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 I:S P:S V:S V1:S V2:S X:S Y:S Z:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 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 (U42 1) 0.002/0.002 (U43 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U53 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 (__ 1 2) 0.002/0.002 (and 1) 0.002/0.002 (isList) 0.002/0.002 (isNeList) 0.002/0.002 (isNePal) 0.002/0.002 (isPal) 0.002/0.002 (isPalListKind) 0.002/0.002 (isQid) 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,V:S) -> U12(isNeList(V:S)) 0.002/0.002 U12(tt) -> tt 0.002/0.002 U21(tt,V1:S,V2:S) -> U22(isList(V1:S),V2:S) 0.002/0.002 U22(tt,V2:S) -> U23(isList(V2:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V:S) -> U32(isQid(V:S)) 0.002/0.002 U32(tt) -> tt 0.002/0.002 U41(tt,V1:S,V2:S) -> U42(isList(V1:S),V2:S) 0.002/0.002 U42(tt,V2:S) -> U43(isNeList(V2:S)) 0.002/0.002 U43(tt) -> tt 0.002/0.002 U51(tt,V1:S,V2:S) -> U52(isNeList(V1:S),V2:S) 0.002/0.002 U52(tt,V2:S) -> U53(isList(V2:S)) 0.002/0.002 U53(tt) -> tt 0.002/0.002 U61(tt,V:S) -> U62(isQid(V:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt,V:S) -> U72(isNePal(V:S)) 0.002/0.002 U72(tt) -> tt 0.002/0.002 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.002/0.002 __(nil,X:S) -> X:S 0.002/0.002 __(X:S,nil) -> X:S 0.002/0.002 and(tt,X:S) -> X:S 0.002/0.002 isList(__(V1:S,V2:S)) -> U21(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isList(nil) -> tt 0.002/0.002 isList(V:S) -> U11(isPalListKind(V:S),V:S) 0.002/0.002 isNeList(__(V1:S,V2:S)) -> U41(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isNeList(__(V1:S,V2:S)) -> U51(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isNeList(V:S) -> U31(isPalListKind(V:S),V:S) 0.002/0.002 isNePal(__(I:S,__(P:S,I:S))) -> and(and(isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 0.002/0.002 isNePal(V:S) -> U61(isPalListKind(V:S),V:S) 0.002/0.002 isPal(nil) -> tt 0.002/0.002 isPal(V:S) -> U71(isPalListKind(V:S),V:S) 0.002/0.002 isPalListKind(__(V1:S,V2:S)) -> and(isPalListKind(V1:S),isPalListKind(V2:S)) 0.002/0.002 isPalListKind(a) -> tt 0.002/0.002 isPalListKind(e) -> tt 0.002/0.002 isPalListKind(i) -> tt 0.002/0.002 isPalListKind(nil) -> tt 0.002/0.002 isPalListKind(o) -> tt 0.002/0.002 isPalListKind(u) -> tt 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 I:S P:S V:S V1:S V2:S X:S Y:S Z:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 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 (U42 1) 0.002/0.002 (U43 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U53 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 (__ 1 2) 0.002/0.002 (and 1) 0.002/0.002 (isList) 0.002/0.002 (isNeList) 0.002/0.002 (isNePal) 0.002/0.002 (isPal) 0.002/0.002 (isPalListKind) 0.002/0.002 (isQid) 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,V:S) -> U12(isNeList(V:S)) 0.002/0.002 U12(tt) -> tt 0.002/0.002 U21(tt,V1:S,V2:S) -> U22(isList(V1:S),V2:S) 0.002/0.002 U22(tt,V2:S) -> U23(isList(V2:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V:S) -> U32(isQid(V:S)) 0.002/0.002 U32(tt) -> tt 0.002/0.002 U41(tt,V1:S,V2:S) -> U42(isList(V1:S),V2:S) 0.002/0.002 U42(tt,V2:S) -> U43(isNeList(V2:S)) 0.002/0.002 U43(tt) -> tt 0.002/0.002 U51(tt,V1:S,V2:S) -> U52(isNeList(V1:S),V2:S) 0.002/0.002 U52(tt,V2:S) -> U53(isList(V2:S)) 0.002/0.002 U53(tt) -> tt 0.002/0.002 U61(tt,V:S) -> U62(isQid(V:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt,V:S) -> U72(isNePal(V:S)) 0.002/0.002 U72(tt) -> tt 0.002/0.002 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.002/0.002 __(nil,X:S) -> X:S 0.002/0.002 __(X:S,nil) -> X:S 0.002/0.002 and(tt,X:S) -> X:S 0.002/0.002 isList(__(V1:S,V2:S)) -> U21(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isList(nil) -> tt 0.002/0.002 isList(V:S) -> U11(isPalListKind(V:S),V:S) 0.002/0.002 isNeList(__(V1:S,V2:S)) -> U41(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isNeList(__(V1:S,V2:S)) -> U51(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isNeList(V:S) -> U31(isPalListKind(V:S),V:S) 0.002/0.002 