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 M:S:S N:S:S V1:S:S V2:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 1) 0.002/0.002 (U13 1) 0.002/0.002 (U14 1) 0.002/0.002 (U15 1) 0.002/0.002 (U16 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U23 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U41 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 (U63 1) 0.002/0.002 (U64 1) 0.002/0.002 (isNat 1) 0.002/0.002 (isNatKind 1) 0.002/0.002 (plus 2) 0.002/0.002 (fSNonEmpty) 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,V1:S:S,V2:S:S) -> U12(isNatKind(V1:S:S),V1:S:S,V2:S:S) 0.002/0.002 U12(tt,V1:S:S,V2:S:S) -> U13(isNatKind(V2:S:S),V1:S:S,V2:S:S) 0.002/0.002 U13(tt,V1:S:S,V2:S:S) -> U14(isNatKind(V2:S:S),V1:S:S,V2:S:S) 0.002/0.002 U14(tt,V1:S:S,V2:S:S) -> U15(isNat(V1:S:S),V2:S:S) 0.002/0.002 U15(tt,V2:S:S) -> U16(isNat(V2:S:S)) 0.002/0.002 U16(tt) -> tt 0.002/0.002 U21(tt,V1:S:S) -> U22(isNatKind(V1:S:S),V1:S:S) 0.002/0.002 U22(tt,V1:S:S) -> U23(isNat(V1:S:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V2:S:S) -> U32(isNatKind(V2:S:S)) 0.002/0.002 U32(tt) -> tt 0.002/0.002 U41(tt) -> tt 0.002/0.002 U51(tt,N:S:S) -> U52(isNatKind(N:S:S),N:S:S) 0.002/0.002 U52(tt,N:S:S) -> N:S:S 0.002/0.002 U61(tt,M:S:S,N:S:S) -> U62(isNatKind(M:S:S),M:S:S,N:S:S) 0.002/0.002 U62(tt,M:S:S,N:S:S) -> U63(isNat(N:S:S),M:S:S,N:S:S) 0.002/0.002 U63(tt,M:S:S,N:S:S) -> U64(isNatKind(N:S:S),M:S:S,N:S:S) 0.002/0.002 U64(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.002/0.002 isNat(plus(V1:S:S,V2:S:S)) -> U11(isNatKind(V1:S:S),V1:S:S,V2:S:S) 0.002/0.002 isNat(num0) -> tt 0.002/0.002 isNat(s(V1:S:S)) -> U21(isNatKind(V1:S:S),V1:S:S) 0.002/0.002 isNatKind(plus(V1:S:S,V2:S:S)) -> U31(isNatKind(V1:S:S),V2:S:S) 0.002/0.002 isNatKind(num0) -> tt 0.002/0.002 isNatKind(s(V1:S:S)) -> U41(isNatKind(V1:S:S)) 0.002/0.002 plus(N:S:S,num0) -> U51(isNat(N:S:S),N:S:S) 0.002/0.002 plus(N:S:S,s(M:S:S)) -> U61(isNat(M:S:S),M:S:S,N:S:S) 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 M:S:S N:S:S V1:S:S V2:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 1) 0.002/0.002 (U13 1) 0.002/0.002 (U14 1) 0.002/0.002 (U15 1) 0.002/0.002 (U16 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U23 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U41 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 (U63 1) 0.002/0.002 (U64 1) 0.002/0.002 (isNat 1) 0.002/0.002 (isNatKind 1) 0.002/0.002 (plus 2) 0.002/0.002 (fSNonEmpty) 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,V1:S:S,V2:S:S) -> U12(isNatKind(V1:S:S),V1:S:S,V2:S:S) 0.002/0.002 U12(tt,V1:S:S,V2:S:S) -> U13(isNatKind(V2:S:S),V1:S:S,V2:S:S) 0.002/0.002 U13(tt,V1:S:S,V2:S:S) -> U14(isNatKind(V2:S:S),V1:S:S,V2:S:S) 0.002/0.002 U14(tt,V1:S:S,V2:S:S) -> U15(isNat(V1:S:S),V2:S:S) 0.002/0.002 U15(tt,V2:S:S) -> U16(isNat(V2:S:S)) 