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 L:S N:S V:S V1:S V2:S X:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (and 1) 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 (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 U11(tt,L:S) -> s(length(L:S)) 0.001/0.001 and(tt,X:S) -> X:S 0.001/0.001 isNat(length(V1:S)) -> isNatList(V1:S) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(V1:S)) -> isNat(V1:S) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(V1:S,V2:S)) -> and(isNat(V1:S),isNatIList(V2:S)) 0.001/0.001 isNatIList(V:S) -> isNatList(V:S) 0.001/0.001 isNatList(cons(V1:S,V2:S)) -> and(isNat(V1:S),isNatList(V2:S)) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> U11(and(isNatList(L:S),isNat(N:S)),L:S) 0.001/0.001 length(nil) -> 0 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 L:S N:S V:S V1:S V2:S X:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (and 1) 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 (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 U11(tt,L:S) -> s(length(L:S)) 0.001/0.001 and(tt,X:S) -> X:S 0.001/0.001 isNat(length(V1:S)) -> isNatList(V1:S) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(V1:S)) -> isNat(V1:S) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(V1:S,V2:S)) -> and(isNat(V1:S),isNatIList(V2:S)) 0.001/0.001 isNatIList(V:S) -> isNatList(V:S) 0.001/0.001 isNatList(cons(V1:S,V2:S)) -> and(isNat(V1:S),isNatList(V2:S)) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> U11(and(isNatList(L:S),isNat(N:S)),L:S) 0.001/0.001 length(nil) -> 0 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 L:S N:S V:S V1:S V2:S X:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (and 1) 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 (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 U11(tt,L:S) -> s(length(L:S)) 0.001/0.001 and(tt,X:S) -> X:S 0.001/0.001 isNat(length(V1:S)) -> isNatList(V1:S) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(V1:S)) -> isNat(V1:S) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(V1:S,V2:S)) -> and(isNat(V1:S),isNatIList(V2:S)) 0.001/0.001 isNatIList(V:S) -> isNatList(V:S) 0.001/0.001 isNatList(cons(V1:S,V2:S)) -> and(isNat(V1:S),isNatList(V2:S)) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> U11(and(isNatList(L:S),isNat(N:S)),L:S) 0.001/0.001 length(nil) -> 0 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 U11(tt,L:S) -> s(length(L:S)) 0.001/0.001 and(tt,X:S) -> X:S 0.001/0.001 isNat(length(V1:S)) -> isNatList(V1:S) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(V1:S)) -> isNat(V1:S) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(V1:S,V2:S)) -> and(isNat(V1:S),isNatIList(V2:S)) 0.001/0.001 isNatIList(V:S) -> isNatList(V:S) 0.001/0.001 isNatList(cons(V1:S,V2:S)) -> and(isNat(V1:S),isNatList(V2:S)) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> U11(and(isNatList(L:S),isNat(N:S)),L:S) 0.001/0.001 length(nil) -> 0 0.001/0.001 zeros -> cons(0,zeros) 0.001/0.001 -> Vars: 0.001/0.001 L, X, V1, V1, V1, V2, V, V1, V2, L, N 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [L], UV-LFrozen: [L], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 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: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 13, UV-LActive: [], 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 0.001/0.001 -> PVars: 0.001/0.001 L: [x7, x16], X: [x8], V1: [x9, x10, x11, x14], V2: [x12, x15], V: [x13], N: [x17] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: U11(tt,x7:S) -> s(length(x7:S)), id: 1, possubterms: U11(tt,x7:S)->[], tt->[1]) 0.001/0.001 (rule: and(tt,x8:S) -> x8:S, id: 2, possubterms: and(tt,x8:S)->[], tt->[1]) 0.001/0.001 (rule: isNat(length(x9:S)) -> isNatList(x9:S), id: 3, possubterms: isNat(length(x9:S))->[]) 0.001/0.001 (rule: isNat(0) -> tt, id: 4, possubterms: isNat(0)->[]) 0.001/0.001 (rule: isNat(s(x10:S)) -> isNat(x10:S), id: 5, possubterms: isNat(s(x10:S))->[]) 0.001/0.001 (rule: isNatIList(zeros) -> tt, id: 6, possubterms: isNatIList(zeros)->[]) 0.001/0.001 (rule: isNatIList(cons(x11:S,x12:S)) -> and(isNat(x11:S),isNatIList(x12:S)), id: 7, possubterms: isNatIList(cons(x11:S,x12:S))->[]) 0.001/0.001 (rule: isNatIList(x13:S) -> isNatList(x13:S), id: 8, possubterms: isNatIList(x13:S)->[]) 0.001/0.001 (rule: isNatList(cons(x14:S,x15:S)) -> and(isNat(x14:S),isNatList(x15:S)), id: 9, possubterms: isNatList(cons(x14:S,x15: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)) -> U11(and(isNatList(x16:S),isNat(x17:S)),x16:S), id: 11, possubterms: length(cons(x17:S,x16:S))->[], cons(x17:S,x16:S)->[1]) 0.001/0.001 (rule: length(nil) -> 0, id: 12, possubterms: length(nil)->[], nil->[1]) 0.001/0.001 (rule: zeros -> cons(0,zeros), id: 13, possubterms: zeros->[]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R8 unifies with R6 at p: [], l: isNatIList(x13:S), lp: isNatIList(x13:S), sig: {x13:S -> zeros}, l': isNatIList(zeros), r: isNatList(x13:S), r': tt) 0.001/0.001 (R8 unifies with R7 at p: [], l: isNatIList(x13:S), lp: isNatIList(x13:S), sig: {x13:S -> cons(V1:S,V2:S)}, l': isNatIList(cons(V1:S,V2:S)), r: isNatList(x13:S), r': and(isNat(V1:S),isNatIList(V2: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 No Convergence Brute Force Processor: 0.001/0.001 -> Rewritings: 0.001/0.001 s: and(isNat(V1:S),isNatIList(V2:S)) 0.001/0.001 Nodes: [0] 0.001/0.001 Edges: [] 0.001/0.001 ID: 0 => ('and(isNat(V1:S),isNatIList(V2:S))', D0) 0.001/0.001 t: isNatList(cons(V1:S,V2:S)) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('isNatList(cons(V1:S,V2:S))', D0) 0.001/0.001 ID: 1 => ('and(isNat(V1:S),isNatList(V2:S))', D1, R9, P[], S{x14:S -> V1:S, x15:S -> V2:S}), NR: 'and(isNat(V1:S),isNatList(V2:S))' 0.001/0.001 and(isNat(V1:S),isNatIList(V2:S)) ->* no union *<- isNatList(cons(V1:S,V2:S)) 0.001/0.001 "Not joinable" 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 69%CPU (0avgtext+0avgdata 10004maxresident)k 0.001/0.001 0inputs+0outputs (0major+808minor)pagefaults 0swaps