0.00/0.07 YES 0.00/0.07 0.00/0.07 Problem 1: 0.00/0.07 0.00/0.07 (VAR v_NonEmpty:S x:S y:S) 0.00/0.07 (RULES 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 ) 0.00/0.07 0.00/0.07 Problem 1: 0.00/0.07 Valid CTRS Processor: 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 -> The system is a deterministic 3-CTRS. 0.00/0.07 0.00/0.07 Problem 1: 0.00/0.07 0.00/0.07 Dependency Pairs Processor: 0.00/0.07 0.00/0.07 Conditional Termination Problem 1: 0.00/0.07 -> Pairs: 0.00/0.07 ADD(s(x:S),y:S) -> ADD(x:S,y:S) 0.00/0.07 GCD(add(x:S,y:S),y:S) -> GCD(x:S,y:S) 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 GCD(y:S,add(x:S,y:S)) -> GCD(x:S,y:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 0.00/0.07 Conditional Termination Problem 2: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 0.00/0.07 0.00/0.07 The problem is decomposed in 2 subproblems. 0.00/0.07 0.00/0.07 Problem 1.1: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 ADD(s(x:S),y:S) -> ADD(x:S,y:S) 0.00/0.07 GCD(add(x:S,y:S),y:S) -> GCD(x:S,y:S) 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 GCD(y:S,add(x:S,y:S)) -> GCD(x:S,y:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 GCD(add(x:S,y:S),y:S) -> GCD(x:S,y:S) 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 GCD(y:S,add(x:S,y:S)) -> GCD(x:S,y:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 ->->-> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 ADD(s(x:S),y:S) -> ADD(x:S,y:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 ->->-> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 0.00/0.07 0.00/0.07 The problem is decomposed in 2 subproblems. 0.00/0.07 0.00/0.07 Problem 1.1.1: 0.00/0.07 0.00/0.07 Reduction Triple Processor: 0.00/0.07 -> Pairs: 0.00/0.07 GCD(add(x:S,y:S),y:S) -> GCD(x:S,y:S) 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 GCD(y:S,add(x:S,y:S)) -> GCD(x:S,y:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 -> Usable rules: 0.00/0.07 Empty 0.00/0.07 ->Interpretation type: 0.00/0.07 Linear 0.00/0.07 ->Coefficients: 0.00/0.07 Natural Numbers 0.00/0.07 ->Dimension: 0.00/0.07 1 0.00/0.07 ->Bound: 0.00/0.07 2 0.00/0.07 ->Interpretation: 0.00/0.07 0.00/0.07 [add](X1,X2) = 2.X1 + 2 0.00/0.07 [gcd](X1,X2) = 0 0.00/0.07 [0] = 0 0.00/0.07 [fSNonEmpty] = 0 0.00/0.07 [false] = 0 0.00/0.07 [leq](X1,X2) = 0 0.00/0.07 [s](X) = 0 0.00/0.07 [ADD](X1,X2) = 0 0.00/0.07 [GCD](X1,X2) = 2.X1 + 2.X2 0.00/0.07 0.00/0.07 Problem 1.1.1: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 GCD(y:S,add(x:S,y:S)) -> GCD(x:S,y:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 GCD(y:S,add(x:S,y:S)) -> GCD(x:S,y:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 ->->-> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 0.00/0.07 Problem 1.1.1: 0.00/0.07 0.00/0.07 Reduction Triple Processor: 0.00/0.07 -> Pairs: 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 GCD(y:S,add(x:S,y:S)) -> GCD(x:S,y:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 -> Usable rules: 0.00/0.07 Empty 0.00/0.07 ->Interpretation type: 0.00/0.07 Linear 0.00/0.07 ->Coefficients: 0.00/0.07 Natural Numbers 0.00/0.07 ->Dimension: 0.00/0.07 1 0.00/0.07 ->Bound: 0.00/0.07 2 0.00/0.07 ->Interpretation: 0.00/0.07 0.00/0.07 [add](X1,X2) = X1 + 1 0.00/0.07 [gcd](X1,X2) = 0 0.00/0.07 [0] = 0 0.00/0.07 [fSNonEmpty] = 0 0.00/0.07 [false] = 0 0.00/0.07 [leq](X1,X2) = 0 0.00/0.07 [s](X) = 0 0.00/0.07 [ADD](X1,X2) = 0 0.00/0.07 [GCD](X1,X2) = 2.X1 + 2.X2 0.00/0.07 0.00/0.07 