isNePal(__(I:S,__(P:S,I:S))) -> and(and(isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 0.002/0.002 isNePal(V:S) -> U61(isPalListKind(V:S),V:S) 0.002/0.002 isPal(nil) -> tt 0.002/0.002 isPal(V:S) -> U71(isPalListKind(V:S),V:S) 0.002/0.002 isPalListKind(__(V1:S,V2:S)) -> and(isPalListKind(V1:S),isPalListKind(V2:S)) 0.002/0.002 isPalListKind(a) -> tt 0.002/0.002 isPalListKind(e) -> tt 0.002/0.002 isPalListKind(i) -> tt 0.002/0.002 isPalListKind(nil) -> tt 0.002/0.002 isPalListKind(o) -> tt 0.002/0.002 isPalListKind(u) -> tt 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 Left-Homogeneous u-Replacing Variables Processor: 0.002/0.002 R satisfies LHRV condition 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 I:S P:S V:S V1:S V2:S X:S Y:S Z:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 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 (U42 1) 0.002/0.002 (U43 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U53 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 (__ 1 2) 0.002/0.002 (and 1) 0.002/0.002 (isList) 0.002/0.002 (isNeList) 0.002/0.002 (isNePal) 0.002/0.002 (isPal) 0.002/0.002 (isPalListKind) 0.002/0.002 (isQid) 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,V:S) -> U12(isNeList(V:S)) 0.002/0.002 U12(tt) -> tt 0.002/0.002 U21(tt,V1:S,V2:S) -> U22(isList(V1:S),V2:S) 0.002/0.002 U22(tt,V2:S) -> U23(isList(V2:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V:S) -> U32(isQid(V:S)) 0.002/0.002 U32(tt) -> tt 0.002/0.002 U41(tt,V1:S,V2:S) -> U42(isList(V1:S),V2:S) 0.002/0.002 U42(tt,V2:S) -> U43(isNeList(V2:S)) 0.002/0.002 U43(tt) -> tt 0.002/0.002 U51(tt,V1:S,V2:S) -> U52(isNeList(V1:S),V2:S) 0.002/0.002 U52(tt,V2:S) -> U53(isList(V2:S)) 0.002/0.002 U53(tt) -> tt 0.002/0.002 U61(tt,V:S) -> U62(isQid(V:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt,V:S) -> U72(isNePal(V:S)) 0.002/0.002 U72(tt) -> tt 0.002/0.002 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.002/0.002 __(nil,X:S) -> X:S 0.002/0.002 __(X:S,nil) -> X:S 0.002/0.002 and(tt,X:S) -> X:S 0.002/0.002 isList(__(V1:S,V2:S)) -> U21(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isList(nil) -> tt 0.002/0.002 isList(V:S) -> U11(isPalListKind(V:S),V:S) 0.002/0.002 isNeList(__(V1:S,V2:S)) -> U41(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isNeList(__(V1:S,V2:S)) -> U51(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isNeList(V:S) -> U31(isPalListKind(V:S),V:S) 0.002/0.002 isNePal(__(I:S,__(P:S,I:S))) -> and(and(isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 0.002/0.002 isNePal(V:S) -> U61(isPalListKind(V:S),V:S) 0.002/0.002 isPal(nil) -> tt 0.002/0.002 isPal(V:S) -> U71(isPalListKind(V:S),V:S) 0.002/0.002 isPalListKind(__(V1:S,V2:S)) -> and(isPalListKind(V1:S),isPalListKind(V2:S)) 0.002/0.002 isPalListKind(a) -> tt 0.002/0.002 isPalListKind(e) -> tt 0.002/0.002 isPalListKind(i) -> tt 0.002/0.002 isPalListKind(nil) -> tt 0.002/0.002 isPalListKind(o) -> tt 0.002/0.002 isPalListKind(u) -> tt 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,V:S) -> U12(isNeList(V:S)) 0.002/0.002 U12(tt) -> tt 0.002/0.002 U21(tt,V1:S,V2:S) -> U22(isList(V1:S),V2:S) 0.002/0.002 U22(tt,V2:S) -> U23(isList(V2:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V:S) -> U32(isQid(V:S)) 0.002/0.002 U32(tt) -> tt 0.002/0.002 U41(tt,V1:S,V2:S) -> U42(isList(V1:S),V2:S) 0.002/0.002 U42(tt,V2:S) -> U43(isNeList(V2:S)) 0.002/0.002 U43(tt) -> tt 0.002/0.002 U51(tt,V1:S,V2:S) -> U52(isNeList(V1:S),V2:S) 0.002/0.002 U52(tt,V2:S) -> U53(isList(V2:S)) 0.002/0.002 U53(tt) -> tt 0.002/0.002 U61(tt,V:S) -> U62(isQid(V:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt,V:S) -> U72(isNePal(V:S)) 0.002/0.002 U72(tt) -> tt 0.002/0.002 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.002/0.002 __(nil,X:S) -> X:S 0.002/0.002 __(X:S,nil) -> X:S 0.002/0.002 and(tt,X:S) -> X:S 0.002/0.002 isList(__(V1:S,V2:S)) -> U21(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isList(nil) -> tt 0.002/0.002 isList(V:S) -> U11(isPalListKind(V:S),V:S) 0.002/0.002 isNeList(__(V1:S,V2:S)) -> U41(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isNeList(__(V1:S,V2:S)) -> U51(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 