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 I:S:S P:S:S V:S:S V1:S:S V2:S:S X:S:S Y:S:S Z:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 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 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (__ 1 2) 0.002/0.002 (isList 1) 0.002/0.002 (isNeList 1) 0.002/0.002 (isNePal 1) 0.002/0.002 (isPal 1) 0.002/0.002 (isQid 1) 0.002/0.002 (a) 0.002/0.002 (e) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (i) 0.002/0.002 (nil) 0.002/0.002 (o) 0.002/0.002 (tt) 0.002/0.002 (u) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt) -> tt 0.002/0.002 U21(tt,V2:S:S) -> U22(isList(V2:S:S)) 0.002/0.002 U22(tt) -> tt 0.002/0.002 U31(tt) -> tt 0.002/0.002 U41(tt,V2:S:S) -> U42(isNeList(V2:S:S)) 0.002/0.002 U42(tt) -> tt 0.002/0.002 U51(tt,V2:S:S) -> U52(isList(V2:S:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt) -> tt 0.002/0.002 U71(tt,P:S:S) -> U72(isPal(P:S:S)) 0.002/0.002 U72(tt) -> tt 0.002/0.002 U81(tt) -> tt 0.002/0.002 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.002/0.002 __(nil,X:S:S) -> X:S:S 0.002/0.002 __(X:S:S,nil) -> X:S:S 0.002/0.002 isList(__(V1:S:S,V2:S:S)) -> U21(isList(V1:S:S),V2:S:S) 0.002/0.002 isList(nil) -> tt 0.002/0.002 isList(V:S:S) -> U11(isNeList(V:S:S)) 0.002/0.002 isNeList(__(V1:S:S,V2:S:S)) -> U41(isList(V1:S:S),V2:S:S) 0.002/0.002 isNeList(__(V1:S:S,V2:S:S)) -> U51(isNeList(V1:S:S),V2:S:S) 0.002/0.002 isNeList(V:S:S) -> U31(isQid(V:S:S)) 0.002/0.002 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> U71(isQid(I:S:S),P:S:S) 0.002/0.002 isNePal(V:S:S) -> U61(isQid(V:S:S)) 0.002/0.002 isPal(nil) -> tt 0.002/0.002 isPal(V:S:S) -> U81(isNePal(V:S:S)) 0.002/0.002 isQid(a) -> tt 0.002/0.002 isQid(e) -> tt 0.002/0.002 isQid(i) -> tt 0.002/0.002 isQid(o) -> tt 0.002/0.002 isQid(u) -> tt 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 I:S:S P:S:S V:S:S V1:S:S V2:S:S X:S:S Y:S:S Z:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 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 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (__ 1 2) 0.002/0.002 (isList 1) 0.002/0.002 (isNeList 1) 0.002/0.002 (isNePal 1) 0.002/0.002 (isPal 1) 0.002/0.002 (isQid 1) 0.002/0.002 (a) 0.002/0.002 (e) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (i) 0.002/0.002 (nil) 0.002/0.002 (o) 0.002/0.002 (tt) 0.002/0.002 (u) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt) -> tt 0.002/0.002 U21(tt,V2:S:S) -> U22(isList(V2:S:S)) 0.002/0.002 U22(tt) -> tt 0.002/0.002 U31(tt) -> tt 0.002/0.002 U41(tt,V2:S:S) -> U42(isNeList(V2:S:S)) 0.002/0.002 U42(tt) -> tt 0.002/0.002 U51(tt,V2:S:S) -> U52(isList(V2:S:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt) -> tt 0.002/0.002 U71(tt,P:S:S) -> U72(isPal(P:S:S)) 0.002/0.002 