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 v_NonEmpty:S:S M:S:S N:S:S V1:S:S V2: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 (U31 1) 0.001/0.001 (U32 1) 0.001/0.001 (U41 1) 0.001/0.001 (U51 1) 0.001/0.001 (U52 1) 0.001/0.001 (U61 1) 0.001/0.001 (U71 1) 0.001/0.001 (U72 1) 0.001/0.001 (isNat 1) 0.001/0.001 (plus 2) 0.001/0.001 (x 2) 0.001/0.001 (fSNonEmpty) 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,V2:S:S) -> U12(isNat(V2:S:S)) 0.001/0.001 U12(tt) -> tt 0.001/0.001 U21(tt) -> tt 0.001/0.001 U31(tt,V2:S:S) -> U32(isNat(V2:S:S)) 0.001/0.001 U32(tt) -> tt 0.001/0.001 U41(tt,N:S:S) -> N:S:S 0.001/0.001 U51(tt,M:S:S,N:S:S) -> U52(isNat(N:S:S),M:S:S,N:S:S) 0.001/0.001 U52(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U61(tt) -> num0 0.001/0.001 U71(tt,M:S:S,N:S:S) -> U72(isNat(N:S:S),M:S:S,N:S:S) 0.001/0.001 U72(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> U11(isNat(V1:S:S),V2:S:S) 0.001/0.001 isNat(x(V1:S:S,V2:S:S)) -> U31(isNat(V1:S:S),V2:S:S) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> U21(isNat(V1:S:S)) 0.001/0.001 plus(N:S:S,num0) -> U41(isNat(N:S:S),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U51(isNat(M:S:S),M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> U61(isNat(N:S:S)) 0.001/0.001 x(N:S:S,s(M:S:S)) -> U71(isNat(M:S:S),M:S:S,N:S:S) 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 M:S:S N:S:S V1:S:S V2: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 (U31 1) 0.001/0.001 (U32 1) 0.001/0.001 (U41 1) 0.001/0.001 (U51 1) 0.001/0.001 (U52 1) 0.001/0.001 (U61 1) 0.001/0.001 (U71 1) 0.001/0.001 (U72 1) 0.001/0.001 (isNat 1) 0.001/0.001 (plus 2) 0.001/0.001 (x 2) 0.001/0.001 (fSNonEmpty) 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,V2:S:S) -> U12(isNat(V2:S:S)) 0.001/0.001 U12(tt) -> tt 0.001/0.001 U21(tt) -> tt 0.001/0.001 U31(tt,V2:S:S) -> U32(isNat(V2:S:S)) 0.001/0.001 U32(tt) -> tt 0.001/0.001 U41(tt,N:S:S) -> N:S:S 0.001/0.001 U51(tt,M:S:S,N:S:S) -> U52(isNat(N:S:S),M:S:S,N:S:S) 0.001/0.001 U52(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U61(tt) -> num0 0.001/0.001 U71(tt,M:S:S,N:S:S) -> U72(isNat(N:S:S),M:S:S,N:S:S) 0.001/0.001 U72(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> U11(isNat(V1:S:S),V2:S:S) 0.001/0.001 isNat(x(V1:S:S,V2:S:S)) -> U31(isNat(V1:S:S),V2:S:S) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> U21(isNat(V1:S:S)) 0.001/0.001 plus(N:S:S,num0) -> U41(isNat(N:S:S),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U51(isNat(M:S:S),M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> U61(isNat(N:S:S)) 0.001/0.001 x(N:S:S,s(M:S:S)) -> U71(isNat(M:S:S),M:S:S,N:S:S) 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 v_NonEmpty:S:S M:S:S N:S:S V1:S:S V2: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 (U31 1) 0.001/0.001 (U32 1) 0.001/0.001 (U41 1) 0.001/0.001 (U51 1) 0.001/0.001 (U52 1) 0.001/0.001 (U61 1) 0.001/0.001 (U71 1) 0.001/0.001 (U72 1) 0.001/0.001 (isNat 1) 0.001/0.001 (plus 2) 0.001/0.001 (x 2) 0.001/0.001 (fSNonEmpty) 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,V2:S:S) -> U12(isNat(V2:S:S)) 0.001/0.001 U12(tt) -> tt 0.001/0.001 U21(tt) -> tt 0.001/0.001 U31(tt,V2:S:S) -> U32(isNat(V2:S:S)) 