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 X:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (U13 1) 0.001/0.001 (U21 1) 0.001/0.001 (U22 1) 0.001/0.001 (U31 1) 0.001/0.001 (U41 1) 0.001/0.001 (and 1) 0.001/0.001 (isNat 1) 0.001/0.001 (isNatKind 1) 0.001/0.001 (plus 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,V1:S:S,V2:S:S) -> U12(isNat(V1:S:S),V2:S:S) 0.001/0.001 U12(tt,V2:S:S) -> U13(isNat(V2:S:S)) 0.001/0.001 U13(tt) -> tt 0.001/0.001 U21(tt,V1:S:S) -> U22(isNat(V1:S:S)) 0.001/0.001 U22(tt) -> tt 0.001/0.001 U31(tt,N:S:S) -> N:S:S 0.001/0.001 U41(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> U11(and(isNatKind(V1:S:S),isNatKind(V2:S:S)),V1:S:S,V2:S:S) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> U21(isNatKind(V1:S:S),V1:S:S) 0.001/0.001 isNatKind(plus(V1:S:S,V2:S:S)) -> and(isNatKind(V1:S:S),isNatKind(V2:S:S)) 0.001/0.001 isNatKind(num0) -> tt 0.001/0.001 isNatKind(s(V1:S:S)) -> isNatKind(V1:S:S) 0.001/0.001 plus(N:S:S,num0) -> U31(and(isNat(N:S:S),isNatKind(N:S:S)),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U41(and(and(isNat(M:S:S),isNatKind(M:S:S)),and(isNat(N:S:S),isNatKind(N: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 X:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (U13 1) 0.001/0.001 (U21 1) 0.001/0.001 (U22 1) 0.001/0.001 (U31 1) 0.001/0.001 (U41 1) 0.001/0.001 (and 1) 0.001/0.001 (isNat 1) 0.001/0.001 (isNatKind 1) 0.001/0.001 (plus 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,V1:S:S,V2:S:S) -> U12(isNat(V1:S:S),V2:S:S) 0.001/0.001 U12(tt,V2:S:S) -> U13(isNat(V2:S:S)) 0.001/0.001 U13(tt) -> tt 0.001/0.001 U21(tt,V1:S:S) -> U22(isNat(V1:S:S)) 0.001/0.001 U22(tt) -> tt 0.001/0.001 U31(tt,N:S:S) -> N:S:S 0.001/0.001 U41(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> U11(and(isNatKind(V1:S:S),isNatKind(V2:S:S)),V1:S:S,V2:S:S) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> U21(isNatKind(V1:S:S),V1:S:S) 0.001/0.001 isNatKind(plus(V1:S:S,V2:S:S)) -> and(isNatKind(V1:S:S),isNatKind(V2:S:S)) 0.001/0.001 isNatKind(num0) -> tt 0.001/0.001 isNatKind(s(V1:S:S)) -> isNatKind(V1:S:S) 0.001/0.001 plus(N:S:S,num0) -> U31(and(isNat(N:S:S),isNatKind(N:S:S)),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U41(and(and(isNat(M:S:S),isNatKind(M:S:S)),and(isNat(N:S:S),isNatKind(N: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 X:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (U13 1) 0.001/0.001 (U21 1) 0.001/0.001 (U22 1) 0.001/0.001 (U31 1) 0.001/0.001 (U41 1) 0.001/0.001 (and 1) 0.001/0.001 (isNat 1) 0.001/0.001 (isNatKind 1) 0.001/0.001 (plus 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,V1:S:S,V2:S:S) -> U12(isNat(V1:S:S),V2:S:S) 0.001/0.001 U12(tt,V2:S:S) -> U13(isNat(V2:S:S)) 0.001/0.001 U13(tt) -> tt 0.001/0.001 U21(tt,V1:S:S) -> U22(isNat(V1:S:S)) 0.001/0.001 U22(tt) -> tt 0.001/0.001 U31(tt,N:S:S) -> N:S:S 