Problem 1.1.1: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 ->->-> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 0.00/0.07 Problem 1.1.1: 0.00/0.07 0.00/0.07 Reduction Pair Processor: 0.00/0.07 -> Pairs: 0.00/0.07 GCD(x:S,y:S) -> GCD(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 -> Needed rules: 0.00/0.07 Empty 0.00/0.07 -> Usable rules: 0.00/0.07 Empty 0.00/0.07 ->Mace4 Output: 0.00/0.07 ============================== Mace4 ================================= 0.00/0.07 Mace4 (64) version 2009-11A, November 2009. 0.00/0.07 Process 44253 was started by sandbox on n042.star.cs.uiowa.edu, 0.00/0.07 Fri Mar 29 01:51:29 2019 0.00/0.07 The command was "./mace4 -c -f /tmp/mace45965166491189641421.in". 0.00/0.07 ============================== end of head =========================== 0.00/0.07 0.00/0.07 ============================== INPUT ================================= 0.00/0.07 0.00/0.07 % Reading from file /tmp/mace45965166491189641421.in 0.00/0.07 0.00/0.07 assign(max_seconds,20). 0.00/0.07 0.00/0.07 formulas(assumptions). 0.00/0.07 arrowStar_s0(x,x) # label(reflexivity). 0.00/0.07 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility). 0.00/0.07 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.07 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.07 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). 0.00/0.07 arrow_s0(x1,y) -> arrow_s0(f2(x1,x2),f2(y,x2)) # label(congruence). 0.00/0.07 arrow_s0(x2,y) -> arrow_s0(f2(x1,x2),f2(x1,y)) # label(congruence). 0.00/0.07 arrow_s0(x1,y) -> arrow_s0(f3(x1,x2),f3(y,x2)) # label(congruence). 0.00/0.07 arrow_s0(x2,y) -> arrow_s0(f3(x1,x2),f3(x1,y)) # label(congruence). 0.00/0.07 arrow_s0(x1,y) -> arrow_s0(f7(x1,x2),f7(y,x2)) # label(congruence). 0.00/0.07 arrow_s0(x2,y) -> arrow_s0(f7(x1,x2),f7(x1,y)) # label(congruence). 0.00/0.07 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence). 0.00/0.07 arrow_s0(x1,y) -> arrow_s0(f13(x1,x2),f13(y,x2)) # label(congruence). 0.00/0.07 arrow_s0(x2,y) -> arrow_s0(f13(x1,x2),f13(x1,y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f2(x1,x2),f2(y,x2)) # label(congruence). 0.00/0.07 arrowN_s0(x2,y) -> arrowN_s0(f2(x1,x2),f2(x1,y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f3(x1,x2),f3(y,x2)) # label(congruence). 0.00/0.07 arrowN_s0(x2,y) -> arrowN_s0(f3(x1,x2),f3(x1,y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f7(x1,x2),f7(y,x2)) # label(congruence). 0.00/0.07 arrowN_s0(x2,y) -> arrowN_s0(f7(x1,x2),f7(x1,y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f11(x1,x2),f11(y,x2)) # label(congruence). 0.00/0.07 arrowN_s0(x2,y) -> arrowN_s0(f11(x1,x2),f11(x1,y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f12(x1,x2),f12(y,x2)) # label(congruence). 0.00/0.07 arrowN_s0(x2,y) -> arrowN_s0(f12(x1,x2),f12(x1,y)) # label(congruence). 0.00/0.07 arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence). 0.00/0.07 arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence). 0.00/0.07 arrow_s0(f13(x3,x4),x3) # label(replacement). 0.00/0.07 arrow_s0(f13(x3,x4),x4) # label(replacement). 0.00/0.07 arrowN_s0(f13(x3,x4),x3) # label(replacement). 0.00/0.07 arrowN_s0(f13(x3,x4),x4) # label(replacement). 0.00/0.07 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). 0.00/0.07 arrowStar_s0(f7(x2,x1),f6) -> sqsupset_s0(f12(x1,x2),f12(x2,x1)) # label(replacement). 0.00/0.07 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.07 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.07 end_of_list. 0.00/0.07 0.00/0.07 formulas(goals). 