0.002/0.002 NO 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S IL:S:S L:S:S M:S:S N:S:S V:S:S V1:S:S V2:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U31 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (U91 1) 0.002/0.002 (U92 1) 0.002/0.002 (U93 1) 0.002/0.002 (isNat 1) 0.002/0.002 (isNatIList 1) 0.002/0.002 (isNatList 1) 0.002/0.002 (length 1) 0.002/0.002 (take 1 2) 0.002/0.002 (zeros) 0.002/0.002 (cons) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (num0) 0.002/0.002 (s) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt) -> tt 0.002/0.002 U21(tt) -> tt 0.002/0.002 U31(tt) -> tt 0.002/0.002 U41(tt,V2:S:S) -> U42(isNatIList(V2:S:S)) 0.002/0.002 U42(tt) -> tt 0.002/0.002 U51(tt,V2:S:S) -> U52(isNatList(V2:S:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt,V2:S:S) -> U62(isNatIList(V2:S:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt,L:S:S,N:S:S) -> U72(isNat(N:S:S),L:S:S) 0.002/0.002 U72(tt,L:S:S) -> s(length(L:S:S)) 0.002/0.002 U81(tt) -> nil 0.002/0.002 U91(tt,IL:S:S,M:S:S,N:S:S) -> U92(isNat(M:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 U92(tt,IL:S:S,M:S:S,N:S:S) -> U93(isNat(N:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 U93(tt,IL:S:S,M:S:S,N:S:S) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.002/0.002 isNat(length(V1:S:S)) -> U11(isNatList(V1:S:S)) 0.002/0.002 isNat(num0) -> tt 0.002/0.002 isNat(s(V1:S:S)) -> U21(isNat(V1:S:S)) 0.002/0.002 isNatIList(zeros) -> tt 0.002/0.002 isNatIList(cons(V1:S:S,V2:S:S)) -> U41(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatIList(V:S:S) -> U31(isNatList(V:S:S)) 0.002/0.002 isNatList(take(V1:S:S,V2:S:S)) -> U61(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatList(cons(V1:S:S,V2:S:S)) -> U51(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatList(nil) -> tt 0.002/0.002 length(cons(N:S:S,L:S:S)) -> U71(isNatList(L:S:S),L:S:S,N:S:S) 0.002/0.002 length(nil) -> num0 0.002/0.002 take(num0,IL:S:S) -> U81(isNatIList(IL:S:S)) 0.002/0.002 take(s(M:S:S),cons(N:S:S,IL:S:S)) -> U91(isNatIList(IL:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 zeros -> cons(num0,zeros) 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 CleanTRS Processor: 0.002/0.002 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S IL:S:S L:S:S M:S:S N:S:S V:S:S V1:S:S V2:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U31 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (U91 1) 0.002/0.002 (U92 1) 0.002/0.002 (U93 1) 0.002/0.002 (isNat 1) 0.002/0.002 (isNatIList 1) 0.002/0.002 (isNatList 1) 0.002/0.002 (length 1) 0.002/0.002 (take 1 2) 0.002/0.002 (zeros) 0.002/0.002 (cons) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (num0) 0.002/0.002 (s) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt) -> tt 0.002/0.002 U21(tt) -> tt 0.002/0.002 U31(tt) -> tt 0.002/0.002 U41(tt,V2:S:S) -> U42(isNatIList(V2:S:S)) 0.002/0.002 U42(tt) -> tt 