0.001/0.001 U32(tt) -> tt 0.001/0.001 U41(tt,N:S:S) -> N:S:S 0.001/0.001 U51(tt,M:S:S,N:S:S) -> U52(isNat(N:S:S),M:S:S,N:S:S) 0.001/0.001 U52(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U61(tt) -> num0 0.001/0.001 U71(tt,M:S:S,N:S:S) -> U72(isNat(N:S:S),M:S:S,N:S:S) 0.001/0.001 U72(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> U11(isNat(V1:S:S),V2:S:S) 0.001/0.001 isNat(x(V1:S:S,V2:S:S)) -> U31(isNat(V1:S:S),V2:S:S) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> U21(isNat(V1:S:S)) 0.001/0.001 plus(N:S:S,num0) -> U41(isNat(N:S:S),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U51(isNat(M:S:S),M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> U61(isNat(N:S:S)) 0.001/0.001 x(N:S:S,s(M:S:S)) -> U71(isNat(M:S:S),M:S:S,N:S:S) 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,V2:S:S) -> U12(isNat(V2:S:S)) 0.001/0.001 U12(tt) -> tt 0.001/0.001 U21(tt) -> tt 0.001/0.001 U31(tt,V2:S:S) -> U32(isNat(V2:S:S)) 0.001/0.001 U32(tt) -> tt 0.001/0.001 U41(tt,N:S:S) -> N:S:S 0.001/0.001 U51(tt,M:S:S,N:S:S) -> U52(isNat(N:S:S),M:S:S,N:S:S) 0.001/0.001 U52(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U61(tt) -> num0 0.001/0.001 U71(tt,M:S:S,N:S:S) -> U72(isNat(N:S:S),M:S:S,N:S:S) 0.001/0.001 U72(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> U11(isNat(V1:S:S),V2:S:S) 0.001/0.001 isNat(x(V1:S:S,V2:S:S)) -> U31(isNat(V1:S:S),V2:S:S) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> U21(isNat(V1:S:S)) 0.001/0.001 plus(N:S:S,num0) -> U41(isNat(N:S:S),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U51(isNat(M:S:S),M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> U61(isNat(N:S:S)) 0.001/0.001 x(N:S:S,s(M:S:S)) -> U71(isNat(M:S:S),M:S:S,N:S:S) 0.001/0.001 -> Vars: 0.001/0.001 V2:S, V2:S, N:S, M:S, N:S, M:S, N:S, M:S, N:S, M:S, N:S, V1:S, V2:S, V1:S, V2:S, V1:S, N:S, M:S, N:S, N:S, M:S, N:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [V2:S], UV-LFrozen: [V2:S], 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: [V2:S], UV-LFrozen: [V2:S], UV-RFrozen: []) 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: [N:S], UV-LFrozen: [N:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 12, UV-LActive: [V2:S], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V2:S]) 0.001/0.001 (UV-RuleId: 13, UV-LActive: [V2:S], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V2:S]) 0.001/0.001 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: [N:S]) 0.001/0.001 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [M:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 18, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 19, UV-LActive: [], UV-RActive: [M:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 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, x26, x27 0.001/0.001 -> PVars: 0.001/0.001 V2:S: [x6, x7, x18, x20], N:S: [x8, x10, x12, x14, x16, x22, x24, x25, x27], M:S: [x9, x11, x13, x15, x23, x26], V1:S: [x17, x19, x21] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: U11(tt,x6:S) -> U12(isNat(x6:S)), id: 1, possubterms: U11(tt,x6:S)->[], tt->[1]) 0.001/0.001 (rule: U12(tt) -> tt, id: 2, possubterms: U12(tt)->[], tt->[1]) 0.001/0.001 (rule: U21(tt) -> tt, id: 