0.002/0.002 U16(tt) -> tt 0.002/0.002 U21(tt,V1:S:S) -> U22(isNatKind(V1:S:S),V1:S:S) 0.002/0.002 U22(tt,V1:S:S) -> U23(isNat(V1:S:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V2:S:S) -> U32(isNatKind(V2:S:S)) 0.002/0.002 U32(tt) -> tt 0.002/0.002 U41(tt) -> tt 0.002/0.002 U51(tt,N:S:S) -> U52(isNatKind(N:S:S),N:S:S) 0.002/0.002 U52(tt,N:S:S) -> N:S:S 0.002/0.002 U61(tt,M:S:S,N:S:S) -> U62(isNatKind(M:S:S),M:S:S,N:S:S) 0.002/0.002 U62(tt,M:S:S,N:S:S) -> U63(isNat(N:S:S),M:S:S,N:S:S) 0.002/0.002 U63(tt,M:S:S,N:S:S) -> U64(isNatKind(N:S:S),M:S:S,N:S:S) 0.002/0.002 U64(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.002/0.002 isNat(plus(V1:S:S,V2:S:S)) -> U11(isNatKind(V1:S:S),V1:S:S,V2:S:S) 0.002/0.002 isNat(num0) -> tt 0.002/0.002 isNat(s(V1:S:S)) -> U21(isNatKind(V1:S:S),V1:S:S) 0.002/0.002 isNatKind(plus(V1:S:S,V2:S:S)) -> U31(isNatKind(V1:S:S),V2:S:S) 0.002/0.002 isNatKind(num0) -> tt 0.002/0.002 isNatKind(s(V1:S:S)) -> U41(isNatKind(V1:S:S)) 0.002/0.002 plus(N:S:S,num0) -> U51(isNat(N:S:S),N:S:S) 0.002/0.002 plus(N:S:S,s(M:S:S)) -> U61(isNat(M:S:S),M:S:S,N:S:S) 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 M:S:S N:S:S V1:S:S V2:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 1) 0.002/0.002 (U13 1) 0.002/0.002 (U14 1) 0.002/0.002 (U15 1) 0.002/0.002 (U16 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U23 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U41 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 (U63 1) 0.002/0.002 (U64 1) 0.002/0.002 (isNat 1) 0.002/0.002 (isNatKind 1) 0.002/0.002 (plus 2) 0.002/0.002 (fSNonEmpty) 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,V1:S:S,V2:S:S) -> U12(isNatKind(V1:S:S),V1:S:S,V2:S:S) 0.002/0.002 U12(tt,V1:S:S,V2:S:S) -> U13(isNatKind(V2:S:S),V1:S:S,V2:S:S) 0.002/0.002 U13(tt,V1:S:S,V2:S:S) -> U14(isNatKind(V2:S:S),V1:S:S,V2:S:S) 0.002/0.002 U14(tt,V1:S:S,V2:S:S) -> U15(isNat(V1:S:S),V2:S:S) 0.002/0.002 U15(tt,V2:S:S) -> U16(isNat(V2:S:S)) 0.002/0.002 U16(tt) -> tt 0.002/0.002 U21(tt,V1:S:S) -> U22(isNatKind(V1:S:S),V1:S:S) 0.002/0.002 U22(tt,V1:S:S) -> U23(isNat(V1:S:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V2:S:S) -> U32(isNatKind(V2:S:S)) 0.002/0.002 U32(tt) -> tt 0.002/0.002 U41(tt) -> tt 0.002/0.002 U51(tt,N:S:S) -> U52(isNatKind(N:S:S),N:S:S) 0.002/0.002 U52(tt,N:S:S) -> N:S:S 0.002/0.002 U61(tt,M:S:S,N:S:S) -> U62(isNatKind(M:S:S),M:S:S,N:S:S) 0.002/0.002 U62(tt,M:S:S,N:S:S) -> U63(isNat(N:S:S),M:S:S,N:S:S) 0.002/0.002 U63(tt,M:S:S,N:S:S) -> U64(isNatKind(N:S:S),M:S:S,N:S:S) 0.002/0.002 U64(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.002/0.002 isNat(plus(V1:S:S,V2:S:S)) -> U11(isNatKind(V1:S:S),V1:S:S,V2:S:S) 0.002/0.002 isNat(num0) -> tt 0.002/0.002 isNat(s(V1:S:S)) -> U21(isNatKind(V1:S:S),V1:S:S) 0.002/0.002 isNatKind(plus(V1:S:S,V2:S:S)) -> U31(isNatKind(V1:S:S),V2:S:S) 