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) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U21 1) 0.001/0.001 (U31 1) 0.001/0.001 (U41 1) 0.001/0.001 (U42 1) 0.001/0.001 (U51 1) 0.001/0.001 (U52 1) 0.001/0.001 (U61 1) 0.001/0.001 (U62 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) -> tt 0.001/0.001 U21(tt) -> tt 0.001/0.001 U31(tt) -> tt 0.001/0.001 U41(tt,V2:S) -> U42(isNatIList(V2:S)) 0.001/0.001 U42(tt) -> tt 0.001/0.001 U51(tt,V2:S) -> U52(isNatList(V2:S)) 0.001/0.001 U52(tt) -> tt 0.001/0.001 U61(tt,L:S,N:S) -> U62(isNat(N:S),L:S) 0.001/0.001 U62(tt,L:S) -> s(length(L:S)) 0.001/0.001 isNat(length(V1:S)) -> U11(isNatList(V1:S)) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(V1:S)) -> U21(isNat(V1:S)) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(V1:S,V2:S)) -> U41(isNat(V1:S),V2:S) 0.001/0.001 isNatIList(V:S) -> U31(isNatList(V:S)) 0.001/0.001 isNatList(cons(V1:S,V2:S)) -> U51(isNat(V1:S),V2:S) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> U61(isNatList(L:S),L:S,N: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) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U21 1) 0.001/0.001 (U31 1) 0.001/0.001 (U41 1) 0.001/0.001 (U42 1) 0.001/0.001 (U51 1) 0.001/0.001 (U52 1) 0.001/0.001 (U61 1) 0.001/0.001 (U62 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) -> tt 0.001/0.001 U21(tt) -> tt 0.001/0.001 U31(tt) -> tt 0.001/0.001 U41(tt,V2:S) -> U42(isNatIList(V2:S)) 0.001/0.001 U42(tt) -> tt 0.001/0.001 U51(tt,V2:S) -> U52(isNatList(V2:S)) 0.001/0.001 U52(tt) -> tt 0.001/0.001 U61(tt,L:S,N:S) -> U62(isNat(N:S),L:S) 0.001/0.001 U62(tt,L:S) -> s(length(L:S)) 0.001/0.001 isNat(length(V1:S)) -> U11(isNatList(V1:S)) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(V1:S)) -> U21(isNat(V1:S)) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(V1:S,V2:S)) -> U41(isNat(V1:S),V2:S) 0.001/0.001 isNatIList(V:S) -> U31(isNatList(V:S)) 0.001/0.001 isNatList(cons(V1:S,V2:S)) -> U51(isNat(V1:S),V2:S) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> U61(isNatList(L:S),L:S,N: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) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U21 1) 0.001/0.001 (U31 1) 0.001/0.001 (U41 1) 0.001/0.001 (U42 1) 0.001/0.001 (U51 1) 0.001/0.001 (U52 1) 0.001/0.001 (U61 1) 0.001/0.001 (U62 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) -> tt 0.001/0.001 U21(tt) -> tt 0.001/0.001 U31(tt) -> tt 0.001/0.001 U41(tt,V2:S) -> U42(isNatIList(V2:S)) 0.001/0.001 U42(tt) -> tt 0.001/0.001 U51(tt,V2:S) -> U52(isNatList(V2:S)) 0.001/0.001 U52(tt) -> tt 0.001/0.001 U61(tt,L:S,N:S) -> U62(isNat(N:S),L:S) 0.001/0.001 U62(tt,L:S) -> s(length(L:S)) 0.001/0.001 isNat(length(V1:S)) -> U11(isNatList(V1:S)) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(V1:S)) -> U21(isNat(V1:S)) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(V1:S,V2:S)) -> U41(isNat(V1:S),V2:S) 0.001/0.001 isNatIList(V:S) -> U31(isNatList(V:S)) 0.001/0.001 isNatList(cons(V1:S,V2:S)) -> U51(isNat(V1:S),V2:S) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> U61(isNatList(L:S),L:S,N: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) -> tt 0.001/0.001 U21(tt) -> tt 0.001/0.001 U31(tt) -> tt 0.001/0.001 U41(tt,V2:S) -> U42(isNatIList(V2:S)) 0.001/0.001 U42(tt) -> tt 0.001/0.001 U51(tt,V2:S) -> U52(isNatList(V2:S)) 0.001/0.001 U52(tt) -> tt 0.001/0.001 U61(tt,L:S,N:S) -> U62(isNat(N:S),L:S) 0.001/0.001 U62(tt,L:S) -> s(length(L:S)) 0.001/0.001 isNat(length(V1:S)) -> U11(isNatList(V1:S)) 0.001/0.001 isNat(0) -> tt 0.001/0.001 isNat(s(V1:S)) -> U21(isNat(V1:S)) 0.001/0.001 isNatIList(zeros) -> tt 0.001/0.001 isNatIList(cons(V1:S,V2:S)) -> U41(isNat(V1:S),V2:S) 0.001/0.001 isNatIList(V:S) -> U31(isNatList(V:S)) 0.001/0.001 isNatList(cons(V1:S,V2:S)) -> U51(isNat(V1:S),V2:S) 0.001/0.001 isNatList(nil) -> tt 0.001/0.001 length(cons(N:S,L:S)) -> U61(isNatList(L:S),L:S,N: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 V2, V2, L, N, L, 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: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 