U72(tt) -> tt 0.002/0.002 U81(tt) -> tt 0.002/0.002 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.002/0.002 __(nil,X:S:S) -> X:S:S 0.002/0.002 __(X:S:S,nil) -> X:S:S 0.002/0.002 isList(__(V1:S:S,V2:S:S)) -> U21(isList(V1:S:S),V2:S:S) 0.002/0.002 isList(nil) -> tt 0.002/0.002 isList(V:S:S) -> U11(isNeList(V:S:S)) 0.002/0.002 isNeList(__(V1:S:S,V2:S:S)) -> U41(isList(V1:S:S),V2:S:S) 0.002/0.002 isNeList(__(V1:S:S,V2:S:S)) -> U51(isNeList(V1:S:S),V2:S:S) 0.002/0.002 isNeList(V:S:S) -> U31(isQid(V:S:S)) 0.002/0.002 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> U71(isQid(I:S:S),P:S:S) 0.002/0.002 isNePal(V:S:S) -> U61(isQid(V:S:S)) 0.002/0.002 isPal(nil) -> tt 0.002/0.002 isPal(V:S:S) -> U81(isNePal(V:S:S)) 0.002/0.002 isQid(a) -> tt 0.002/0.002 isQid(e) -> tt 0.002/0.002 isQid(i) -> tt 0.002/0.002 isQid(o) -> tt 0.002/0.002 isQid(u) -> tt 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 I:S:S P:S:S V:S:S V1:S:S V2:S:S X:S:S Y:S:S Z:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 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 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (__ 1 2) 0.002/0.002 (isList 1) 0.002/0.002 (isNeList 1) 0.002/0.002 (isNePal 1) 0.002/0.002 (isPal 1) 0.002/0.002 (isQid 1) 0.002/0.002 (a) 0.002/0.002 (e) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (i) 0.002/0.002 (nil) 0.002/0.002 (o) 0.002/0.002 (tt) 0.002/0.002 (u) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt) -> tt 0.002/0.002 U21(tt,V2:S:S) -> U22(isList(V2:S:S)) 0.002/0.002 U22(tt) -> tt 0.002/0.002 U31(tt) -> tt 0.002/0.002 U41(tt,V2:S:S) -> U42(isNeList(V2:S:S)) 0.002/0.002 U42(tt) -> tt 0.002/0.002 U51(tt,V2:S:S) -> U52(isList(V2:S:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt) -> tt 0.002/0.002 U71(tt,P:S:S) -> U72(isPal(P:S:S)) 0.002/0.002 U72(tt) -> tt 0.002/0.002 U81(tt) -> tt 0.002/0.002 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.002/0.002 __(nil,X:S:S) -> X:S:S 0.002/0.002 __(X:S:S,nil) -> X:S:S 0.002/0.002 isList(__(V1:S:S,V2:S:S)) -> U21(isList(V1:S:S),V2:S:S) 0.002/0.002 isList(nil) -> tt 0.002/0.002 isList(V:S:S) -> U11(isNeList(V:S:S)) 0.002/0.002 isNeList(__(V1:S:S,V2:S:S)) -> U41(isList(V1:S:S),V2:S:S) 0.002/0.002 isNeList(__(V1:S:S,V2:S:S)) -> U51(isNeList(V1:S:S),V2:S:S) 0.002/0.002 isNeList(V:S:S) -> U31(isQid(V:S:S)) 0.002/0.002 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> U71(isQid(I:S:S),P:S:S) 0.002/0.002 isNePal(V:S:S) -> U61(isQid(V:S:S)) 0.002/0.002 isPal(nil) -> tt 0.002/0.002 isPal(V:S:S) -> U81(isNePal(V:S:S)) 0.002/0.002 isQid(a) -> tt 0.002/0.002 isQid(e) -> tt 0.002/0.002 isQid(i) -> tt 0.002/0.002 isQid(o) -> tt 0.002/0.002 isQid(u) -> tt 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,V2:S:S) -> U22(isList(V2:S:S)) 