0.002/0.002 isNatKind(num0) -> tt 0.002/0.002 isNatKind(s(V1:S:S)) -> U41(isNatKind(V1:S:S)) 0.002/0.002 plus(N:S:S,num0) -> U51(isNat(N:S:S),N:S:S) 0.002/0.002 plus(N:S:S,s(M:S:S)) -> U61(isNat(M:S:S),M:S:S,N:S:S) 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,V1:S:S,V2:S:S) -> U12(isNatKind(V1:S:S),V1:S:S,V2:S:S) 0.002/0.002 U12(tt,V1:S:S,V2:S:S) -> U13(isNatKind(V2:S:S),V1:S:S,V2:S:S) 0.002/0.002 U13(tt,V1:S:S,V2:S:S) -> U14(isNatKind(V2:S:S),V1:S:S,V2:S:S) 0.002/0.002 U14(tt,V1:S:S,V2:S:S) -> U15(isNat(V1:S:S),V2:S:S) 0.002/0.002 U15(tt,V2:S:S) -> U16(isNat(V2:S:S)) 0.002/0.002 U16(tt) -> tt 0.002/0.002 U21(tt,V1:S:S) -> U22(isNatKind(V1:S:S),V1:S:S) 0.002/0.002 U22(tt,V1:S:S) -> U23(isNat(V1:S:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V2:S:S) -> U32(isNatKind(V2:S:S)) 0.002/0.002 U32(tt) -> tt 0.002/0.002 U41(tt) -> tt 0.002/0.002 U51(tt,N:S:S) -> U52(isNatKind(N:S:S),N:S:S) 0.002/0.002 U52(tt,N:S:S) -> N:S:S 0.002/0.002 U61(tt,M:S:S,N:S:S) -> U62(isNatKind(M:S:S),M:S:S,N:S:S) 0.002/0.002 U62(tt,M:S:S,N:S:S) -> U63(isNat(N:S:S),M:S:S,N:S:S) 0.002/0.002 U63(tt,M:S:S,N:S:S) -> U64(isNatKind(N:S:S),M:S:S,N:S:S) 0.002/0.002 U64(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.002/0.002 isNat(plus(V1:S:S,V2:S:S)) -> U11(isNatKind(V1:S:S),V1:S:S,V2:S:S) 0.002/0.002 isNat(num0) -> tt 0.002/0.002 isNat(s(V1:S:S)) -> U21(isNatKind(V1:S:S),V1:S:S) 0.002/0.002 isNatKind(plus(V1:S:S,V2:S:S)) -> U31(isNatKind(V1:S:S),V2:S:S) 0.002/0.002 isNatKind(num0) -> tt 0.002/0.002 isNatKind(s(V1:S:S)) -> U41(isNatKind(V1:S:S)) 0.002/0.002 plus(N:S:S,num0) -> U51(isNat(N:S:S),N:S:S) 0.002/0.002 plus(N:S:S,s(M:S:S)) -> U61(isNat(M:S:S),M:S:S,N:S:S) 0.002/0.002 -> Vars: 0.002/0.002 V1:S, V2:S, V1:S, V2:S, V1:S, V2:S, V1:S, V2:S, V2:S, V1:S, V1:S, V2:S, N: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, V1:S, V2:S, V1:S, N:S, M:S, N:S 0.002/0.002 -> UVars: 0.002/0.002 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S, V2:S], UV-RFrozen: [V1:S, V2:S]) 0.002/0.002 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [V2:S], UV-LFrozen: [V1:S, V2:S], UV-RFrozen: [V1:S, V2:S]) 0.002/0.002 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [V2:S], UV-LFrozen: [V1:S, V2:S], UV-RFrozen: [V1:S, V2:S]) 0.002/0.002 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S, V2:S], UV-RFrozen: [V2:S]) 0.002/0.002 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [V2:S], UV-LFrozen: [V2:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V1:S]) 0.002/0.002 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1: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: [V2:S], UV-LFrozen: [V2:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 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: [N:S], UV-LFrozen: [N:S], UV-RFrozen: [N:S]) 0.002/0.002 