0.001/0.001 U41(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> U11(and(isNatKind(V1:S:S),isNatKind(V2:S:S)),V1:S:S,V2:S:S) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> U21(isNatKind(V1:S:S),V1:S:S) 0.001/0.001 isNatKind(plus(V1:S:S,V2:S:S)) -> and(isNatKind(V1:S:S),isNatKind(V2:S:S)) 0.001/0.001 isNatKind(num0) -> tt 0.001/0.001 isNatKind(s(V1:S:S)) -> isNatKind(V1:S:S) 0.001/0.001 plus(N:S:S,num0) -> U31(and(isNat(N:S:S),isNatKind(N:S:S)),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U41(and(and(isNat(M:S:S),isNatKind(M:S:S)),and(isNat(N:S:S),isNatKind(N: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,V1:S:S,V2:S:S) -> U12(isNat(V1:S:S),V2:S:S) 0.001/0.001 U12(tt,V2:S:S) -> U13(isNat(V2:S:S)) 0.001/0.001 U13(tt) -> tt 0.001/0.001 U21(tt,V1:S:S) -> U22(isNat(V1:S:S)) 0.001/0.001 U22(tt) -> tt 0.001/0.001 U31(tt,N:S:S) -> N:S:S 0.001/0.001 U41(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> U11(and(isNatKind(V1:S:S),isNatKind(V2:S:S)),V1:S:S,V2:S:S) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> U21(isNatKind(V1:S:S),V1:S:S) 0.001/0.001 isNatKind(plus(V1:S:S,V2:S:S)) -> and(isNatKind(V1:S:S),isNatKind(V2:S:S)) 0.001/0.001 isNatKind(num0) -> tt 0.001/0.001 isNatKind(s(V1:S:S)) -> isNatKind(V1:S:S) 0.001/0.001 plus(N:S:S,num0) -> U31(and(isNat(N:S:S),isNatKind(N:S:S)),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U41(and(and(isNat(M:S:S),isNatKind(M:S:S)),and(isNat(N:S:S),isNatKind(N:S:S))),M:S:S,N:S:S) 0.001/0.001 -> Vars: 0.001/0.001 V1:S, V2:S, V2:S, V1:S, N:S, M:S, N:S, X:S, V1:S, V2:S, V1:S, V1:S, V2:S, V1:S, N:S, M:S, N:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S, V2:S], UV-RFrozen: [V2:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [V2:S], UV-LFrozen: [V2:S], 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: [V1:S], UV-LFrozen: [V1: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: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [V2:S], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V1:S, V2:S]) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V1: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: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: [N:S]) 0.001/0.001 (UV-RuleId: 16, 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 x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23 0.001/0.001 -> PVars: 0.001/0.001 V1:S: [x7, x10, x15, x17, x18, x20], V2:S: [x8, x9, x16, x19], N:S: [x11, x13, x21, x23], M:S: [x12, x22], X:S: [x14] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: U11(tt,x7:S,x8:S) -> U12(isNat(x7:S),x8:S), id: 1, possubterms: U11(tt,x7:S,x8:S)->[], tt->[1]) 0.001/0.001 (rule: U12(tt,x9:S) -> U13(isNat(x9:S)), id: 2, possubterms: U12(tt,x9:S)->[], tt->[1]) 0.001/0.001 (rule: U13(tt) -> tt, id: 3, possubterms: U13(tt)->[], tt->[1]) 0.001/0.001 (rule: U21(tt,x10:S) -> U22(isNat(x10:S)), id: 4, possubterms: U21(tt,x10:S)->[], tt->[1]) 0.001/0.001 (rule: U22(tt) -> tt, id: 5, possubterms: U22(tt)->[], tt->[1]) 0.001/0.001 (rule: U31(tt,x11:S) -> x11:S, id: 6, possubterms: U31(tt,x11:S)->[], tt->[1]) 0.001/0.001 (rule: U41(tt,x12:S,x13:S) -> s(plus(x13:S,x12:S)), id: 7, possubterms: U41(tt,x12:S,x13:S)->[], tt->[1]) 0.001/0.001 (rule: and(tt,x14:S) -> x14:S, id: 8, possubterms: and(tt,x14:S)->[], tt->[1]) 0.001/0.001 (rule: isNat(plus(x15:S,x16:S)) -> U11(and(isNatKind(x15:S),isNatKind(x16:S)),x15:S,x16:S), id: 9, possubterms: isNat(plus(x15:S,x16:S))->[], plus(x15:S,x16:S)->[1]) 0.001/0.001 (rule: isNat(num0) -> tt, id: 10, possubterms: isNat(num0)->[], num0->[1]) 0.001/0.001 (rule: isNat(s(x17:S)) -> U21(isNatKind(x17:S),x17:S), id: 11, possubterms: isNat(s(x17:S))->[], s(x17:S)->[1]) 0.001/0.001 (rule: isNatKind(plus(x18:S,x19:S)) -> and(isNatKind(x18:S),isNatKind(x19:S)), id: 12, possubterms: isNatKind(plus(x18:S,x19:S))->[], plus(x18:S,x19:S)->[1]) 0.001/0.001 (rule: isNatKind(num0) -> tt, id: 13, possubterms: isNatKind(num0)->[], num0->[1]) 0.001/0.001 (rule: isNatKind(s(x20:S)) -> isNatKind(x20:S), id: 14, possubterms: isNatKind(s(x20:S))->[], s(x20:S)->[1]) 0.001/0.001 (rule: plus(x21:S,num0) -> U31(and(isNat(x21:S),isNatKind(x21:S)),x21:S), id: 15, possubterms: plus(x21:S,num0)->[], num0->[2]) 0.001/0.001 (rule: plus(x23:S,s(x22:S)) -> U41(and(and(isNat(x22:S),isNatKind(x22:S)),and(isNat(x23:S),isNatKind(x23:S))),x22:S,x23:S), id: 16, possubterms: plus(x23:S,s(x22:S))->[], s(x22:S)->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R9 unifies with R15 at p: [1], l: isNat(plus(x15:S,x16:S)), lp: plus(x15:S,x16:S), sig: {x15:S -> N:S:S,x16:S -> num0}, l': plus(N:S:S,num0), r: U11(and(isNatKind(x15:S),isNatKind(x16:S)),x15:S,x16:S), r': U31(and(isNat(N:S:S),isNatKind(N:S:S)),N:S:S)) 0.001/0.001 (R9 unifies with R16 at p: [1], l: isNat(plus(x15:S,x16:S)), lp: plus(x15:S,x16:S), sig: {x15:S -> N:S:S,x16:S -> s(M:S:S)}, l': plus(N:S:S,s(M:S:S)), r: U11(and(isNatKind(x15:S),isNatKind(x16:S)),x15:S,x16:S), r': U41(and(and(isNat(M:S:S),isNatKind(M:S:S)),and(isNat(N:S:S),isNatKind(N:S:S))),M:S:S,N:S:S)) 0.001/0.001 (R12 unifies with R15 at p: [1], l: isNatKind(plus(x18:S,x19:S)), lp: plus(x18:S,x19:S), sig: {x18:S -> N:S:S,x19:S -> num0}, l': plus(N:S:S,num0), r: and(isNatKind(x18:S),isNatKind(x19:S)), r': U31(and(isNat(N:S:S),isNatKind(N:S:S)),N:S:S)) 0.001/0.001 (R12 unifies with R16 at p: [1], l: isNatKind(plus(x18:S,x19:S)), lp: plus(x18:S,x19:S), sig: {x18:S -> N:S:S,x19:S -> s(M:S:S)}, l': plus(N:S:S,s(M:S:S)), r: and(isNatKind(x18:S),isNatKind(x19:S)), r': U41(and(and(isNat(M:S:S),isNatKind(M:S:S)),and(isNat(N:S:S),isNatKind(N: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 0.01user 0.00system 0:00.01elapsed 83%CPU (0avgtext+0avgdata 10600maxresident)k 0.001/0.001 8inputs+0outputs (0major+950minor)pagefaults 0swaps