0.002/0.002 U51(tt,V2:S:S) -> U52(isNatList(V2:S:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt,V2:S:S) -> U62(isNatIList(V2:S:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt,L:S:S,N:S:S) -> U72(isNat(N:S:S),L:S:S) 0.002/0.002 U72(tt,L:S:S) -> s(length(L:S:S)) 0.002/0.002 U81(tt) -> nil 0.002/0.002 U91(tt,IL:S:S,M:S:S,N:S:S) -> U92(isNat(M:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 U92(tt,IL:S:S,M:S:S,N:S:S) -> U93(isNat(N:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 U93(tt,IL:S:S,M:S:S,N:S:S) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.002/0.002 isNat(length(V1:S:S)) -> U11(isNatList(V1:S:S)) 0.002/0.002 isNat(num0) -> tt 0.002/0.002 isNat(s(V1:S:S)) -> U21(isNat(V1:S:S)) 0.002/0.002 isNatIList(zeros) -> tt 0.002/0.002 isNatIList(cons(V1:S:S,V2:S:S)) -> U41(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatIList(V:S:S) -> U31(isNatList(V:S:S)) 0.002/0.002 isNatList(take(V1:S:S,V2:S:S)) -> U61(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatList(cons(V1:S:S,V2:S:S)) -> U51(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatList(nil) -> tt 0.002/0.002 length(cons(N:S:S,L:S:S)) -> U71(isNatList(L:S:S),L:S:S,N:S:S) 0.002/0.002 length(nil) -> num0 0.002/0.002 take(num0,IL:S:S) -> U81(isNatIList(IL:S:S)) 0.002/0.002 take(s(M:S:S),cons(N:S:S,IL:S:S)) -> U91(isNatIList(IL:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 zeros -> cons(num0,zeros) 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 Modular Confluence Combinations Decomposition Processor: 0.002/0.002 It is a CTRS -> No modular confluence 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 CS-TRS Processor: 0.002/0.002 R is a CS-TRS 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S IL:S:S L:S:S M:S:S N:S:S V:S:S V1:S:S V2:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U31 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (U91 1) 0.002/0.002 (U92 1) 0.002/0.002 (U93 1) 0.002/0.002 (isNat 1) 0.002/0.002 (isNatIList 1) 0.002/0.002 (isNatList 1) 0.002/0.002 (length 1) 0.002/0.002 (take 1 2) 0.002/0.002 (zeros) 0.002/0.002 (cons) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (num0) 0.002/0.002 (s) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt) -> tt 0.002/0.002 U21(tt) -> tt 0.002/0.002 U31(tt) -> tt 0.002/0.002 U41(tt,V2:S:S) -> U42(isNatIList(V2:S:S)) 0.002/0.002 U42(tt) -> tt 0.002/0.002 U51(tt,V2:S:S) -> U52(isNatList(V2:S:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt,V2:S:S) -> U62(isNatIList(V2:S:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt,L:S:S,N:S:S) -> U72(isNat(N:S:S),L:S:S) 0.002/0.002 U72(tt,L:S:S) -> s(length(L:S:S)) 0.002/0.002 U81(tt) -> nil 0.002/0.002 U91(tt,IL:S:S,M:S:S,N:S:S) -> U92(isNat(M:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 U92(tt,IL:S:S,M:S:S,N:S:S) -> U93(isNat(N:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 