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: [V2], UV-RFrozen: [V2]) 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: [V2], UV-RFrozen: [V2]) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L, N], UV-RFrozen: [L, N]) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [L], UV-LFrozen: [L], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.001/0.001 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.001/0.001 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.001/0.001 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.001/0.001 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 18, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [L], UV-RFrozen: [L, N]) 0.001/0.001 (UV-RuleId: 19, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 20, 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 0.001/0.001 -> PVars: 0.001/0.001 V2: [x6, x7, x14, x17], L: [x8, x10, x18], N: [x9, x19], V1: [x11, x12, x13, x16], V: [x15] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: U11(tt) -> tt, id: 1, possubterms: U11(tt)->[], tt->[1]) 0.001/0.001 (rule: U21(tt) -> tt, id: 2, possubterms: U21(tt)->[], tt->[1]) 0.001/0.001 (rule: U31(tt) -> tt, id: 3, possubterms: U31(tt)->[], tt->[1]) 0.001/0.001 (rule: U41(tt,x6:S) -> U42(isNatIList(x6:S)), id: 4, possubterms: U41(tt,x6:S)->[], tt->[1]) 0.001/0.001 (rule: U42(tt) -> tt, id: 5, possubterms: U42(tt)->[], tt->[1]) 0.001/0.001 (rule: U51(tt,x7:S) -> U52(isNatList(x7:S)), id: 6, possubterms: U51(tt,x7:S)->[], tt->[1]) 0.001/0.001 (rule: U52(tt) -> tt, id: 7, possubterms: U52(tt)->[], tt->[1]) 0.001/0.001 (rule: U61(tt,x8:S,x9:S) -> U62(isNat(x9:S),x8:S), id: 8, possubterms: U61(tt,x8:S,x9:S)->[], tt->[1]) 0.001/0.001 (rule: U62(tt,x10:S) -> s(length(x10:S)), id: 9, possubterms: U62(tt,x10:S)->[], tt->[1]) 0.001/0.001 (rule: isNat(length(x11:S)) -> U11(isNatList(x11:S)), id: 10, possubterms: isNat(length(x11:S))->[]) 0.001/0.001 (rule: isNat(0) -> tt, id: 11, possubterms: isNat(0)->[]) 0.001/0.001 (rule: isNat(s(x12:S)) -> U21(isNat(x12:S)), id: 12, possubterms: isNat(s(x12:S))->[]) 0.001/0.001 (rule: isNatIList(zeros) -> tt, id: 13, possubterms: isNatIList(zeros)->[]) 0.001/0.001 (rule: isNatIList(cons(x13:S,x14:S)) -> U41(isNat(x13:S),x14:S), id: 14, possubterms: isNatIList(cons(x13:S,x14:S))->[]) 0.001/0.001 (rule: isNatIList(x15:S) -> U31(isNatList(x15:S)), id: 15, possubterms: isNatIList(x15:S)->[]) 0.001/0.001 (rule: isNatList(cons(x16:S,x17:S)) -> U51(isNat(x16:S),x17:S), id: 16, possubterms: isNatList(cons(x16:S,x17:S))->[]) 0.001/0.001 (rule: isNatList(nil) -> tt, id: 17, possubterms: isNatList(nil)->[]) 0.001/0.001 (rule: length(cons(x19:S,x18:S)) -> U61(isNatList(x18:S),x18:S,x19:S), id: 18, possubterms: length(cons(x19:S,x18:S))->[], cons(x19:S,x18:S)->[1]) 0.001/0.001 (rule: length(nil) -> 0, id: 19, possubterms: length(nil)->[], nil->[1]) 0.001/0.001 (rule: zeros -> cons(0,zeros), id: 20, possubterms: zeros->[]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R15 unifies with R13 at p: [], l: isNatIList(x15:S), lp: isNatIList(x15:S), sig: {x15:S -> zeros}, l': isNatIList(zeros), r: U31(isNatList(x15:S)), r': tt) 0.001/0.001 (R15 unifies with R14 at p: [], l: isNatIList(x15:S), lp: isNatIList(x15:S), sig: {x15:S -> cons(V1:S,V2:S)}, l': isNatIList(cons(V1:S,V2:S)), r: U31(isNatList(x15:S)), r': U41(isNat(V1:S),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: U41(isNat(V1:S),V2:S) 0.001/0.001 Nodes: [0] 0.001/0.001 Edges: [] 0.001/0.001 ID: 0 => ('U41(isNat(V1:S),V2:S)', D0) 0.001/0.001 t: U31(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 => ('U31(isNatList(cons(V1:S,V2:S)))', D0) 0.001/0.001 ID: 1 => ('U31(U51(isNat(V1:S),V2:S))', D1, R16, P[1], S{x16:S -> V1:S, x17:S -> V2:S}), NR: 'U51(isNat(V1:S),V2:S)' 0.001/0.001 U41(isNat(V1:S),V2:S) ->* no union *<- U31(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 61%CPU (0avgtext+0avgdata 9948maxresident)k 0.001/0.001 0inputs+0outputs (0major+873minor)pagefaults 0swaps