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) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (U21 1) 0.001/0.001 (U22 1) 0.001/0.001 (U23 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 U11(tt,L:S:S) -> U12(tt,L:S:S) 0.001/0.001 U12(tt,L:S:S) -> s(length(L:S:S)) 0.001/0.001 U21(tt,IL:S:S,M:S:S,N:S:S) -> U22(tt,IL:S:S,M:S:S,N:S:S) 0.001/0.001 U22(tt,IL:S:S,M:S:S,N:S:S) -> U23(tt,IL:S:S,M:S:S,N:S:S) 0.001/0.001 U23(tt,IL:S:S,M:S:S,N:S:S) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.001/0.001 length(cons(N:S:S,L:S:S)) -> U11(tt,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)) -> U21(tt,IL:S:S,M:S:S,N: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) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (U21 1) 0.001/0.001 (U22 1) 0.001/0.001 (U23 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 U11(tt,L:S:S) -> U12(tt,L:S:S) 0.001/0.001 U12(tt,L:S:S) -> s(length(L:S:S)) 0.001/0.001 U21(tt,IL:S:S,M:S:S,N:S:S) -> U22(tt,IL:S:S,M:S:S,N:S:S) 0.001/0.001 U22(tt,IL:S:S,M:S:S,N:S:S) -> U23(tt,IL:S:S,M:S:S,N:S:S) 0.001/0.001 U23(tt,IL:S:S,M:S:S,N:S:S) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.001/0.001 length(cons(N:S:S,L:S:S)) -> U11(tt,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)) -> U21(tt,IL:S:S,M:S:S,N: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) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (U21 1) 0.001/0.001 (U22 1) 0.001/0.001 (U23 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 U11(tt,L:S:S) -> U12(tt,L:S:S) 0.001/0.001 U12(tt,L:S:S) -> s(length(L:S:S)) 0.001/0.001 U21(tt,IL:S:S,M:S:S,N:S:S) -> U22(tt,IL:S:S,M:S:S,N:S:S) 0.001/0.001 U22(tt,IL:S:S,M:S:S,N:S:S) -> U23(tt,IL:S:S,M:S:S,N:S:S) 0.001/0.001 U23(tt,IL:S:S,M:S:S,N:S:S) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.001/0.001 length(cons(N:S:S,L:S:S)) -> U11(tt,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)) -> U21(tt,IL:S:S,M:S:S,N: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 U11(tt,L:S:S) -> U12(tt,L:S:S) 0.001/0.001 U12(tt,L:S:S) -> s(length(L:S:S)) 0.001/0.001 U21(tt,IL:S:S,M:S:S,N:S:S) -> U22(tt,IL:S:S,M:S:S,N:S:S) 0.001/0.001 U22(tt,IL:S:S,M:S:S,N:S:S) -> U23(tt,IL:S:S,M:S:S,N:S:S) 0.001/0.001 U23(tt,IL:S:S,M:S:S,N:S:S) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.001/0.001 length(cons(N:S:S,L:S:S)) -> U11(tt,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)) -> U21(tt,IL:S:S,M:S:S,N:S:S) 0.001/0.001 zeros -> cons(num0,zeros) 0.001/0.001 -> Vars: 0.001/0.001 L:S, L:S, IL:S, M:S, N:S, IL:S, M:S, N:S, IL:S, M:S, N: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: [], UV-LFrozen: [L:S], UV-RFrozen: [L:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L:S], UV-RFrozen: [L:S]) 0.001/0.001 (UV-RuleId: 3, 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: 4, 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: 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: [L:S, N:S], UV-RFrozen: [L:S]) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [IL:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 9, 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: 10, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22 0.001/0.001 -> PVars: 0.001/0.001 L:S: [x6, x7, x17], IL:S: [x8, x11, x14, x19, x20], M:S: [x9, x12, x15, x21], N:S: [x10, x13, x16, x18, x22] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: U11(tt,x6:S) -> U12(tt,x6:S), id: 1, possubterms: U11(tt,x6:S)->[], tt->[1]) 0.001/0.001 (rule: U12(tt,x7:S) -> s(length(x7:S)), id: 2, possubterms: U12(tt,x7:S)->[], tt->[1]) 0.001/0.001 (rule: U21(tt,x8:S,x9:S,x10:S) -> U22(tt,x8:S,x9:S,x10:S), id: 3, possubterms: U21(tt,x8:S,x9:S,x10:S)->[], tt->[1]) 0.001/0.001 (rule: U22(tt,x11:S,x12:S,x13:S) -> U23(tt,x11:S,x12:S,x13:S), id: 4, possubterms: U22(tt,x11:S,x12:S,x13:S)->[], tt->[1]) 0.001/0.001 (rule: U23(tt,x14:S,x15:S,x16:S) -> cons(x16:S,take(x15:S,x14:S)), id: 5, possubterms: U23(tt,x14:S,x15:S,x16:S)->[], tt->[1]) 0.001/0.001 (rule: length(cons(x18:S,x17:S)) -> U11(tt,x17:S), id: 6, possubterms: length(cons(x18:S,x17:S))->[], cons(x18:S,x17:S)->[1]) 0.001/0.001 (rule: length(nil) -> num0, id: 7, possubterms: length(nil)->[], nil->[1]) 0.001/0.001 (rule: take(num0,x19:S) -> nil, id: 8, possubterms: take(num0,x19:S)->[], num0->[1]) 0.001/0.001 (rule: take(s(x21:S),cons(x22:S,x20:S)) -> U21(tt,x20:S,x21:S,x22:S), id: 9, possubterms: take(s(x21:S),cons(x22:S,x20:S))->[], s(x21:S)->[1], cons(x22:S,x20:S)->[2]) 0.001/0.001 (rule: zeros -> cons(num0,zeros), id: 10, 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 45%CPU (0avgtext+0avgdata 8472maxresident)k 0.001/0.001 8inputs+0outputs (0major+700minor)pagefaults 0swaps