(mult(op_c, X1), Y0), ld(mult(op_c, X1), ld(op_c, X1))))))) -> Y0
% 59.46/59.50 mult(op_c, mult(op_c, mult(op_c, mult(op_c, mult(X1, mult(ld(mult(op_c, mult(X1, op_c)), Y0), ld(mult(op_c, mult(X1, op_c)), X1))))))) -> Y0
% 59.46/59.50 mult(op_c, mult(op_c, mult(op_c, mult(op_c, mult(X1, mult(ld(mult(op_c, mult(op_c, X1)), Y0), ld(mult(op_c, mult(op_c, X1)), X1))))))) -> Y0
% 59.46/59.50 mult(op_c, mult(op_c, mult(op_c, rd(Y0, mult(op_c, mult(op_c, op_c)))))) -> Y0
% 59.46/59.50 mult(op_c, mult(op_c, rd(X0, mult(op_c, op_c)))) -> X0
% 59.46/59.50 mult(op_c, mult(rd(X0, mult(op_c, Y1)), Y1)) -> X0
% 59.46/59.50 mult(op_c, mult(rd(X0, op_c), Y1)) -> mult(X0, Y1)
% 59.46/59.50 mult(op_c, mult(rd(X0, op_c), ld(op_c, Y2))) -> mult(rd(X0, op_c), Y2)
% 59.46/59.50 mult(op_c, rd(Y0, op_c)) -> Y0
% 59.46/59.50 mult(rd(A, B), B) -> A
% 59.46/59.50 mult(rd(X0, X0), Y0) -> Y0
% 59.46/59.50 mult(rd(X0, rd(X0, Y1)), mult(rd(X0, Y1), Y2)) -> mult(rd(X0, Y1), mult(Y1, Y2))
% 59.46/59.50 mult(rd(X1, Y0), mult(Y0, Y2)) -> mult(Y0, mult(ld(Y0, X1), Y2))
% 59.46/59.50 mult(rd(Y0, Y0), mult(Y0, Y2)) -> mult(Y0, Y2)
% 59.46/59.50 mult(rd(Y0, Y0), mult(op_c, Y0)) -> mult(Y0, op_c)
% 59.46/59.50 mult(rd(Y0, Y1), mult(op_c, Y1)) -> mult(Y0, op_c)
% 59.46/59.50 mult(rd(Y0, ld(X0, X0)), Y1) -> mult(Y0, Y1)
% 59.46/59.50 mult(rd(Y0, rd(X0, X0)), Y1) -> mult(Y0, Y1)
% 59.46/59.50 mult(rd(Y1, unit), Y2) -> mult(Y1, Y2)
% 59.46/59.50 mult(rd(ld(X1, X1), Y1), mult(op_c, Y1)) -> op_c
% 59.46/59.50 mult(rd(ld(false__, false__), Y1), mult(op_c, Y1)) -> op_c
% 59.46/59.50 mult(rd(mult(A, B), A), mult(A, C)) -> mult(A, mult(B, C))
% 59.46/59.50 mult(rd(mult(X0, X1), mult(X0, X1)), mult(mult(X0, op_c), X1)) -> mult(mult(X0, X1), op_c)
% 59.46/59.50 mult(rd(mult(X0, mult(X1, X2)), rd(mult(X0, X1), X0)), mult(rd(mult(X0, X1), X0), Y2)) -> mult(rd(mult(X0, X1), X0), mult(mult(X0, X2), Y2))
% 59.46/59.50 mult(rd(mult(Y0, Y1), Y0), mult(op_c, Y0)) -> mult(Y0, mult(Y1, op_c))
% 59.46/59.50 mult(rd(mult(mult(X0, X1), Y1), mult(X0, X1)), mult(mult(X0, Y2), ld(Y2, mult(X1, Y2)))) -> mult(mult(X0, X1), mult(Y1, Y2))
% 59.46/59.50 mult(rd(mult(mult(X0, X2), X1), mult(X0, X1)), mult(mult(X0, X1), Y2)) -> mult(mult(X0, X1), mult(ld(X1, mult(X2, X1)), Y2))
% 59.46/59.50 mult(rd(mult(mult(X0, Y1), ld(Y1, mult(X1, Y1))), mult(X0, X1)), mult(mult(X0, X1), Y2)) -> mult(mult(X0, X1), mult(Y1, Y2))
% 59.46/59.50 mult(rd(mult(op_c, Y1), op_c), mult(Y2, op_c)) -> mult(op_c, mult(Y1, Y2))
% 59.46/59.50 mult(rd(mult(rd(X0, Y2), Y1), rd(X0, Y2)), X0) -> mult(rd(X0, Y2), mult(Y1, Y2))