0.00/0.07 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). 0.00/0.07 end_of_list. 0.00/0.07 0.00/0.07 ============================== end of input ========================== 0.00/0.07 0.00/0.07 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.00/0.07 0.00/0.07 % Formulas that are not ordinary clauses: 0.00/0.07 1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 5 arrow_s0(x1,y) -> arrow_s0(f2(x1,x2),f2(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 6 arrow_s0(x2,y) -> arrow_s0(f2(x1,x2),f2(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 7 arrow_s0(x1,y) -> arrow_s0(f3(x1,x2),f3(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 8 arrow_s0(x2,y) -> arrow_s0(f3(x1,x2),f3(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 9 arrow_s0(x1,y) -> arrow_s0(f7(x1,x2),f7(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 10 arrow_s0(x2,y) -> arrow_s0(f7(x1,x2),f7(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 11 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 12 arrow_s0(x1,y) -> arrow_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 13 arrow_s0(x2,y) -> arrow_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 14 arrowN_s0(x1,y) -> arrowN_s0(f2(x1,x2),f2(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 15 arrowN_s0(x2,y) -> arrowN_s0(f2(x1,x2),f2(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 16 arrowN_s0(x1,y) -> arrowN_s0(f3(x1,x2),f3(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 17 arrowN_s0(x2,y) -> arrowN_s0(f3(x1,x2),f3(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 18 arrowN_s0(x1,y) -> arrowN_s0(f7(x1,x2),f7(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 19 arrowN_s0(x2,y) -> arrowN_s0(f7(x1,x2),f7(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 20 arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 21 arrowN_s0(x1,y) -> arrowN_s0(f11(x1,x2),f11(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 22 arrowN_s0(x2,y) -> arrowN_s0(f11(x1,x2),f11(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 23 arrowN_s0(x1,y) -> arrowN_s0(f12(x1,x2),f12(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 24 arrowN_s0(x2,y) -> arrowN_s0(f12(x1,x2),f12(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 25 arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 26 arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.07 27 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.07 28 arrowStar_s0(f7(x2,x1),f6) -> sqsupset_s0(f12(x1,x2),f12(x2,x1)) # label(replacement) # label(non_clause). [assumption]. 0.00/0.07 29 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.07 30 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.07 31 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. 0.00/0.07 0.00/0.07 ============================== end of process non-clausal formulas === 0.00/0.07 0.00/0.07 ============================== CLAUSES FOR SEARCH ==================== 0.00/0.07 0.00/0.07 formulas(mace4_clauses). 0.00/0.07 arrowStar_s0(x,x) # label(reflexivity). 0.00/0.07 -arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility). 