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 Z:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1) 0.001/0.001 (and 1) 0.001/0.001 (first 1 2) 0.001/0.001 (from) 0.001/0.001 (if 1) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (nil) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 add(num0,X:S:S) -> X:S:S 0.001/0.001 add(s(X:S:S),Y:S:S) -> s(add(X:S:S,Y:S:S)) 0.001/0.001 and(ffalse,Y:S:S) -> ffalse 0.001/0.001 and(ftrue,X:S:S) -> X:S:S 0.001/0.001 first(num0,X:S:S) -> nil 0.001/0.001 first(s(X:S:S),cons(Y:S:S,Z:S:S)) -> cons(Y:S:S,first(X:S:S,Z:S:S)) 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X: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 ) 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 Z:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1) 0.001/0.001 (and 1) 0.001/0.001 (first 1 2) 0.001/0.001 (from) 0.001/0.001 (if 1) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (nil) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 add(num0,X:S:S) -> X:S:S 0.001/0.001 add(s(X:S:S),Y:S:S) -> s(add(X:S:S,Y:S:S)) 0.001/0.001 and(ffalse,Y:S:S) -> ffalse 0.001/0.001 and(ftrue,X:S:S) -> X:S:S 0.001/0.001 first(num0,X:S:S) -> nil 0.001/0.001 first(s(X:S:S),cons(Y:S:S,Z:S:S)) -> cons(Y:S:S,first(X:S:S,Z:S:S)) 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X: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 ) 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 Z:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1) 0.001/0.001 (and 1) 0.001/0.001 (first 1 2) 0.001/0.001 (from) 0.001/0.001 (if 1) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (nil) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 add(num0,X:S:S) -> X:S:S 0.001/0.001 add(s(X:S:S),Y:S:S) -> s(add(X:S:S,Y:S:S)) 0.001/0.001 and(ffalse,Y:S:S) -> ffalse 0.001/0.001 and(ftrue,X:S:S) -> X:S:S 0.001/0.001 first(num0,X:S:S) -> nil 0.001/0.001 first(s(X:S:S),cons(Y:S:S,Z:S:S)) -> cons(Y:S:S,first(X:S:S,Z:S:S)) 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X: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 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Huet Levy Processor: 0.001/0.001 -> Rules: 0.001/0.001 add(num0,X:S:S) -> X:S:S 0.001/0.001 add(s(X:S:S),Y:S:S) -> s(add(X:S:S,Y:S:S)) 0.001/0.001 and(ffalse,Y:S:S) -> ffalse 0.001/0.001 and(ftrue,X:S:S) -> X:S:S 0.001/0.001 first(num0,X:S:S) -> nil 0.001/0.001 first(s(X:S:S),cons(Y:S:S,Z:S:S)) -> cons(Y:S:S,first(X:S:S,Z:S:S)) 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X: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 -> Vars: 0.001/0.001 X:S, X:S, Y:S, Y:S, X:S, X:S, X:S, Y:S, Z:S, X:S, X:S, Y:S, X:S, Y:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [X:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S, Z:S], UV-RFrozen: [X:S, Y:S, Z:S]) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: [X:S]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x5, x6, x9, x10, x11, x14, x15, x17], Y:S: [x7, x8, x12, x16, x18], Z:S: [x13] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: add(num0,x5:S) -> x5:S, id: 1, possubterms: add(num0,x5:S)->[], num0->[1]) 0.001/0.001 (rule: add(s(x6:S),x7:S) -> s(add(x6:S,x7:S)), id: 2, possubterms: add(s(x6:S),x7:S)->[], s(x6:S)->[1]) 0.001/0.001 (rule: and(ffalse,x8:S) -> ffalse, id: 3, possubterms: and(ffalse,x8:S)->[], ffalse->[1]) 0.001/0.001 (rule: and(ftrue,x9:S) -> x9:S, id: 4, possubterms: and(ftrue,x9:S)->[], ftrue->[1]) 0.001/0.001 (rule: first(num0,x10:S) -> nil, id: 5, possubterms: first(num0,x10:S)->[], num0->[1]) 0.001/0.001 (rule: first(s(x11:S),cons(x12:S,x13:S)) -> cons(x12:S,first(x11:S,x13:S)), id: 6, possubterms: first(s(x11:S),cons(x12:S,x13:S))->[], s(x11:S)->[1], cons(x12:S,x13:S)->[2]) 0.001/0.001 (rule: from(x14:S) -> cons(x14:S,from(s(x14:S))), id: 7, possubterms: from(x14:S)->[]) 0.001/0.001 (rule: if(ffalse,x15:S,x16:S) -> x16:S, id: 8, possubterms: if(ffalse,x15:S,x16:S)->[], ffalse->[1]) 0.001/0.001 (rule: if(ftrue,x17:S,x18:S) -> x17:S, id: 9, possubterms: if(ftrue,x17:S,x18:S)->[], ftrue->[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 33%CPU (0avgtext+0avgdata 8560maxresident)k 0.001/0.001 8inputs+0outputs (0major+684minor)pagefaults 0swaps