% 59.46/59.50 mult(rd(mult(rd(mult(X0, X1), X0), Y1), rd(mult(X0, X1), X0)), mult(X0, mult(X1, X2))) -> mult(rd(mult(X0, X1), X0), mult(Y1, mult(X0, X2)))
% 59.46/59.50 mult(rd(rd(X0, Y1), rd(X0, Y1)), X0) -> X0
% 59.46/59.50 mult(unit, A) -> A
% 59.46/59.50 rd(X0, ld(Y1, ld(op_c, X0))) -> mult(op_c, Y1)
% 59.46/59.50 rd(X0, mult(op_c, mult(X1, mult(ld(mult(op_c, X1), X0), ld(mult(op_c, X1), X1))))) -> op_c
% 59.46/59.50 rd(X0, mult(op_c, rd(X0, mult(op_c, op_c)))) -> op_c
% 59.46/59.50 rd(X0, op_c) -> ld(op_c, X0)
% 59.46/59.50 rd(X0, rd(X0, op_c)) -> op_c
% 59.46/59.50 rd(X1, ld(Y0, X1)) -> Y0
% 59.46/59.50 rd(X1, mult(Y0, ld(mult(Y0, op_c), X1))) -> op_c
% 59.46/59.50 rd(X1, mult(op_c, ld(Y1, ld(op_c, X1)))) -> Y1
% 59.46/59.50 rd(Y0, ld(X0, X0)) -> Y0
% 59.46/59.50 rd(Y0, rd(X0, X0)) -> Y0
% 59.46/59.50 rd(Y0, unit) -> Y0
% 59.46/59.50 rd(mult(A, B), B) -> A
% 59.46/59.50 rd(mult(X0, X1), ld(X1, X1)) -> mult(X0, X1)
% 59.46/59.50 rd(mult(X0, X1), mult(X0, X1)) -> rd(X0, X0)
% 59.46/59.50 rd(mult(X0, X1), mult(X0, ld(op_c, X1))) -> op_c
% 59.46/59.50 rd(mult(X0, X1), mult(ld(op_c, X0), X1)) -> op_c
% 59.46/59.50 rd(mult(X0, mult(X1, X2)), mult(X0, X2)) -> rd(mult(X0, X1), X0)
% 59.46/59.50 rd(mult(X0, mult(X1, ld(X0, Y1))), Y1) -> rd(mult(X0, X1), X0)
% 59.46/59.50 rd(mult(X0, mult(X1, ld(X0, op_c))), rd(mult(X0, X1), X0)) -> op_c
% 59.46/59.50 rd(mult(X0, mult(X1, op_c)), mult(X0, X1)) -> op_c
% 59.46/59.50 rd(mult(X0, mult(op_c, X1)), op_c) -> mult(X0, X1)
% 59.46/59.50 rd(mult(X0, mult(op_c, op_c)), mult(op_c, X0)) -> op_c
% 59.46/59.50 rd(mult(X0, op_c), Y1) -> mult(rd(X0, Y1), op_c)
% 59.46/59.50 rd(mult(X0, op_c), mult(op_c, X0)) -> ld(false__, false__)
% 59.46/59.50 rd(mult(X1, mult(ld(X1, Y1), op_c)), Y1) -> op_c
% 59.46/59.50 rd(mult(X1, op_c), ld(X0, X1)) -> mult(X0, op_c)
% 59.46/59.50 rd(mult(X1, op_c), ld(X0, X1)) -> mult(op_c, X0)
% 59.46/59.50 rd(mult(Y0, Y1), Y0) -> mult(Y0, mult(Y1, ld(Y0, rd(false__, false__))))
% 59.46/59.50 rd(mult(Y0, mult(X1, op_c)), mult(op_c, mult(Y0, X1))) -> ld(false__, false__)
% 59.46/59.50 rd(mult(Y0, mult(op_c, X1)), mult(op_c, mult(Y0, X1))) -> ld(false__, false__)
% 59.46/59.50 rd(mult(Y0, mult(op_c, Y1)), Y1) -> mult(Y0, op_c)
% 59.46/59.50 rd(mult(Y1, op_c), Y1) -> op_c
% 59.46/59.50 rd(mult(mult(X0, X2), X1), ld(X1, mult(X2, X1))) -> mult(X0, X1)
% 59.46/59.50 rd(mult(mult(X0, Y1), ld(Y1, mult(X1, Y1))), Y1) -> mult(X0, X1)
% 59.46/59.50 rd(mult(mult(X0, Y1), op_c), Y1) -> mult(X0, op_c)
% 59.46/59.50 rd(mult(mult(X0, mult(op_c, X1)), Y1), mult(mult(X0, X1), Y1)) -> op_c
