0.001/0.001 NO 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 IL:S L:S M:S N:S T:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (and 1 2) 0.001/0.001 (isNat) 0.001/0.001 (isNatIList) 0.001/0.001 (isNatList) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (uLength 1) 0.001/0.001 (uTake1 1) 0.001/0.001 (uTake2 1) 0.001/0.001 (zeros) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 and(tt,T:S) -> T:S 0.001/0.001 isNat(length(L:S)) -> isNatList(L:S) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(N:S)) -> isNat(N:S) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(N:S,IL:S)) -> and(isNat(N:S),isNatIList(IL:S)) 0.001/0.001 isNatIList(IL:S) -> isNatList(IL:S) 0.001/0.001 isNatList(take(N:S,IL:S)) -> and(isNat(N:S),isNatIList(IL:S)) 0.001/0.001 isNatList(cons(N:S,L:S)) -> and(isNat(N:S),isNatList(L:S)) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> uLength(and(isNat(N:S),isNatList(L:S)),L:S) 0.001/0.001 take(0,IL:S) -> uTake1(isNatIList(IL:S)) 0.001/0.001 take(s(M:S),cons(N:S,IL:S)) -> uTake2(and(isNat(M:S),and(isNat(N:S),isNatIList(IL:S))),M:S,N:S,IL:S) 0.001/0.001 uLength(tt,L:S) -> s(length(L:S)) 0.001/0.001 uTake1(tt) -> nil 0.001/0.001 uTake2(tt,M:S,N:S,IL:S) -> cons(N:S,take(M:S,IL:S)) 0.001/0.001 zeros -> cons(0,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 IL:S L:S M:S N:S T:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (and 1 2) 0.001/0.001 (isNat) 0.001/0.001 (isNatIList) 0.001/0.001 (isNatList) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (uLength 1) 0.001/0.001 (uTake1 1) 0.001/0.001 (uTake2 1) 0.001/0.001 (zeros) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 and(tt,T:S) -> T:S 0.001/0.001 isNat(length(L:S)) -> isNatList(L:S) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(N:S)) -> isNat(N:S) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(N:S,IL:S)) -> and(isNat(N:S),isNatIList(IL:S)) 0.001/0.001 isNatIList(IL:S) -> isNatList(IL:S) 0.001/0.001 isNatList(take(N:S,IL:S)) -> and(isNat(N:S),isNatIList(IL:S)) 0.001/0.001 isNatList(cons(N:S,L:S)) -> and(isNat(N:S),isNatList(L:S)) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> uLength(and(isNat(N:S),isNatList(L:S)),L:S) 0.001/0.001 take(0,IL:S) -> uTake1(isNatIList(IL:S)) 0.001/0.001 take(s(M:S),cons(N:S,IL:S)) -> uTake2(and(isNat(M:S),and(isNat(N:S),isNatIList(IL:S))),M:S,N:S,IL:S) 0.001/0.001 uLength(tt,L:S) -> s(length(L:S)) 0.001/0.001 uTake1(tt) -> nil 0.001/0.001 uTake2(tt,M:S,N:S,IL:S) -> cons(N:S,take(M:S,IL:S)) 0.001/0.001 zeros -> cons(0,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 CS-TRS Processor: 0.001/0.001 R is a CS-TRS 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 IL:S L:S M:S N:S T:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (and 1 2) 0.001/0.001 (isNat) 0.001/0.001 (isNatIList) 0.001/0.001 (isNatList) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (uLength 1) 0.001/0.001 (uTake1 1) 0.001/0.001 (uTake2 1) 0.001/0.001 (zeros) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 and(tt,T:S) -> T:S 0.001/0.001 