0.00/0.07 -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.07 -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.07 -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f2(x,z),f2(y,z)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f2(z,x),f2(z,y)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f3(x,z),f3(y,z)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f3(z,x),f3(z,y)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f7(x,z),f7(y,z)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f7(z,x),f7(z,y)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f8(x),f8(y)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f13(x,z),f13(y,z)) # label(congruence). 0.00/0.07 -arrow_s0(x,y) | arrow_s0(f13(z,x),f13(z,y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f2(x,z),f2(y,z)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f2(z,x),f2(z,y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f3(x,z),f3(y,z)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f3(z,x),f3(z,y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f7(x,z),f7(y,z)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f7(z,x),f7(z,y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f8(x),f8(y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f11(x,z),f11(y,z)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f11(z,x),f11(z,y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f12(x,z),f12(y,z)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f12(z,x),f12(z,y)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f13(x,z),f13(y,z)) # label(congruence). 0.00/0.07 -arrowN_s0(x,y) | arrowN_s0(f13(z,x),f13(z,y)) # label(congruence). 0.00/0.07 arrow_s0(f13(x,y),x) # label(replacement). 0.00/0.07 arrow_s0(f13(x,y),y) # label(replacement). 0.00/0.07 arrowN_s0(f13(x,y),x) # label(replacement). 0.00/0.07 arrowN_s0(f13(x,y),y) # label(replacement). 0.00/0.07 -arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). 0.00/0.07 -arrowStar_s0(f7(x,y),f6) | sqsupset_s0(f12(y,x),f12(x,y)) # label(replacement). 0.00/0.07 -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.07 -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.07 -sqsupsetStar_s0(x,x) # label(wellfoundedness). 0.00/0.07 end_of_list. 0.00/0.07 0.00/0.07 ============================== end of clauses for search ============= 0.00/0.07 0.00/0.07 % There are no natural numbers in the input. 0.00/0.07 0.00/0.07 ============================== DOMAIN SIZE 2 ========================= 0.00/0.07 0.00/0.07 ============================== MODEL ================================= 0.00/0.07 0.00/0.07 interpretation( 2, [number=1, seconds=0], [ 0.00/0.07 0.00/0.07 function(f6, [ 0 ]), 0.00/0.07 0.00/0.07 function(f8(_), [ 0, 0 ]), 0.00/0.07 0.00/0.07 function(f11(_,_), [ 0.00/0.07 0, 0, 0.00/0.07 0, 0 ]), 0.00/0.07 0.00/0.07 function(f12(_,_), [ 0.00/0.07 0, 0, 0.00/0.07 0, 0 ]), 0.00/0.07 0.00/0.07 function(f13(_,_), [ 0.00/0.07 0, 0, 0.00/0.07 0, 0 ]), 0.00/0.07 0.00/0.07 function(f2(_,_), [ 0.00/0.07 0, 0, 0.00/0.07 0, 0 ]), 0.00/0.07 0.00/0.07 function(f3(_,_), [ 0.00/0.07 0, 0, 0.00/0.07 0, 0 ]), 0.00/0.07 0.00/0.07 function(f7(_,_), [ 0.00/0.07 1, 1, 0.00/0.07 1, 1 ]), 0.00/0.07 0.00/0.07 relation(arrowN_s0(_,_), [ 0.00/0.07 1, 1, 0.00/0.07 0, 1 ]), 0.00/0.07 0.00/0.07 relation(arrowStar_s0(_,_), [ 0.00/0.07 1, 1, 0.00/0.07 0, 1 ]), 0.00/0.07 0.00/0.07 relation(arrow_s0(_,_), [ 0.00/0.07 1, 1, 0.00/0.07 0, 1 ]), 0.00/0.07 0.00/0.07 relation(gtrsim_s0(_,_), [ 0.00/0.07 1, 1, 0.00/0.07 0, 1 ]), 0.00/0.07 0.00/0.07 relation(sqsupsetStar_s0(_,_), [ 0.00/0.07 0, 0, 0.00/0.07 0, 0 ]), 0.00/0.07 0.00/0.07 relation(sqsupset_s0(_,_), [ 0.00/0.07 0, 0, 0.00/0.07 0, 0 ]), 0.00/0.07 0.00/0.07 relation(succeq_s0(_,_), [ 0.00/0.07 0, 0, 0.00/0.07 0, 0 ]) 0.00/0.07 ]). 