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 IL:S:S L:S:S M:S:S N:S:S X:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (and 1) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (zeros) 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 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 length(cons(N:S:S,L:S:S)) -> s(length(L:S:S)) 0.001/0.001 length(nil) -> num0 0.001/0.001 take(num0,IL:S:S) -> nil 0.001/0.001 take(s(M:S:S),cons(N:S:S,IL:S:S)) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.001/0.001 zeros -> cons(num0,zeros) 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 IL:S:S L:S:S M:S:S N:S:S X:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (and 1) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (zeros) 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 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 length(cons(N:S:S,L:S:S)) -> s(length(L:S:S)) 0.001/0.001 length(nil) -> num0 0.001/0.001 take(num0,IL:S:S) -> nil 0.001/0.001 take(s(M:S:S),cons(N:S:S,IL:S:S)) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.001/0.001 zeros -> cons(num0,zeros) 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 IL:S:S L:S:S M:S:S N:S:S X:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (and 1) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (zeros) 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 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 length(cons(N:S:S,L:S:S)) -> s(length(L:S:S)) 0.001/0.001 length(nil) -> num0 0.001/0.001 take(num0,IL:S:S) -> nil 0.001/0.001 take(s(M:S:S),cons(N:S:S,IL:S:S)) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.001/0.001 zeros -> cons(num0,zeros) 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 and(tt,X:S:S) -> X:S:S 0.001/0.001 length(cons(N:S:S,L:S:S)) -> s(length(L:S:S)) 0.001/0.001 length(nil) -> num0 0.001/0.001 take(num0,IL:S:S) -> nil 0.001/0.001 take(s(M:S:S),cons(N:S:S,IL:S:S)) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.001/0.001 zeros -> cons(num0,zeros) 0.001/0.001 -> Vars: 0.001/0.001 X:S, L:S, N:S, IL:S, IL:S, M:S, N: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: [L:S, N:S], UV-RFrozen: [L:S]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [IL:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL:S, M:S, N:S], UV-RFrozen: [IL:S, M:S, N:S]) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x7, x8, x9, x10, x11, x12, x13 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x7], L:S: [x8], N:S: [x9, x13], IL:S: [x10, x11], M:S: [x12] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: and(tt,x7:S) -> x7:S, id: 1, possubterms: and(tt,x7:S)->[], tt->[1]) 0.001/0.001 (rule: length(cons(x9:S,x8:S)) -> s(length(x8:S)), id: 2, possubterms: length(cons(x9:S,x8:S))->[], cons(x9:S,x8:S)->[1]) 0.001/0.001 (rule: length(nil) -> num0, id: 3, possubterms: length(nil)->[], nil->[1]) 0.001/0.001 (rule: take(num0,x10:S) -> nil, id: 4, possubterms: take(num0,x10:S)->[], num0->[1]) 0.001/0.001 (rule: take(s(x12:S),cons(x13:S,x11:S)) -> cons(x13:S,take(x12:S,x11:S)), id: 5, possubterms: take(s(x12:S),cons(x13:S,x11:S))->[], s(x12:S)->[1], cons(x13:S,x11:S)->[2]) 0.001/0.001 (rule: zeros -> cons(num0,zeros), id: 6, possubterms: zeros->[]) 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, Right linear, 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 41%CPU (0avgtext+0avgdata 8260maxresident)k 0.001/0.001 8inputs+0outputs (0major+676minor)pagefaults 0swaps