isNat(length(L:S)) -> isNatList(L:S) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(N:S)) -> isNat(N:S) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(N:S,IL:S)) -> and(isNat(N:S),isNatIList(IL:S)) 0.001/0.001 isNatIList(IL:S) -> isNatList(IL:S) 0.001/0.001 isNatList(take(N:S,IL:S)) -> and(isNat(N:S),isNatIList(IL:S)) 0.001/0.001 isNatList(cons(N:S,L:S)) -> and(isNat(N:S),isNatList(L:S)) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> uLength(and(isNat(N:S),isNatList(L:S)),L:S) 0.001/0.001 take(0,IL:S) -> uTake1(isNatIList(IL:S)) 0.001/0.001 take(s(M:S),cons(N:S,IL:S)) -> uTake2(and(isNat(M:S),and(isNat(N:S),isNatIList(IL:S))),M:S,N:S,IL:S) 0.001/0.001 uLength(tt,L:S) -> s(length(L:S)) 0.001/0.001 uTake1(tt) -> nil 0.001/0.001 uTake2(tt,M:S,N:S,IL:S) -> cons(N:S,take(M:S,IL:S)) 0.001/0.001 zeros -> cons(0,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,T:S) -> T:S 0.001/0.001 isNat(length(L:S)) -> isNatList(L:S) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(N:S)) -> isNat(N:S) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(N:S,IL:S)) -> and(isNat(N:S),isNatIList(IL:S)) 0.001/0.001 isNatIList(IL:S) -> isNatList(IL:S) 0.001/0.001 isNatList(take(N:S,IL:S)) -> and(isNat(N:S),isNatIList(IL:S)) 0.001/0.001 isNatList(cons(N:S,L:S)) -> and(isNat(N:S),isNatList(L:S)) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> uLength(and(isNat(N:S),isNatList(L:S)),L:S) 0.001/0.001 take(0,IL:S) -> uTake1(isNatIList(IL:S)) 0.001/0.001 take(s(M:S),cons(N:S,IL:S)) -> uTake2(and(isNat(M:S),and(isNat(N:S),isNatIList(IL:S))),M:S,N:S,IL:S) 0.001/0.001 uLength(tt,L:S) -> s(length(L:S)) 0.001/0.001 uTake1(tt) -> nil 0.001/0.001 uTake2(tt,M:S,N:S,IL:S) -> cons(N:S,take(M:S,IL:S)) 0.001/0.001 zeros -> cons(0,zeros) 0.001/0.001 -> Vars: 0.001/0.001 T, L, N, IL, N, IL, IL, N, L, N, L, N, IL, IL, M, N, L, IL, M, N 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [T], UV-RActive: [T], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L], UV-RFrozen: [L]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N], UV-RFrozen: [N]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL, N], UV-RFrozen: [IL, N]) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL], UV-RFrozen: [IL]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL, N], UV-RFrozen: [IL, N]) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L, N], UV-RFrozen: [L, N]) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [L], UV-RFrozen: [L, N]) 0.001/0.001 (UV-RuleId: 12, UV-LActive: [IL], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [IL]) 0.001/0.001 (UV-RuleId: 13, UV-LActive: [M, N], UV-RActive: [], UV-LFrozen: [IL], UV-RFrozen: [IL, M, N]) 0.001/0.001 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [L], UV-LFrozen: [L], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [N], UV-LFrozen: [IL, M, N], UV-RFrozen: [IL, M]) 0.001/0.001 (UV-RuleId: 17, 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, x23, x24, x25 0.001/0.001 -> PVars: 0.001/0.001 T: [x6], L: [x7, x14, x16, x22], N: [x8, x10, x13, x15, x17, x21, x25], IL: [x9, x11, x12, x18, x19, x23], M: [x20, x24] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: and(tt,x6:S) -> x6:S, id: 1, possubterms: and(tt,x6:S)->[], tt->[1]) 0.001/0.001 (rule: isNat(length(x7:S)) -> isNatList(x7:S), id: 2, possubterms: isNat(length(x7:S))->[]) 0.001/0.001 (rule: isNat(0) -> tt, id: 3, possubterms: isNat(0)->[]) 0.001/0.001 (rule: isNat(s(x8:S)) -> isNat(x8:S), id: 4, possubterms: isNat(s(x8:S))->[]) 0.001/0.001 (rule: isNatIList(zeros) -> tt, id: 5, possubterms: isNatIList(zeros)->[]) 0.001/0.001 (rule: isNatIList(cons(x10:S,x9:S)) -> and(isNat(x10:S),isNatIList(x9:S)), id: 6, possubterms: isNatIList(cons(x10:S,x9:S))->[]) 0.001/0.001 (rule: isNatIList(x11:S) -> isNatList(x11:S), id: 7, possubterms: isNatIList(x11:S)->[]) 0.001/0.001 (rule: isNatList(take(x13:S,x12:S)) -> and(isNat(x13:S),isNatIList(x12:S)), id: 8, possubterms: isNatList(take(x13:S,x12:S))->[]) 0.001/0.001 (rule: isNatList(cons(x15:S,x14:S)) -> and(isNat(x15:S),isNatList(x14:S)), id: 9, possubterms: isNatList(cons(x15:S,x14:S))->[]) 0.001/0.001 (rule: isNatList(nil) -> tt, id: 10, possubterms: isNatList(nil)->[]) 0.001/0.001 (rule: length(cons(x17:S,x16:S)) -> uLength(and(isNat(x17:S),isNatList(x16:S)),x16:S), id: 11, possubterms: length(cons(x17:S,x16:S))->[], cons(x17:S,x16:S)->[1]) 0.001/0.001 (rule: take(0,x18:S) -> uTake1(isNatIList(x18:S)), id: 12, possubterms: take(0,x18:S)->[], 0->[1]) 0.001/0.001 (rule: take(s(x20:S),cons(x21:S,x19:S)) -> uTake2(and(isNat(x20:S),and(isNat(x21:S),isNatIList(x19:S))),x20:S,x21:S,x19:S), id: 13, possubterms: take(s(x20:S),cons(x21:S,x19:S))->[], s(x20:S)->[1], cons(x21:S,x19:S)->[2]) 0.001/0.001 (rule: uLength(tt,x22:S) -> s(length(x22:S)), id: 14, possubterms: uLength(tt,x22:S)->[], tt->[1]) 0.001/0.001 (rule: uTake1(tt) -> nil, id: 15, possubterms: uTake1(tt)->[], tt->[1]) 0.001/0.001 (rule: uTake2(tt,x24:S,x25:S,x23:S) -> cons(x25:S,take(x24:S,x23:S)), id: 16, possubterms: uTake2(tt,x24:S,x25:S,x23:S)->[], tt->[1]) 0.001/0.001 (rule: zeros -> cons(0,zeros), id: 17, possubterms: zeros->[]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R7 unifies with R5 at p: [], l: isNatIList(x11:S), lp: isNatIList(x11:S), sig: {x11:S -> zeros}, l': isNatIList(zeros), r: isNatList(x11:S), r': tt) 0.001/0.001 (R7 unifies with R6 at p: [], l: isNatIList(x11:S), lp: isNatIList(x11:S), sig: {x11:S -> cons(N:S,IL:S)}, l': isNatIList(cons(N:S,IL:S)), r: isNatList(x11:S), r': and(isNat(N:S),isNatIList(IL:S))) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 => Not trivial, Overlay, NW0, N1 0.001/0.001 => Not trivial, Overlay, NW0, N2 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 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.001/0.001 Not Huet-Levy confluent, Not Newman confluent 0.001/0.001 R is a CS-TRS, Not left-homogeneous u-replacing variables 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 Different Normal CP Terms Processor: 0.001/0.001 => Not trivial, Overlay, NW0, N1, Normal and not trivial cp 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 64%CPU (0avgtext+0avgdata 10364maxresident)k 0.001/0.001 0inputs+0outputs (0major+869minor)pagefaults 0swaps