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [M:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.002/0.002 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.002/0.002 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.002/0.002 (UV-RuleId: 18, UV-LActive: [], UV-RActive: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.002/0.002 (UV-RuleId: 19, UV-LActive: [V2:S], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V1:S, V2:S]) 0.002/0.002 (UV-RuleId: 20, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 21, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V1:S]) 0.002/0.002 (UV-RuleId: 22, UV-LActive: [V2:S], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V2:S]) 0.002/0.002 (UV-RuleId: 23, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 24, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 25, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: [N:S]) 0.002/0.002 (UV-RuleId: 26, UV-LActive: [], UV-RActive: [M:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.002/0.002 -> FVars: 0.002/0.002 x6, x7, x8, 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 0.002/0.002 -> PVars: 0.002/0.002 V1:S: [x6, x8, x10, x12, x15, x16, x28, x30, x31, x33], V2:S: [x7, x9, x11, x13, x14, x17, x29, x32], N:S: [x18, x19, x21, x23, x25, x27, x34, x36], M:S: [x20, x22, x24, x26, x35] 0.002/0.002 0.002/0.002 -> Rlps: 0.002/0.002 (rule: U11(tt,x6:S,x7:S) -> U12(isNatKind(x6:S),x6:S,x7:S), id: 1, possubterms: U11(tt,x6:S,x7:S)->[], tt->[1]) 0.002/0.002 (rule: U12(tt,x8:S,x9:S) -> U13(isNatKind(x9:S),x8:S,x9:S), id: 2, possubterms: U12(tt,x8:S,x9:S)->[], tt->[1]) 0.002/0.002 (rule: U13(tt,x10:S,x11:S) -> U14(isNatKind(x11:S),x10:S,x11:S), id: 3, possubterms: U13(tt,x10:S,x11:S)->[], tt->[1]) 0.002/0.002 (rule: U14(tt,x12:S,x13:S) -> U15(isNat(x12:S),x13:S), id: 4, possubterms: U14(tt,x12:S,x13:S)->[], tt->[1]) 0.002/0.002 (rule: U15(tt,x14:S) -> U16(isNat(x14:S)), id: 5, possubterms: U15(tt,x14:S)->[], tt->[1]) 0.002/0.002 (rule: U16(tt) -> tt, id: 6, possubterms: U16(tt)->[], tt->[1]) 0.002/0.002 (rule: U21(tt,x15:S) -> U22(isNatKind(x15:S),x15:S), id: 7, possubterms: U21(tt,x15:S)->[], tt->[1]) 0.002/0.002 (rule: U22(tt,x16:S) -> U23(isNat(x16:S)), id: 8, possubterms: U22(tt,x16:S)->[], tt->[1]) 0.002/0.002 (rule: U23(tt) -> tt, id: 9, possubterms: U23(tt)->[], tt->[1]) 0.002/0.002 (rule: U31(tt,x17:S) -> U32(isNatKind(x17:S)), id: 10, possubterms: U31(tt,x17:S)->[], tt->[1]) 0.002/0.002 (rule: U32(tt) -> tt, id: 11, possubterms: U32(tt)->[], tt->[1]) 0.002/0.002 (rule: U41(tt) -> tt, id: 12, possubterms: U41(tt)->[], tt->[1]) 0.002/0.002 (rule: U51(tt,x18:S) -> U52(isNatKind(x18:S),x18:S), id: 13, possubterms: U51(tt,x18:S)->[], tt->[1]) 0.002/0.002 (rule: U52(tt,x19:S) -> x19:S, id: 14, possubterms: U52(tt,x19:S)->[], tt->[1]) 0.002/0.002 (rule: U61(tt,x20:S,x21:S) -> U62(isNatKind(x20:S),x20:S,x21:S), id: 