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 N:S:S X:S:S XS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (from) 0.001/0.001 (head 1) 0.001/0.001 (num2nd 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (take 1 2) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 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 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 head(cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 num2nd(cons(X:S:S,XS:S:S)) -> head(XS:S:S) 0.001/0.001 sel(num0,cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 sel(s(N:S:S),cons(X:S:S,XS:S:S)) -> sel(N:S:S,XS:S:S) 0.001/0.001 take(num0,XS:S:S) -> nil 0.001/0.001 take(s(N:S:S),cons(X:S:S,XS:S:S)) -> cons(X:S:S,take(N:S:S,XS: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 N:S:S X:S:S XS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (from) 0.001/0.001 (head 1) 0.001/0.001 (num2nd 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (take 1 2) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 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 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 head(cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 num2nd(cons(X:S:S,XS:S:S)) -> head(XS:S:S) 0.001/0.001 sel(num0,cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 sel(s(N:S:S),cons(X:S:S,XS:S:S)) -> sel(N:S:S,XS:S:S) 0.001/0.001 take(num0,XS:S:S) -> nil 0.001/0.001 take(s(N:S:S),cons(X:S:S,XS:S:S)) -> cons(X:S:S,take(N:S:S,XS: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 N:S:S X:S:S XS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (from) 0.001/0.001 (head 1) 0.001/0.001 (num2nd 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (take 1 2) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 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 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 head(cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 num2nd(cons(X:S:S,XS:S:S)) -> head(XS:S:S) 0.001/0.001 sel(num0,cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 sel(s(N:S:S),cons(X:S:S,XS:S:S)) -> sel(N:S:S,XS:S:S) 0.001/0.001 take(num0,XS:S:S) -> nil 0.001/0.001 take(s(N:S:S),cons(X:S:S,XS:S:S)) -> cons(X:S:S,take(N:S:S,XS: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 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 head(cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 num2nd(cons(X:S:S,XS:S:S)) -> head(XS:S:S) 0.001/0.001 sel(num0,cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 sel(s(N:S:S),cons(X:S:S,XS:S:S)) -> sel(N:S:S,XS:S:S) 0.001/0.001 take(num0,XS:S:S) -> nil 0.001/0.001 take(s(N:S:S),cons(X:S:S,XS:S:S)) -> cons(X:S:S,take(N:S:S,XS:S:S)) 0.001/0.001 -> Vars: 0.001/0.001 X:S, X:S, XS:S, X:S, XS:S, X:S, XS:S, N:S, X:S, XS:S, XS:S, N:S, X:S, XS:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: [X:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [XS:S], UV-LFrozen: [X:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [N:S, XS:S], UV-LFrozen: [N:S, X:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [XS:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, X:S, XS:S], UV-RFrozen: [N:S, X:S, XS:S]) 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, x8, x10, x13, x17], XS:S: [x7, x9, x11, x14, x15, x18], N:S: [x12, x16] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: from(x5:S) -> cons(x5:S,from(s(x5:S))), id: 1, possubterms: from(x5:S)->[]) 0.001/0.001 (rule: head(cons(x6:S,x7:S)) -> x6:S, id: 2, possubterms: head(cons(x6:S,x7:S))->[], cons(x6:S,x7:S)->[1]) 0.001/0.001 (rule: num2nd(cons(x8:S,x9:S)) -> head(x9:S), id: 3, possubterms: num2nd(cons(x8:S,x9:S))->[], cons(x8:S,x9:S)->[1]) 0.001/0.001 (rule: sel(num0,cons(x10:S,x11:S)) -> x10:S, id: 4, possubterms: sel(num0,cons(x10:S,x11:S))->[], num0->[1], cons(x10:S,x11:S)->[2]) 0.001/0.001 (rule: sel(s(x12:S),cons(x13:S,x14:S)) -> sel(x12:S,x14:S), id: 5, possubterms: sel(s(x12:S),cons(x13:S,x14:S))->[], s(x12:S)->[1], cons(x13:S,x14:S)->[2]) 0.001/0.001 (rule: take(num0,x15:S) -> nil, id: 6, possubterms: take(num0,x15:S)->[], num0->[1]) 0.001/0.001 (rule: take(s(x16:S),cons(x17:S,x18:S)) -> cons(x17:S,take(x16:S,x18:S)), id: 7, possubterms: take(s(x16:S),cons(x17:S,x18:S))->[], s(x16:S)->[1], cons(x17:S,x18:S)->[2]) 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 66%CPU (0avgtext+0avgdata 8564maxresident)k 0.001/0.001 8inputs+0outputs (0major+680minor)pagefaults 0swaps