U93(tt,IL:S:S,M:S:S,N:S:S) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.002/0.002 isNat(length(V1:S:S)) -> U11(isNatList(V1:S:S)) 0.002/0.002 isNat(num0) -> tt 0.002/0.002 isNat(s(V1:S:S)) -> U21(isNat(V1:S:S)) 0.002/0.002 isNatIList(zeros) -> tt 0.002/0.002 isNatIList(cons(V1:S:S,V2:S:S)) -> U41(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatIList(V:S:S) -> U31(isNatList(V:S:S)) 0.002/0.002 isNatList(take(V1:S:S,V2:S:S)) -> U61(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatList(cons(V1:S:S,V2:S:S)) -> U51(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatList(nil) -> tt 0.002/0.002 length(cons(N:S:S,L:S:S)) -> U71(isNatList(L:S:S),L:S:S,N:S:S) 0.002/0.002 length(nil) -> num0 0.002/0.002 take(num0,IL:S:S) -> U81(isNatIList(IL:S:S)) 0.002/0.002 take(s(M:S:S),cons(N:S:S,IL:S:S)) -> U91(isNatIList(IL:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 zeros -> cons(num0,zeros) 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 Huet Levy Processor: 0.002/0.002 -> Rules: 0.002/0.002 U11(tt) -> tt 0.002/0.002 U21(tt) -> tt 0.002/0.002 U31(tt) -> tt 0.002/0.002 U41(tt,V2:S:S) -> U42(isNatIList(V2:S:S)) 0.002/0.002 U42(tt) -> tt 0.002/0.002 U51(tt,V2:S:S) -> U52(isNatList(V2:S:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt,V2:S:S) -> U62(isNatIList(V2:S:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt,L:S:S,N:S:S) -> U72(isNat(N:S:S),L:S:S) 0.002/0.002 U72(tt,L:S:S) -> s(length(L:S:S)) 0.002/0.002 U81(tt) -> nil 0.002/0.002 U91(tt,IL:S:S,M:S:S,N:S:S) -> U92(isNat(M:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 U92(tt,IL:S:S,M:S:S,N:S:S) -> U93(isNat(N:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 U93(tt,IL:S:S,M:S:S,N:S:S) -> cons(N:S:S,take(M:S:S,IL:S:S)) 0.002/0.002 isNat(length(V1:S:S)) -> U11(isNatList(V1:S:S)) 0.002/0.002 isNat(num0) -> tt 0.002/0.002 isNat(s(V1:S:S)) -> U21(isNat(V1:S:S)) 0.002/0.002 isNatIList(zeros) -> tt 0.002/0.002 isNatIList(cons(V1:S:S,V2:S:S)) -> U41(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatIList(V:S:S) -> U31(isNatList(V:S:S)) 0.002/0.002 isNatList(take(V1:S:S,V2:S:S)) -> U61(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatList(cons(V1:S:S,V2:S:S)) -> U51(isNat(V1:S:S),V2:S:S) 0.002/0.002 isNatList(nil) -> tt 0.002/0.002 length(cons(N:S:S,L:S:S)) -> U71(isNatList(L:S:S),L:S:S,N:S:S) 0.002/0.002 length(nil) -> num0 0.002/0.002 take(num0,IL:S:S) -> U81(isNatIList(IL:S:S)) 0.002/0.002 take(s(M:S:S),cons(N:S:S,IL:S:S)) -> U91(isNatIList(IL:S:S),IL:S:S,M:S:S,N:S:S) 0.002/0.002 zeros -> cons(num0,zeros) 0.002/0.002 -> Vars: 0.002/0.002 V2:S, V2:S, V2:S, L:S, N:S, L:S, IL:S, M:S, N:S, IL:S, M:S, N:S, IL:S, M:S, N:S, V1:S, V1:S, V1:S, V2:S, V:S, V1:S, V2:S, V1:S, V2:S, L:S, N:S, IL:S, IL:S, M:S, N:S 0.002/0.002 -> UVars: 0.002/0.002 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [V2:S], UV-LFrozen: [V2:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [V2:S], UV-LFrozen: [V2:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [V2:S], UV-LFrozen: [V2:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [L:S, N:S], UV-RFrozen: [L:S]) 0.002/0.002 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L:S], UV-RFrozen: [L:S]) 0.002/0.002 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [M:S], UV-LFrozen: [IL:S, M:S, N:S], UV-RFrozen: [IL:S, M:S, N:S]) 0.002/0.002 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [IL:S, M:S, N:S], UV-RFrozen: [IL:S, M:S, N:S]) 0.002/0.002 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL:S, M:S, N:S], UV-RFrozen: [IL:S, M:S, N:S]) 0.002/0.002 (UV-RuleId: 16, UV-LActive: [V1:S], UV-RActive: [V1:S], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 18, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 19, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 20, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S, V2:S], UV-RFrozen: [V2:S]) 0.002/0.002 (UV-RuleId: 21, UV-LActive: [V:S], UV-RActive: [V:S], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 22, UV-LActive: [V1:S, V2:S], UV-RActive: [V1:S], UV-LFrozen: [], UV-RFrozen: [V2:S]) 0.002/0.002 (UV-RuleId: 23, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S, V2:S], UV-RFrozen: [V2:S]) 0.002/0.002 (UV-RuleId: 24, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 25, UV-LActive: [], UV-RActive: [L:S], UV-LFrozen: [L:S, N:S], UV-RFrozen: [L:S, N:S]) 0.002/0.002 (UV-RuleId: 26, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 27, UV-LActive: [IL:S], UV-RActive: [IL:S], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 28, UV-LActive: [], UV-RActive: [IL:S], UV-LFrozen: [IL:S, M:S, N:S], UV-RFrozen: [IL:S, M:S, N:S]) 0.002/0.002 (UV-RuleId: 29, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 -> FVars: 0.002/0.002 x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38 0.002/0.002 -> PVars: 0.002/0.002 V2:S: [x9, x10, x11, x27, x30, x32], L:S: [x12, x14, x33], N:S: [x13, x17, x20, x23, x34, x38], IL:S: [x15, x18, x21, x35, x36], M:S: [x16, x19, x22, x37], V1:S: [x24, x25, x26, x29, x31], V:S: [x28] 0.002/0.002 0.002/0.002 -> Rlps: 0.002/0.002 (rule: U11(tt) -> tt, id: 1, possubterms: U11(tt)->[], tt->[1]) 0.002/0.002 (rule: U21(tt) -> tt, id: 2, possubterms: U21(tt)->[], tt->[1]) 0.002/0.002 (rule: U31(tt) -> tt, id: 3, possubterms: U31(tt)->[], tt->[1]) 0.002/0.002 (rule: U41(tt,x9:S) -> U42(isNatIList(x9:S)), id: 4, possubterms: U41(tt,x9:S)->[], tt->[1]) 0.002/0.002 (rule: U42(tt) -> tt, id: 5, possubterms: U42(tt)->[], tt->[1]) 0.002/0.002 (rule: U51(tt,x10:S) -> U52(isNatList(x10:S)), id: 6, possubterms: U51(tt,x10:S)->[], tt->[1]) 0.002/0.002 (rule: U52(tt) -> tt, id: 7, possubterms: U52(tt)->[], tt->[1]) 0.002/0.002 (rule: U61(tt,x11:S) -> U62(isNatIList(x11:S)), id: 8, possubterms: U61(tt,x11:S)->[], tt->[1]) 0.002/0.002 (rule: U62(tt) -> tt, id: 9, possubterms: U62(tt)->[], tt->[1]) 0.002/0.002 (rule: U71(tt,x12:S,x13:S) -> U72(isNat(x13:S),x12:S), id: 10, possubterms: U71(tt,x12:S,x13:S)->[], tt->[1]) 0.002/0.002 (rule: U72(tt,x14:S) -> s(length(x14:S)), id: 11, possubterms: U72(tt,x14:S)->[], tt->[1]) 0.002/0.002 (rule: U81(tt) -> nil, id: 12, possubterms: U81(tt)->[], tt->[1]) 0.002/0.002 (rule: U91(tt,x15:S,x16:S,x17:S) -> U92(isNat(x16:S),x15:S,x16:S,x17:S), id: 13, possubterms: U91(tt,x15:S,x16:S,x17:S)->[], tt->[1]) 0.002/0.002 (rule: U92(tt,x18:S,x19:S,x20:S) -> U93(isNat(x20:S),x18:S,x19:S,x20:S), id: 14, possubterms: U92(tt,x18:S,x19:S,x20:S)->[], tt->[1]) 0.002/0.002 (rule: U93(tt,x21:S,x22:S,x23:S) -> cons(x23:S,take(x22:S,x21:S)), id: 15, possubterms: U93(tt,x21:S,x22:S,x23:S)->[], tt->[1]) 0.002/0.002 (rule: isNat(length(x24:S)) -> U11(isNatList(x24:S)), id: 16, possubterms: isNat(length(x24:S))->[], length(x24:S)->[1]) 0.002/0.002 (rule: isNat(num0) -> tt, id: 17, possubterms: isNat(num0)->[], num0->[1]) 0.002/0.002 (rule: isNat(s(x25:S)) -> U21(isNat(x25:S)), id: 18, possubterms: isNat(s(x25:S))->[], s(x25:S)->[1]) 0.002/0.002 (rule: isNatIList(zeros) -> tt, id: 19, possubterms: isNatIList(zeros)->[], zeros->[1]) 0.002/0.002 (rule: isNatIList(cons(x26:S,x27:S)) -> U41(isNat(x26:S),x27:S), id: 20, possubterms: isNatIList(cons(x26:S,x27:S))->[], cons(x26:S,x27:S)->[1]) 0.002/0.002 (rule: isNatIList(x28:S) -> U31(isNatList(x28:S)), id: 21, possubterms: isNatIList(x28:S)->[]) 0.002/0.002 (rule: isNatList(take(x29:S,x30:S)) -> U61(isNat(x29:S),x30:S), id: 22, possubterms: isNatList(take(x29:S,x30:S))->[], take(x29:S,x30:S)->[1]) 0.002/0.002 (rule: isNatList(cons(x31:S,x32:S)) -> U51(isNat(x31:S),x32:S), id: 23, possubterms: isNatList(cons(x31:S,x32:S))->[], cons(x31:S,x32:S)->[1]) 0.002/0.002 (rule: isNatList(nil) -> tt, id: 24, possubterms: isNatList(nil)->[], nil->[1]) 0.002/0.002 (rule: length(cons(x34:S,x33:S)) -> U71(isNatList(x33:S),x33:S,x34:S), id: 25, possubterms: length(cons(x34:S,x33:S))->[], cons(x34:S,x33:S)->[1]) 0.002/0.002 (rule: length(nil) -> num0, id: 26, possubterms: length(nil)->[], nil->[1]) 0.002/0.002 (rule: take(num0,x35:S) -> U81(isNatIList(x35:S)), id: 27, possubterms: take(num0,x35:S)->[], num0->[1]) 0.002/0.002 (rule: take(s(x37:S),cons(x38:S,x36:S)) -> U91(isNatIList(x36:S),x36:S,x37:S,x38:S), id: 28, possubterms: take(s(x37:S),cons(x38:S,x36:S))->[], s(x37:S)->[1], cons(x38:S,x36:S)->[2]) 0.002/0.002 (rule: zeros -> cons(num0,zeros), id: 29, possubterms: zeros->[]) 0.002/0.002 0.002/0.002 -> Unifications: 0.002/0.002 (R16 unifies with R25 at p: [1], l: isNat(length(x24:S)), lp: length(x24:S), sig: {x24:S -> cons(N:S:S,L:S:S)}, l': length(cons(N:S:S,L:S:S)), r: U11(isNatList(x24:S)), r': U71(isNatList(L:S:S),L:S:S,N:S:S)) 0.002/0.002 (R16 unifies with R26 at p: [1], l: isNat(length(x24:S)), lp: length(x24:S), sig: {x24:S -> nil}, l': length(nil), r: U11(isNatList(x24:S)), r': num0) 