0.002/0.002 U22(tt) -> tt 0.002/0.002 U31(tt) -> tt 0.002/0.002 U41(tt,V2:S:S) -> U42(isNeList(V2:S:S)) 0.002/0.002 U42(tt) -> tt 0.002/0.002 U51(tt,V2:S:S) -> U52(isList(V2:S:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt) -> tt 0.002/0.002 U71(tt,P:S:S) -> U72(isPal(P:S:S)) 0.002/0.002 U72(tt) -> tt 0.002/0.002 U81(tt) -> tt 0.002/0.002 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.002/0.002 __(nil,X:S:S) -> X:S:S 0.002/0.002 __(X:S:S,nil) -> X:S:S 0.002/0.002 isList(__(V1:S:S,V2:S:S)) -> U21(isList(V1:S:S),V2:S:S) 0.002/0.002 isList(nil) -> tt 0.002/0.002 isList(V:S:S) -> U11(isNeList(V:S:S)) 0.002/0.002 isNeList(__(V1:S:S,V2:S:S)) -> U41(isList(V1:S:S),V2:S:S) 0.002/0.002 isNeList(__(V1:S:S,V2:S:S)) -> U51(isNeList(V1:S:S),V2:S:S) 0.002/0.002 isNeList(V:S:S) -> U31(isQid(V:S:S)) 0.002/0.002 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> U71(isQid(I:S:S),P:S:S) 0.002/0.002 isNePal(V:S:S) -> U61(isQid(V:S:S)) 0.002/0.002 isPal(nil) -> tt 0.002/0.002 isPal(V:S:S) -> U81(isNePal(V:S:S)) 0.002/0.002 isQid(a) -> tt 0.002/0.002 isQid(e) -> tt 0.002/0.002 isQid(i) -> tt 0.002/0.002 isQid(o) -> tt 0.002/0.002 isQid(u) -> tt 0.002/0.002 -> Vars: 0.002/0.002 V2:S, V2:S, V2:S, P:S, X:S, Y:S, Z:S, X:S, X:S, V1:S, V2:S, V:S, V1:S, V2:S, V1:S, V2:S, V:S, I:S, P:S, V:S, V: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: [V2:S], UV-LFrozen: [V2:S], 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: [], UV-LFrozen: [], UV-RFrozen: []) 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: [V2:S], UV-LFrozen: [V2:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], 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: [P:S], UV-LFrozen: [P: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: [X:S, Y:S, Z:S], UV-RActive: [X:S, Y:S, Z:S], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 14, UV-LActive: [X:S], UV-RActive: [X:S], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 15, UV-LActive: [X:S], UV-RActive: [X:S], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 16, UV-LActive: [V1:S, V2:S], UV-RActive: [V1:S], UV-LFrozen: [], UV-RFrozen: [V2:S]) 0.002/0.002 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 18, UV-LActive: [V:S], UV-RActive: [V:S], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 19, UV-LActive: [V1:S, V2:S], UV-RActive: [V1:S], UV-LFrozen: [], UV-RFrozen: [V2:S]) 0.002/0.002 (UV-RuleId: 20, UV-LActive: [V1:S, V2:S], UV-RActive: [V1:S], UV-LFrozen: [], 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: [I:S, P:S], UV-RActive: [I:S], UV-LFrozen: [], UV-RFrozen: [P:S]) 0.002/0.002 (UV-RuleId: 23, UV-LActive: [V:S], UV-RActive: [V:S], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 24, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 25, UV-LActive: [V:S], UV-RActive: [V:S], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 26, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 27, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 28, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 29, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 30, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 -> FVars: 0.002/0.002 x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30 0.002/0.002 -> PVars: 0.002/0.002 V2:S: [x10, x11, x12, x20, x23, x25], P:S: [x13, x28], X:S: [x14, x17, x18], Y:S: [x15], Z:S: [x16], V1:S: [x19, x22, x24], V:S: [x21, x26, x29, x30], I:S: [x27] 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,x10:S) -> U22(isList(x10:S)), id: 2, possubterms: U21(tt,x10:S)->[], tt->[1]) 0.002/0.002 (rule: U22(tt) -> tt, id: 3, possubterms: U22(tt)->[], tt->[1]) 0.002/0.002 (rule: U31(tt) -> tt, id: 4, possubterms: U31(tt)->[], tt->[1]) 0.002/0.002 (rule: U41(tt,x11:S) -> U42(isNeList(x11:S)), id: 5, possubterms: U41(tt,x11:S)->[], tt->[1]) 0.002/0.002 (rule: U42(tt) -> tt, id: 6, possubterms: U42(tt)->[], tt->[1]) 0.002/0.002 (rule: U51(tt,x12:S) -> U52(isList(x12:S)), id: 7, possubterms: U51(tt,x12:S)->[], tt->[1]) 0.002/0.002 (rule: U52(tt) -> tt, id: 8, possubterms: U52(tt)->[], tt->[1]) 0.002/0.002 (rule: U61(tt) -> tt, id: 9, possubterms: U61(tt)->[], tt->[1]) 0.002/0.002 (rule: U71(tt,x13:S) -> U72(isPal(x13:S)), id: 10, possubterms: U71(tt,x13:S)->[], tt->[1]) 0.002/0.002 (rule: U72(tt) -> tt, id: 11, possubterms: U72(tt)->[], tt->[1]) 0.002/0.002 (rule: U81(tt) -> tt, id: 12, possubterms: U81(tt)->[], tt->[1]) 0.002/0.002 (rule: __(__(x14:S,x15:S),x16:S) -> __(x14:S,__(x15:S,x16:S)), id: 13, possubterms: __(__(x14:S,x15:S),x16:S)->[], __(x14:S,x15:S)->[1]) 0.002/0.002 (rule: __(nil,x17:S) -> x17:S, id: 14, possubterms: __(nil,x17:S)->[], nil->[1]) 0.002/0.002 (rule: __(x18:S,nil) -> x18:S, id: 15, possubterms: __(x18:S,nil)->[], nil->[2]) 0.002/0.002 (rule: isList(__(x19:S,x20:S)) -> U21(isList(x19:S),x20:S), id: 16, possubterms: isList(__(x19:S,x20:S))->[], __(x19:S,x20:S)->[1]) 0.002/0.002 (rule: isList(nil) -> tt, id: 17, possubterms: isList(nil)->[], nil->[1]) 0.002/0.002 (rule: isList(x21:S) -> U11(isNeList(x21:S)), id: 18, possubterms: isList(x21:S)->[]) 0.002/0.002 (rule: isNeList(__(x22:S,x23:S)) -> U41(isList(x22:S),x23:S), id: 19, possubterms: isNeList(__(x22:S,x23:S))->[], __(x22:S,x23:S)->[1]) 0.002/0.002 (rule: isNeList(__(x24:S,x25:S)) -> U51(isNeList(x24:S),x25:S), id: 20, possubterms: isNeList(__(x24:S,x25:S))->[], __(x24:S,x25:S)->[1]) 0.002/0.002 (rule: isNeList(x26:S) -> U31(isQid(x26:S)), id: 21, possubterms: isNeList(x26:S)->[]) 0.002/0.002 (rule: isNePal(__(x27:S,__(x28:S,x27:S))) -> U71(isQid(x27:S),x28:S), id: 