15, possubterms: U61(tt,x20:S,x21:S)->[], tt->[1]) 0.002/0.002 (rule: U62(tt,x22:S,x23:S) -> U63(isNat(x23:S),x22:S,x23:S), id: 16, possubterms: U62(tt,x22:S,x23:S)->[], tt->[1]) 0.002/0.002 (rule: U63(tt,x24:S,x25:S) -> U64(isNatKind(x25:S),x24:S,x25:S), id: 17, possubterms: U63(tt,x24:S,x25:S)->[], tt->[1]) 0.002/0.002 (rule: U64(tt,x26:S,x27:S) -> s(plus(x27:S,x26:S)), id: 18, possubterms: U64(tt,x26:S,x27:S)->[], tt->[1]) 0.002/0.002 (rule: isNat(plus(x28:S,x29:S)) -> U11(isNatKind(x28:S),x28:S,x29:S), id: 19, possubterms: isNat(plus(x28:S,x29:S))->[], plus(x28:S,x29:S)->[1]) 0.002/0.002 (rule: isNat(num0) -> tt, id: 20, possubterms: isNat(num0)->[], num0->[1]) 0.002/0.002 (rule: isNat(s(x30:S)) -> U21(isNatKind(x30:S),x30:S), id: 21, possubterms: isNat(s(x30:S))->[], s(x30:S)->[1]) 0.002/0.002 (rule: isNatKind(plus(x31:S,x32:S)) -> U31(isNatKind(x31:S),x32:S), id: 22, possubterms: isNatKind(plus(x31:S,x32:S))->[], plus(x31:S,x32:S)->[1]) 0.002/0.002 (rule: isNatKind(num0) -> tt, id: 23, possubterms: isNatKind(num0)->[], num0->[1]) 0.002/0.002 (rule: isNatKind(s(x33:S)) -> U41(isNatKind(x33:S)), id: 24, possubterms: isNatKind(s(x33:S))->[], s(x33:S)->[1]) 0.002/0.002 (rule: plus(x34:S,num0) -> U51(isNat(x34:S),x34:S), id: 25, possubterms: plus(x34:S,num0)->[], num0->[2]) 0.002/0.002 (rule: plus(x36:S,s(x35:S)) -> U61(isNat(x35:S),x35:S,x36:S), id: 26, possubterms: plus(x36:S,s(x35:S))->[], s(x35:S)->[2]) 0.002/0.002 0.002/0.002 -> Unifications: 0.002/0.002 (R19 unifies with R25 at p: [1], l: isNat(plus(x28:S,x29:S)), lp: plus(x28:S,x29:S), sig: {x28:S -> N:S:S,x29:S -> num0}, l': plus(N:S:S,num0), r: U11(isNatKind(x28:S),x28:S,x29:S), r': U51(isNat(N:S:S),N:S:S)) 0.002/0.002 (R19 unifies with R26 at p: [1], l: isNat(plus(x28:S,x29:S)), lp: plus(x28:S,x29:S), sig: {x28:S -> N:S:S,x29:S -> s(M:S:S)}, l': plus(N:S:S,s(M:S:S)), r: U11(isNatKind(x28:S),x28:S,x29:S), r': U61(isNat(M:S:S),M:S:S,N:S:S)) 0.002/0.002 (R22 unifies with R25 at p: [1], l: isNatKind(plus(x31:S,x32:S)), lp: plus(x31:S,x32:S), sig: {x31:S -> N:S:S,x32:S -> num0}, l': plus(N:S:S,num0), r: U31(isNatKind(x31:S),x32:S), r': U51(isNat(N:S:S),N:S:S)) 0.002/0.002 (R22 unifies with R26 at p: [1], l: isNatKind(plus(x31:S,x32:S)), lp: plus(x31:S,x32:S), sig: {x31:S -> N:S:S,x32:S -> s(M:S:S)}, l': plus(N:S:S,s(M:S:S)), r: U31(isNatKind(x31:S),x32:S), r': U61(isNat(M: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, Not overlay, NW0, N4 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 Different Normal CP Terms Processor: 0.002/0.002 => Not trivial, Not overlay, NW0, N1, Normal and not trivial cp 0.002/0.002 0.002/0.002 The problem is not joinable. 0.002/0.002 0.01user 0.00system 0:00.02elapsed 54%CPU (0avgtext+0avgdata 11504maxresident)k 0.002/0.002 8inputs+0outputs (0major+1124minor)pagefaults 0swaps