0.002/0.002 (R19 unifies with R29 at p: [1], l: isNatIList(zeros), lp: zeros, sig: {}, l': zeros, r: tt, r': cons(num0,zeros)) 0.002/0.002 (R21 unifies with R19 at p: [], l: isNatIList(x28:S), lp: isNatIList(x28:S), sig: {x28:S -> zeros}, l': isNatIList(zeros), r: U31(isNatList(x28:S)), r': tt) 0.002/0.002 (R21 unifies with R20 at p: [], l: isNatIList(x28:S), lp: isNatIList(x28:S), sig: {x28:S -> cons(V1:S:S,V2:S:S)}, l': isNatIList(cons(V1:S:S,V2:S:S)), r: U31(isNatList(x28:S)), r': U41(isNat(V1:S:S),V2:S:S)) 0.002/0.002 (R22 unifies with R27 at p: [1], l: isNatList(take(x29:S,x30:S)), lp: take(x29:S,x30:S), sig: {x29:S -> num0,x30:S -> IL:S:S}, l': take(num0,IL:S:S), r: U61(isNat(x29:S),x30:S), r': U81(isNatIList(IL:S:S))) 0.002/0.002 (R22 unifies with R28 at p: [1], l: isNatList(take(x29:S,x30:S)), lp: take(x29:S,x30:S), sig: {x29:S -> s(M:S:S),x30:S -> cons(N:S:S,IL:S:S)}, l': take(s(M:S:S),cons(N:S:S,IL:S:S)), r: U61(isNat(x29:S),x30:S), r': U91(isNatIList(IL:S:S),IL:S:S,M:S:S,N:S:S)) 0.002/0.002 0.002/0.002 -> Critical pairs info: 0.002/0.002 => Not trivial, Not overlay, NW0, N1 0.002/0.002 => Not trivial, Not overlay, NW0, N2 0.002/0.002 => Not trivial, Not overlay, NW0, N3 0.002/0.002 => Not trivial, Overlay, NW0, N4 0.002/0.002 => Not trivial, Overlay, NW0, N5 0.002/0.002 => Not trivial, Not overlay, NW0, N6 0.002/0.002 => Not trivial, Not overlay, NW0, N7 0.002/0.002 0.002/0.002 -> Problem conclusions: 0.002/0.002 Left linear, Not right linear, Not linear 0.002/0.002 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.002/0.002 Not Huet-Levy confluent, Not Newman confluent 0.002/0.002 R is a CS-TRS, Not left-homogeneous u-replacing variables 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 No Convergence Brute Force Processor: 0.002/0.002 -> Rewritings: 0.002/0.002 s: isNatList(U81(isNatIList(IL:S:S))) 0.002/0.002 Nodes: [0,1] 0.002/0.002 Edges: [(0,1)] 0.002/0.002 ID: 0 => ('isNatList(U81(isNatIList(IL:S:S)))', D0) 0.002/0.002 ID: 1 => ('isNatList(U81(U31(isNatList(IL:S:S))))', D1, R21, P[1, 1], S{x28:S -> IL:S:S}), NR: 'U31(isNatList(IL:S:S))' 0.002/0.002 t: U61(isNat(num0),IL:S:S) 0.002/0.002 Nodes: [0,1,2,3] 0.002/0.002 Edges: [(0,1),(1,2),(2,3)] 0.002/0.002 ID: 0 => ('U61(isNat(num0),IL:S:S)', D0) 0.002/0.002 ID: 1 => ('U61(tt,IL:S:S)', D1, R17, P[1], S{}), NR: 'tt' 0.002/0.002 ID: 2 => ('U62(isNatIList(IL:S:S))', D2, R8, P[], S{x11:S -> IL:S:S}), NR: 'U62(isNatIList(IL:S:S))' 0.002/0.002 ID: 3 => ('U62(U31(isNatList(IL:S:S)))', D3, R21, P[1], S{x28:S -> IL:S:S}), NR: 'U31(isNatList(IL:S:S))' 0.002/0.002 isNatList(U81(isNatIList(IL:S:S))) ->* no union *<- U61(isNat(num0),IL:S:S) 0.002/0.002 "Not joinable" 0.002/0.002 0.002/0.002 The problem is not joinable. 0.002/0.002 0.01user 0.00system 0:00.02elapsed 65%CPU (0avgtext+0avgdata 11812maxresident)k 0.002/0.002 8inputs+0outputs (0major+1160minor)pagefaults 0swaps