22, possubterms: isNePal(__(x27:S,__(x28:S,x27:S)))->[], __(x27:S,__(x28:S,x27:S))->[1], __(x28:S,x27:S)->[1, 2]) 0.002/0.002 (rule: isNePal(x29:S) -> U61(isQid(x29:S)), id: 23, possubterms: isNePal(x29:S)->[]) 0.002/0.002 (rule: isPal(nil) -> tt, id: 24, possubterms: isPal(nil)->[], nil->[1]) 0.002/0.002 (rule: isPal(x30:S) -> U81(isNePal(x30:S)), id: 25, possubterms: isPal(x30:S)->[]) 0.002/0.002 (rule: isQid(a) -> tt, id: 26, possubterms: isQid(a)->[], a->[1]) 0.002/0.002 (rule: isQid(e) -> tt, id: 27, possubterms: isQid(e)->[], e->[1]) 0.002/0.002 (rule: isQid(i) -> tt, id: 28, possubterms: isQid(i)->[], i->[1]) 0.002/0.002 (rule: isQid(o) -> tt, id: 29, possubterms: isQid(o)->[], o->[1]) 0.002/0.002 (rule: isQid(u) -> tt, id: 30, possubterms: isQid(u)->[], u->[1]) 0.002/0.002 0.002/0.002 -> Unifications: 0.002/0.002 (R13 unifies with R13 at p: [1], l: __(__(x14:S,x15:S),x16:S), lp: __(x14:S,x15:S), sig: {x14:S -> __(X:S:S,Y:S:S),x15:S -> Z:S:S}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: __(x14:S,__(x15:S,x16:S)), r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.002/0.002 (R13 unifies with R14 at p: [1], l: __(__(x14:S,x15:S),x16:S), lp: __(x14:S,x15:S), sig: {x14:S -> nil,x15:S -> X:S:S}, l': __(nil,X:S:S), r: __(x14:S,__(x15:S,x16:S)), r': X:S:S) 0.002/0.002 (R13 unifies with R15 at p: [1], l: __(__(x14:S,x15:S),x16:S), lp: __(x14:S,x15:S), sig: {x14:S -> X:S:S,x15:S -> nil}, l': __(X:S:S,nil), r: __(x14:S,__(x15:S,x16:S)), r': X:S:S) 0.002/0.002 (R15 unifies with R13 at p: [], l: __(x18:S,nil), lp: __(x18:S,nil), sig: {Z:S:S -> nil,x18:S -> __(X:S:S,Y:S:S)}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: x18:S, r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.002/0.002 (R15 unifies with R14 at p: [], l: __(x18:S,nil), lp: __(x18:S,nil), sig: {X:S:S -> nil,x18:S -> nil}, l': __(nil,X:S:S), r: x18:S, r': X:S:S) 0.002/0.002 (R16 unifies with R13 at p: [1], l: isList(__(x19:S,x20:S)), lp: __(x19:S,x20:S), sig: {x19:S -> __(X:S:S,Y:S:S),x20:S -> Z:S:S}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: U21(isList(x19:S),x20:S), r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.002/0.002 (R16 unifies with R14 at p: [1], l: isList(__(x19:S,x20:S)), lp: __(x19:S,x20:S), sig: {x19:S -> nil,x20:S -> X:S:S}, l': __(nil,X:S:S), r: U21(isList(x19:S),x20:S), r': X:S:S) 0.002/0.002 (R16 unifies with R15 at p: [1], l: isList(__(x19:S,x20:S)), lp: __(x19:S,x20:S), sig: {x19:S -> X:S:S,x20:S -> nil}, l': __(X:S:S,nil), r: U21(isList(x19:S),x20:S), r': X:S:S) 0.002/0.002 (R18 unifies with R16 at p: [], l: isList(x21:S), lp: isList(x21:S), sig: {x21:S -> __(V1:S:S,V2:S:S)}, l': isList(__(V1:S:S,V2:S:S)), r: U11(isNeList(x21:S)), r': U21(isList(V1:S:S),V2:S:S)) 0.002/0.002 (R18 