0.001/0.001 YES 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (diff) 0.001/0.001 (if 1) 0.001/0.001 (leq 1 2) 0.001/0.001 (p 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 diff(X:S:S,Y:S:S) -> if(leq(X:S:S,Y:S:S),num0,s(diff(p(X:S:S),Y:S:S))) 0.001/0.001 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.001/0.001 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.001/0.001 leq(num0,Y:S:S) -> ftrue 0.001/0.001 leq(s(X:S:S),num0) -> ffalse 0.001/0.001 leq(s(X:S:S),s(Y:S:S)) -> leq(X:S:S,Y:S:S) 0.001/0.001 p(num0) -> num0 0.001/0.001 p(s(X:S:S)) -> X:S:S 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 CleanTRS Processor: 0.001/0.001 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (diff) 0.001/0.001 (if 1) 0.001/0.001 (leq 1 2) 0.001/0.001 (p 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 diff(X:S:S,Y:S:S) -> if(leq(X:S:S,Y:S:S),num0,s(diff(p(X:S:S),Y:S:S))) 0.001/0.001 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.001/0.001 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.001/0.001 leq(num0,Y:S:S) -> ftrue 0.001/0.001 leq(s(X:S:S),num0) -> ffalse 0.001/0.001 leq(s(X:S:S),s(Y:S:S)) -> leq(X:S:S,Y:S:S) 0.001/0.001 p(num0) -> num0 0.001/0.001 p(s(X:S:S)) -> X:S:S 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 Modular Confluence Combinations Decomposition Processor: 0.001/0.001 It is a CTRS -> No modular confluence 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 Left-Homogeneous u-Replacing Variables Processor: 0.001/0.001 R satisfies LHRV condition 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (diff) 0.001/0.001 (if 1) 0.001/0.001 (leq 1 2) 0.001/0.001 (p 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 diff(X:S:S,Y:S:S) -> if(leq(X:S:S,Y:S:S),num0,s(diff(p(X:S:S),Y:S:S))) 0.001/0.001 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.001/0.001 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.001/0.001 leq(num0,Y:S:S) -> ftrue 0.001/0.001 leq(s(X:S:S),num0) -> ffalse 0.001/0.001 leq(s(X:S:S),s(Y:S:S)) -> leq(X:S:S,Y:S:S) 0.001/0.001 p(num0) -> num0 0.001/0.001 p(s(X:S:S)) -> X:S:S 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Huet Levy Processor: 0.001/0.001 -> Rules: 0.001/0.001 diff(X:S:S,Y:S:S) -> if(leq(X:S:S,Y:S:S),num0,s(diff(p(X:S:S),Y:S:S))) 0.001/0.001 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.001/0.001 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.001/0.001 leq(num0,Y:S:S) -> ftrue 0.001/0.001 leq(s(X:S:S),num0) -> ffalse 0.001/0.001 leq(s(X:S:S),s(Y:S:S)) -> leq(X:S:S,Y:S:S) 0.001/0.001 p(num0) -> num0 0.001/0.001 p(s(X:S:S)) -> X:S:S 0.001/0.001 -> Vars: 0.001/0.001 X:S, Y:S, X:S, Y:S, X:S, Y:S, Y:S, X:S, X:S, Y:S, X:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [X:S, Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [Y:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [X:S, Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x4, x6, x8, x11, x12, x14], Y:S: [x5, x7, x9, x10, x13] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: diff(x4:S,x5:S) -> if(leq(x4:S,x5:S),num0,s(diff(p(x4:S),x5:S))), id: 1, possubterms: diff(x4:S,x5:S)->[]) 0.001/0.001 (rule: if(ffalse,x6:S,x7:S) -> x7:S, id: 2, possubterms: if(ffalse,x6:S,x7:S)->[], ffalse->[1]) 0.001/0.001 (rule: if(ftrue,x8:S,x9:S) -> x8:S, id: 3, possubterms: if(ftrue,x8:S,x9:S)->[], ftrue->[1]) 0.001/0.001 (rule: leq(num0,x10:S) -> ftrue, id: 4, possubterms: leq(num0,x10:S)->[], num0->[1]) 0.001/0.001 (rule: leq(s(x11:S),num0) -> ffalse, id: 5, possubterms: leq(s(x11:S),num0)->[], s(x11:S)->[1], num0->[2]) 0.001/0.001 (rule: leq(s(x12:S),s(x13:S)) -> leq(x12:S,x13:S), id: 6, possubterms: leq(s(x12:S),s(x13:S))->[], s(x12:S)->[1], s(x13:S)->[2]) 0.001/0.001 (rule: p(num0) -> num0, id: 7, possubterms: p(num0)->[], num0->[1]) 0.001/0.001 (rule: p(s(x14:S)) -> x14:S, id: 8, possubterms: p(s(x14:S))->[], s(x14:S)->[1]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 0.001/0.001 0.001/0.001 -> Problem conclusions: 0.001/0.001 Left linear, Not right linear, Not linear 0.001/0.001 Weakly orthogonal, Almost orthogonal, Orthogonal 0.001/0.001 Huet-Levy confluent, Not Newman confluent 0.001/0.001 R is a CS-TRS, Left-homogeneous u-replacing variables 0.001/0.001 0.001/0.001 0.001/0.001 The problem is joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 58%CPU (0avgtext+0avgdata 8544maxresident)k 0.001/0.001 8inputs+0outputs (0major+678minor)pagefaults 0swaps