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 L:S:S X:S:S XS:S:S Y:S:S YS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (app 1) 0.001/0.001 (from) 0.001/0.001 (prefix) 0.001/0.001 (zWadr 1 2) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 app(cons(X:S:S,XS:S:S),YS:S:S) -> cons(X:S:S,app(XS:S:S,YS:S:S)) 0.001/0.001 app(nil,YS:S:S) -> YS:S:S 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 prefix(L:S:S) -> cons(nil,zWadr(L:S:S,prefix(L:S:S))) 0.001/0.001 zWadr(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(app(Y:S:S,cons(X:S:S,nil)),zWadr(XS:S:S,YS:S:S)) 0.001/0.001 zWadr(nil,YS:S:S) -> nil 0.001/0.001 zWadr(XS:S:S,nil) -> nil 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 L:S:S X:S:S XS:S:S Y:S:S YS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (app 1) 0.001/0.001 (from) 0.001/0.001 (prefix) 0.001/0.001 (zWadr 1 2) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 app(cons(X:S:S,XS:S:S),YS:S:S) -> cons(X:S:S,app(XS:S:S,YS:S:S)) 0.001/0.001 app(nil,YS:S:S) -> YS:S:S 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 prefix(L:S:S) -> cons(nil,zWadr(L:S:S,prefix(L:S:S))) 0.001/0.001 zWadr(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(app(Y:S:S,cons(X:S:S,nil)),zWadr(XS:S:S,YS:S:S)) 0.001/0.001 zWadr(nil,YS:S:S) -> nil 0.001/0.001 zWadr(XS:S:S,nil) -> nil 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 L:S:S X:S:S XS:S:S Y:S:S YS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (app 1) 0.001/0.001 (from) 0.001/0.001 (prefix) 0.001/0.001 (zWadr 1 2) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 app(cons(X:S:S,XS:S:S),YS:S:S) -> cons(X:S:S,app(XS:S:S,YS:S:S)) 0.001/0.001 app(nil,YS:S:S) -> YS:S:S 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 prefix(L:S:S) -> cons(nil,zWadr(L:S:S,prefix(L:S:S))) 0.001/0.001 zWadr(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(app(Y:S:S,cons(X:S:S,nil)),zWadr(XS:S:S,YS:S:S)) 0.001/0.001 zWadr(nil,YS:S:S) -> nil 0.001/0.001 zWadr(XS:S:S,nil) -> nil 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 app(cons(X:S:S,XS:S:S),YS:S:S) -> cons(X:S:S,app(XS:S:S,YS:S:S)) 0.001/0.001 app(nil,YS:S:S) -> YS:S:S 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 prefix(L:S:S) -> cons(nil,zWadr(L:S:S,prefix(L:S:S))) 0.001/0.001 zWadr(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(app(Y:S:S,cons(X:S:S,nil)),zWadr(XS:S:S,YS:S:S)) 0.001/0.001 zWadr(nil,YS:S:S) -> nil 0.001/0.001 zWadr(XS:S:S,nil) -> nil 0.001/0.001 -> Vars: 0.001/0.001 X:S, XS:S, YS:S, YS:S, X:S, L:S, X:S, XS:S, Y:S, YS:S, YS:S, XS:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, XS:S, YS:S], UV-RFrozen: [X:S, XS:S, YS:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [YS:S], UV-LFrozen: [YS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: [X:S]) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L:S], UV-RFrozen: [L:S]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, XS:S, Y:S, YS:S], UV-RFrozen: [X:S, XS:S, Y:S, YS:S]) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [YS:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [XS:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x7, x11, x13], XS:S: [x8, x14, x18], YS:S: [x9, x10, x16, x17], L:S: [x12], Y:S: [x15] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: app(cons(x7:S,x8:S),x9:S) -> cons(x7:S,app(x8:S,x9:S)), id: 1, possubterms: app(cons(x7:S,x8:S),x9:S)->[], cons(x7:S,x8:S)->[1]) 0.001/0.001 (rule: app(nil,x10:S) -> x10:S, id: 2, possubterms: app(nil,x10:S)->[], nil->[1]) 0.001/0.001 (rule: from(x11:S) -> cons(x11:S,from(s(x11:S))), id: 3, possubterms: from(x11:S)->[]) 0.001/0.001 (rule: prefix(x12:S) -> cons(nil,zWadr(x12:S,prefix(x12:S))), id: 4, possubterms: prefix(x12:S)->[]) 0.001/0.001 (rule: zWadr(cons(x13:S,x14:S),cons(x15:S,x16:S)) -> cons(app(x15:S,cons(x13:S,nil)),zWadr(x14:S,x16:S)), id: 5, possubterms: zWadr(cons(x13:S,x14:S),cons(x15:S,x16:S))->[], cons(x13:S,x14:S)->[1], cons(x15:S,x16:S)->[2]) 0.001/0.001 (rule: zWadr(nil,x17:S) -> nil, id: 6, possubterms: zWadr(nil,x17:S)->[], nil->[1]) 0.001/0.001 (rule: zWadr(x18:S,nil) -> nil, id: 7, possubterms: zWadr(x18:S,nil)->[], nil->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R7 unifies with R6 at p: [], l: zWadr(x18:S,nil), lp: zWadr(x18:S,nil), sig: {YS:S:S -> nil,x18:S -> nil}, l': zWadr(nil,YS:S:S), r: nil, r': nil) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 => Trivial, Overlay, NW0, N1 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, Not 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 46%CPU (0avgtext+0avgdata 8560maxresident)k 0.001/0.001 8inputs+0outputs (0major+692minor)pagefaults 0swaps