% 59.46/59.50 rd(mult(mult(X0, op_c), X1), mult(X0, X1)) -> op_c
% 59.46/59.50 rd(mult(mult(X0, op_c), X1), op_c) -> mult(X0, X1)
% 59.46/59.50 rd(mult(mult(X1, op_c), X0), ld(X0, mult(X1, X0))) -> mult(op_c, X0)
% 59.46/59.50 rd(mult(mult(Y0, X1), op_c), mult(op_c, X1)) -> Y0
% 59.46/59.50 rd(mult(mult(Y1, op_c), ld(Y1, mult(X0, Y1))), Y1) -> mult(op_c, X0)
% 59.46/59.50 rd(mult(mult(op_c, X0), X1), op_c) -> mult(X0, X1)
% 59.46/59.50 rd(mult(mult(rd(op_c, X1), X2), X1), op_c) -> ld(X1, mult(X2, X1))
% 59.46/59.50 rd(mult(op_c, X0), mult(Y1, op_c)) -> rd(X0, Y1)
% 59.46/59.50 rd(mult(op_c, X0), mult(op_c, X1)) -> rd(X0, X1)
% 59.46/59.50 rd(mult(op_c, X1), mult(ld(Y0, X1), op_c)) -> Y0
% 59.46/59.50 rd(mult(op_c, X1), mult(op_c, ld(Y0, X1))) -> Y0
% 59.46/59.50 rd(mult(op_c, Y0), ld(Y1, Y0)) -> mult(op_c, Y1)
% 59.46/59.50 rd(mult(op_c, Y0), op_c) -> Y0
% 59.46/59.50 rd(mult(op_c, Y1), mult(Y1, op_c)) -> ld(false__, false__)
% 59.46/59.50 rd(mult(op_c, mult(X0, Y1)), Y1) -> mult(X0, op_c)
% 59.46/59.50 rd(mult(op_c, mult(X0, op_c)), mult(op_c, X0)) -> op_c
% 59.46/59.50 rd(mult(op_c, mult(Y0, X1)), mult(X1, op_c)) -> Y0
% 59.46/59.50 rd(mult(op_c, mult(Y0, X1)), mult(Y0, mult(X1, op_c))) -> ld(false__, false__)
% 59.46/59.50 rd(mult(op_c, mult(Y0, X1)), mult(Y0, mult(op_c, X1))) -> ld(false__, false__)
% 59.46/59.50 rd(mult(op_c, mult(Y1, op_c)), Y1) -> mult(op_c, op_c)
% 59.46/59.50 rd(mult(op_c, mult(op_c, X0)), mult(X0, op_c)) -> op_c
% 59.46/59.50 rd(mult(op_c, mult(op_c, Y0)), mult(op_c, op_c)) -> Y0
% 59.46/59.50 rd(mult(op_c, mult(op_c, Y1)), Y1) -> mult(op_c, op_c)
% 59.46/59.50 rd(mult(op_c, mult(op_c, mult(Y0, X1))), mult(Y0, mult(X1, op_c))) -> op_c
% 59.46/59.50 rd(mult(op_c, mult(op_c, mult(Y0, X1))), mult(Y0, mult(op_c, X1))) -> op_c
% 59.46/59.50 rd(mult(op_c, mult(op_c, mult(op_c, X0))), mult(X0, mult(op_c, op_c))) -> op_c
% 59.46/59.50 rd(mult(rd(Y1, X1), mult(op_c, X1)), Y1) -> op_c
% 59.46/59.50 rd(op_c, ld(Y1, ld(false__, false__))) -> mult(Y1, op_c)
% 59.46/59.50 rd(op_c, ld(Y1, ld(false__, false__))) -> mult(op_c, Y1)
% 59.46/59.50 rd(op_c, mult(ld(Y1, ld(false__, false__)), op_c)) -> Y1
% 59.46/59.50 rd(op_c, mult(op_c, X0)) -> rd(ld(false__, false__), X0)
% 59.46/59.50 true__ -> false__
% 59.46/59.50 with the LPO induced by
% 59.46/59.50 x1 > x0 > f1 > op_c > unit > rd > ld > mult > true__ > false__
% 59.46/59.50
% 59.46/59.50 % SZS output end Proof
% 59.46/59.50
%------------------------------------------------------------------------------