0.00/0.07 0.00/0.07 ============================== end of model ========================== 0.00/0.07 0.00/0.07 ============================== STATISTICS ============================ 0.00/0.07 0.00/0.07 For domain size 2. 0.00/0.07 0.00/0.07 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.00/0.07 Ground clauses: seen=240, kept=236. 0.00/0.07 Selections=27, assignments=27, propagations=28, current_models=1. 0.00/0.07 Rewrite_terms=368, rewrite_bools=376, indexes=29. 0.00/0.07 Rules_from_neg_clauses=7, cross_offs=7. 0.00/0.07 0.00/0.07 ============================== end of statistics ===================== 0.00/0.07 0.00/0.07 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.00/0.07 0.00/0.07 Exiting with 1 model. 0.00/0.07 0.00/0.07 Process 44253 exit (max_models) Fri Mar 29 01:51:29 2019 0.00/0.07 The process finished Fri Mar 29 01:51:29 2019 0.00/0.07 0.00/0.07 0.00/0.07 Mace4 cooked interpretation: 0.00/0.07 0.00/0.07 % number = 1 0.00/0.07 % seconds = 0 0.00/0.07 0.00/0.07 % Interpretation of size 2 0.00/0.07 0.00/0.07 f6 = 0. 0.00/0.07 0.00/0.07 f8(0) = 0. 0.00/0.07 f8(1) = 0. 0.00/0.07 0.00/0.07 f11(0,0) = 0. 0.00/0.07 f11(0,1) = 0. 0.00/0.07 f11(1,0) = 0. 0.00/0.07 f11(1,1) = 0. 0.00/0.07 0.00/0.07 f12(0,0) = 0. 0.00/0.07 f12(0,1) = 0. 0.00/0.07 f12(1,0) = 0. 0.00/0.07 f12(1,1) = 0. 0.00/0.07 0.00/0.07 f13(0,0) = 0. 0.00/0.07 f13(0,1) = 0. 0.00/0.07 f13(1,0) = 0. 0.00/0.07 f13(1,1) = 0. 0.00/0.07 0.00/0.07 f2(0,0) = 0. 0.00/0.07 f2(0,1) = 0. 0.00/0.07 f2(1,0) = 0. 0.00/0.07 f2(1,1) = 0. 0.00/0.07 0.00/0.07 f3(0,0) = 0. 0.00/0.07 f3(0,1) = 0. 0.00/0.07 f3(1,0) = 0. 0.00/0.07 f3(1,1) = 0. 0.00/0.07 0.00/0.07 f7(0,0) = 1. 0.00/0.07 f7(0,1) = 1. 0.00/0.07 f7(1,0) = 1. 0.00/0.07 f7(1,1) = 1. 0.00/0.07 0.00/0.07 arrowN_s0(0,0). 0.00/0.07 arrowN_s0(0,1). 0.00/0.07 - arrowN_s0(1,0). 0.00/0.07 arrowN_s0(1,1). 0.00/0.07 0.00/0.07 arrowStar_s0(0,0). 0.00/0.07 arrowStar_s0(0,1). 0.00/0.07 - arrowStar_s0(1,0). 0.00/0.07 arrowStar_s0(1,1). 0.00/0.07 0.00/0.07 arrow_s0(0,0). 0.00/0.07 arrow_s0(0,1). 0.00/0.07 - arrow_s0(1,0). 0.00/0.07 arrow_s0(1,1). 0.00/0.07 0.00/0.07 gtrsim_s0(0,0). 0.00/0.07 gtrsim_s0(0,1). 0.00/0.07 - gtrsim_s0(1,0). 0.00/0.07 gtrsim_s0(1,1). 0.00/0.07 0.00/0.07 - sqsupsetStar_s0(0,0). 0.00/0.07 - sqsupsetStar_s0(0,1). 0.00/0.07 - sqsupsetStar_s0(1,0). 0.00/0.07 - sqsupsetStar_s0(1,1). 0.00/0.07 0.00/0.07 - sqsupset_s0(0,0). 0.00/0.07 - sqsupset_s0(0,1). 0.00/0.07 - sqsupset_s0(1,0). 0.00/0.07 - sqsupset_s0(1,1). 0.00/0.07 0.00/0.07 - succeq_s0(0,0). 0.00/0.07 - succeq_s0(0,1). 0.00/0.07 - succeq_s0(1,0). 0.00/0.07 - succeq_s0(1,1). 0.00/0.07 0.00/0.07 0.00/0.07 Problem 1.1.1: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 0.00/0.07 Problem 1.1.2: 0.00/0.07 0.00/0.07 Conditional Subterm Processor: 0.00/0.07 -> Pairs: 0.00/0.07 ADD(s(x:S),y:S) -> ADD(x:S,y:S) 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 ->Projection: 0.00/0.07 pi(ADD) = 1 0.00/0.07 0.00/0.07 Problem 1.1.2: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 0.00/0.07 Problem 1.2: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> QPairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 add(0,y:S) -> y:S 0.00/0.07 add(s(x:S),y:S) -> s(add(x:S,y:S)) 0.00/0.07 gcd(add(x:S,y:S),y:S) -> gcd(x:S,y:S) 0.00/0.07 gcd(0,x:S) -> x:S 0.00/0.07 gcd(x:S,0) -> x:S 0.00/0.07 gcd(x:S,y:S) -> gcd(y:S,x:S) | leq(y:S,x:S) ->* ffalse 0.00/0.07 gcd(y:S,add(x:S,y:S)) -> gcd(x:S,y:S) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 EOF