unifies with R17 at p: [], l: isList(x21:S), lp: isList(x21:S), sig: {x21:S -> nil}, l': isList(nil), r: U11(isNeList(x21:S)), r': tt) 0.002/0.002 (R19 unifies with R13 at p: [1], l: isNeList(__(x22:S,x23:S)), lp: __(x22:S,x23:S), sig: {x22:S -> __(X:S:S,Y:S:S),x23:S -> Z:S:S}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: U41(isList(x22:S),x23:S), r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.002/0.002 (R19 unifies with R14 at p: [1], l: isNeList(__(x22:S,x23:S)), lp: __(x22:S,x23:S), sig: {x22:S -> nil,x23:S -> X:S:S}, l': __(nil,X:S:S), r: U41(isList(x22:S),x23:S), r': X:S:S) 0.002/0.002 (R19 unifies with R15 at p: [1], l: isNeList(__(x22:S,x23:S)), lp: __(x22:S,x23:S), sig: {x22:S -> X:S:S,x23:S -> nil}, l': __(X:S:S,nil), r: U41(isList(x22:S),x23:S), r': X:S:S) 0.002/0.002 (R20 unifies with R19 at p: [], l: isNeList(__(x24:S,x25:S)), lp: isNeList(__(x24:S,x25:S)), sig: {x24:S -> V1:S:S,x25:S -> V2:S:S}, l': isNeList(__(V1:S:S,V2:S:S)), r: U51(isNeList(x24:S),x25:S), r': U41(isList(V1:S:S),V2:S:S)) 0.002/0.002 (R20 unifies with R13 at p: [1], l: isNeList(__(x24:S,x25:S)), lp: __(x24:S,x25:S), sig: {x24:S -> __(X:S:S,Y:S:S),x25:S -> Z:S:S}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: U51(isNeList(x24:S),x25:S), r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.002/0.002 (R20 unifies with R14 at p: [1], l: isNeList(__(x24:S,x25:S)), lp: __(x24:S,x25:S), sig: {x24:S -> nil,x25:S -> X:S:S}, l': __(nil,X:S:S), r: U51(isNeList(x24:S),x25:S), r': X:S:S) 0.002/0.002 (R20 unifies with R15 at p: [1], l: isNeList(__(x24:S,x25:S)), lp: __(x24:S,x25:S), sig: {x24:S -> X:S:S,x25:S -> nil}, l': __(X:S:S,nil), r: U51(isNeList(x24:S),x25:S), r': X:S:S) 0.002/0.002 (R21 unifies with R19 at p: [], l: isNeList(x26:S), lp: isNeList(x26:S), sig: {x26:S -> __(V1:S:S,V2:S:S)}, l': isNeList(__(V1:S:S,V2:S:S)), r: U31(isQid(x26:S)), r': U41(isList(V1:S:S),V2:S:S)) 0.002/0.002 (R21 unifies with R20 at p: [], l: isNeList(x26:S), lp: isNeList(x26:S), sig: {x26:S -> __(V1:S:S,V2:S:S)}, l': isNeList(__(V1:S:S,V2:S:S)), r: U31(isQid(x26:S)), r': U51(isNeList(V1:S:S),V2:S:S)) 0.002/0.002 (R22 unifies with R13 at p: [1], l: isNePal(__(x27:S,__(x28:S,x27:S))), lp: __(x27:S,__(x28:S,x27:S)), sig: {Z:S:S -> __(x28:S,__(X:S:S,Y:S:S)),x27:S -> __(X:S:S,Y:S:S)}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: U71(isQid(x27:S),x28:S), r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.002/0.002 (R22 unifies with R14 at p: [1], l: isNePal(__(x27:S,__(x28:S,x27:S))), lp: __(x27:S,__(x28:S,x27:S)), sig: {X:S:S -> __(x28:S,nil),x27:S -> nil}, l': __(nil,X:S:S), r: U71(isQid(x27:S),x28:S), r': X:S:S) 0.002/0.002 (R22 unifies with R13 at p: [1,2], l: isNePal(__(x27:S,__(x28:S,x27:S))), lp: __(x28:S,x27:S), sig: {x27:S -> Z:S:S,x28:S -> __(X:S:S,Y:S:S)}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: U71(isQid(x27:S),x28:S), r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.002/0.002 (R22 unifies with R14 at p: [1,2], l: isNePal(__(x27:S,__(x28:S,x27:S))), lp: __(x28:S,x27:S), sig: {x27:S -> X:S:S,x28:S -> nil}, l': __(nil,X:S:S), r: U71(isQid(x27:S),x28:S), r': X:S:S) 0.002/0.002 (R22 unifies with R15 at p: [1,2], l: isNePal(__(x27:S,__(x28:S,x27:S))), lp: __(x28:S,x27:S), sig: {x27:S -> nil,x28:S -> X:S:S}, l': __(X:S:S,nil), r: U71(isQid(x27:S),x28:S), r': X:S:S) 0.002/0.002 (R23 unifies with R22 at p: [], l: isNePal(x29:S), lp: isNePal(x29:S), sig: {x29:S -> __(I:S:S,__(P:S:S,I:S:S))}, l': isNePal(__(I:S:S,__(P:S:S,I:S:S))), r: U61(isQid(x29:S)), r': U71(isQid(I:S:S),P:S:S)) 0.002/0.002 (R25 unifies with R24 at p: [], l: isPal(x30:S), lp: isPal(x30:S), sig: {x30:S -> nil}, l': isPal(nil), r: U81(isNePal(x30:S)), r': tt) 0.002/0.002 0.002/0.002 -> Critical pairs info: 0.002/0.002 => Not trivial, Overlay, NW0, N1 0.002/0.002 => Not trivial, Overlay, NW0, N2 0.002/0.002 => Not trivial, Overlay, NW0, N3 0.002/0.002 => Not trivial, Not overlay, NW0, N4 0.002/0.002 => Not trivial, Not overlay, NW0, N5 0.002/0.002 => Not trivial, Overlay, NW0, N6 0.002/0.002 => Not trivial, Overlay, NW0, N7 0.002/0.002 => Not trivial, Not overlay, NW0, N8 0.002/0.002 => Not trivial, Not overlay, NW0, N9 0.002/0.002 => Not trivial, Not overlay, NW0, N10 0.002/0.002 => Not trivial, Not overlay, NW0, N11 0.002/0.002 <__(__(X:S:S,__(Y:S:S,Z:S:S)),Z:S:S),__(__(X:S:S,Y:S:S),__(Z:S:S,Z:S:S))> => Not trivial, Not overlay, NW0, N12 0.002/0.002 => Not trivial, Not overlay, NW0, N13 0.002/0.002 <__(X:S:S,Z:S:S),__(nil,__(X:S:S,Z:S:S))> => Not trivial, Not overlay, NW0, N14 0.002/0.002 <__(X:S:S,__(Y:S:S,nil)),__(X:S:S,Y:S:S)> => Not trivial, Overlay, NW0, N15 0.002/0.002 => Not trivial, Not overlay, NW0, N16 0.002/0.002 => Not trivial, Not overlay, NW0, N17 0.002/0.002 => Not trivial, Not overlay, NW0, N18 0.002/0.002 <__(X:S:S,Z:S:S),__(X:S:S,__(nil,Z:S:S))> => Not trivial, Not overlay, NW0, N19 0.002/0.002 => Not trivial, Overlay, NW0, N20 0.002/0.002 => Trivial, Overlay, NW0, N21 0.002/0.002 => Not trivial, Overlay, NW0, N22 0.002/0.002 => Not trivial, Not overlay, NW0, N23 0.002/0.002 => Not trivial, Not overlay, NW0, N24 0.002/0.002 => Not trivial, Not overlay, NW0, N25 0.002/0.002 => Not trivial, Not overlay, NW0, N26 0.002/0.002 0.002/0.002 -> Problem conclusions: 0.002/0.002 Not left linear, 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, 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 0.02user 0.00system 0:00.02elapsed 104%CPU (0avgtext+0avgdata 14880maxresident)k 0.002/0.002 8inputs+0outputs (0major+2424minor)pagefaults 0swaps