3, possubterms: U21(tt)->[], tt->[1]) 0.001/0.001 (rule: U31(tt,x7:S) -> U32(isNat(x7:S)), id: 4, possubterms: U31(tt,x7:S)->[], tt->[1]) 0.001/0.001 (rule: U32(tt) -> tt, id: 5, possubterms: U32(tt)->[], tt->[1]) 0.001/0.001 (rule: U41(tt,x8:S) -> x8:S, id: 6, possubterms: U41(tt,x8:S)->[], tt->[1]) 0.001/0.001 (rule: U51(tt,x9:S,x10:S) -> U52(isNat(x10:S),x9:S,x10:S), id: 7, possubterms: U51(tt,x9:S,x10:S)->[], tt->[1]) 0.001/0.001 (rule: U52(tt,x11:S,x12:S) -> s(plus(x12:S,x11:S)), id: 8, possubterms: U52(tt,x11:S,x12:S)->[], tt->[1]) 0.001/0.001 (rule: U61(tt) -> num0, id: 9, possubterms: U61(tt)->[], tt->[1]) 0.001/0.001 (rule: U71(tt,x13:S,x14:S) -> U72(isNat(x14:S),x13:S,x14:S), id: 10, possubterms: U71(tt,x13:S,x14:S)->[], tt->[1]) 0.001/0.001 (rule: U72(tt,x15:S,x16:S) -> plus(x(x16:S,x15:S),x16:S), id: 11, possubterms: U72(tt,x15:S,x16:S)->[], tt->[1]) 0.001/0.001 (rule: isNat(plus(x17:S,x18:S)) -> U11(isNat(x17:S),x18:S), id: 12, possubterms: isNat(plus(x17:S,x18:S))->[], plus(x17:S,x18:S)->[1]) 0.001/0.001 (rule: isNat(x(x19:S,x20:S)) -> U31(isNat(x19:S),x20:S), id: 13, possubterms: isNat(x(x19:S,x20:S))->[], x(x19:S,x20:S)->[1]) 0.001/0.001 (rule: isNat(num0) -> tt, id: 14, possubterms: isNat(num0)->[], num0->[1]) 0.001/0.001 (rule: isNat(s(x21:S)) -> U21(isNat(x21:S)), id: 15, possubterms: isNat(s(x21:S))->[], s(x21:S)->[1]) 0.001/0.001 (rule: plus(x22:S,num0) -> U41(isNat(x22:S),x22:S), id: 16, possubterms: plus(x22:S,num0)->[], num0->[2]) 0.001/0.001 (rule: plus(x24:S,s(x23:S)) -> U51(isNat(x23:S),x23:S,x24:S), id: 17, possubterms: plus(x24:S,s(x23:S))->[], s(x23:S)->[2]) 0.001/0.001 (rule: x(x25:S,num0) -> U61(isNat(x25:S)), id: 18, possubterms: x(x25:S,num0)->[], num0->[2]) 0.001/0.001 (rule: x(x27:S,s(x26:S)) -> U71(isNat(x26:S),x26:S,x27:S), id: 19, possubterms: x(x27:S,s(x26:S))->[], s(x26:S)->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R12 unifies with R16 at p: [1], l: isNat(plus(x17:S,x18:S)), lp: plus(x17:S,x18:S), sig: {x17:S -> N:S:S,x18:S -> num0}, l': plus(N:S:S,num0), r: U11(isNat(x17:S),x18:S), r': U41(isNat(N:S:S),N:S:S)) 0.001/0.001 (R12 unifies with R17 at p: [1], l: isNat(plus(x17:S,x18:S)), lp: plus(x17:S,x18:S), sig: {x17:S -> N:S:S,x18:S -> s(M:S:S)}, l': plus(N:S:S,s(M:S:S)), r: U11(isNat(x17:S),x18:S), r': U51(isNat(M:S:S),M:S:S,N:S:S)) 0.001/0.001 (R13 unifies with R18 at p: [1], l: isNat(x(x19:S,x20:S)), lp: x(x19:S,x20:S), sig: {x19:S -> N:S:S,x20:S -> num0}, l': x(N:S:S,num0), r: U31(isNat(x19:S),x20:S), r': U61(isNat(N:S:S))) 0.001/0.001 (R13 unifies with R19 at p: [1], l: isNat(x(x19:S,x20:S)), lp: x(x19:S,x20:S), sig: {x19:S -> N:S:S,x20:S -> s(M:S:S)}, l': x(N:S:S,s(M:S:S)), r: U31(isNat(x19:S),x20:S), r': U71(isNat(M:S:S),M:S:S,N:S:S)) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 => Not trivial, Not overlay, NW0, N1 0.001/0.001 => Not trivial, Not overlay, NW0, N2 0.001/0.001 => Not trivial, Not overlay, NW0, N3 0.001/0.001 => Not trivial, Not overlay, NW0, N4 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, Not 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 83%CPU (0avgtext+0avgdata 10628maxresident)k 0.001/0.001 8inputs+0outputs (0major+955minor)pagefaults 0swaps