isNeList(V:S) -> U31(isPalListKind(V:S),V:S) 0.002/0.002 isNePal(__(I:S,__(P:S,I:S))) -> and(and(isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 0.002/0.002 isNePal(V:S) -> U61(isPalListKind(V:S),V:S) 0.002/0.002 isPal(nil) -> tt 0.002/0.002 isPal(V:S) -> U71(isPalListKind(V:S),V:S) 0.002/0.002 isPalListKind(__(V1:S,V2:S)) -> and(isPalListKind(V1:S),isPalListKind(V2:S)) 0.002/0.002 isPalListKind(a) -> tt 0.002/0.002 isPalListKind(e) -> tt 0.002/0.002 isPalListKind(i) -> tt 0.002/0.002 isPalListKind(nil) -> tt 0.002/0.002 isPalListKind(o) -> tt 0.002/0.002 isPalListKind(u) -> tt 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 V, V1, V2, V2, V, V1, V2, V2, V1, V2, V2, V, V, X, Y, Z, X, X, X, V1, V2, V, V1, V2, V1, V2, V, I, P, V, V, V1, V2 0.002/0.002 -> UVars: 0.002/0.002 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 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: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 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: [], UV-LFrozen: [V], UV-RFrozen: [V]) 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: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.002/0.002 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.002/0.002 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.002/0.002 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.002/0.002 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 18, UV-LActive: [X, Y, Z], UV-RActive: [X, Y, Z], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 19, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 20, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 21, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 22, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 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: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.002/0.002 (UV-RuleId: 25, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 26, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 27, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.002/0.002 (UV-RuleId: 28, UV-LActive: [], UV-RActive: [], UV-LFrozen: [I, P], UV-RFrozen: [I, P]) 0.002/0.002 (UV-RuleId: 29, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.002/0.002 (UV-RuleId: 30, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 31, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.002/0.002 (UV-RuleId: 32, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 33, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 34, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 35, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 36, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 37, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 38, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 39, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 40, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 41, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 42, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 43, 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, x39, x40, x41 0.002/0.002 -> PVars: 0.002/0.002 V: [x9, x13, x20, x21, x30, x35, x38, x39], V1: [x10, x14, x17, x28, x31, x33, x40], V2: [x11, x12, x15, x16, x18, x19, x29, x32, x34, x41], X: [x22, x25, x26, x27], Y: [x23], Z: [x24], I: [x36], P: [x37] 0.002/0.002 0.002/0.002 -> Rlps: 0.002/0.002 (rule: U11(tt,x9:S) -> U12(isNeList(x9:S)), id: 1, possubterms: U11(tt,x9:S)->[], tt->[1]) 0.002/0.002 (rule: U12(tt) -> tt, id: 2, possubterms: U12(tt)->[], tt->[1]) 0.002/0.002 (rule: U21(tt,x10:S,x11:S) -> U22(isList(x10:S),x11:S), id: 3, possubterms: U21(tt,x10:S,x11:S)->[], tt->[1]) 0.002/0.002 (rule: U22(tt,x12:S) -> U23(isList(x12:S)), id: 4, possubterms: U22(tt,x12:S)->[], tt->[1]) 0.002/0.002 (rule: U23(tt) -> tt, id: 5, possubterms: U23(tt)->[], tt->[1]) 0.002/0.002 (rule: U31(tt,x13:S) -> U32(isQid(x13:S)), id: 6, possubterms: U31(tt,x13:S)->[], tt->[1]) 0.002/0.002 (rule: U32(tt) -> tt, id: 7, possubterms: U32(tt)->[], tt->[1]) 0.002/0.002 (rule: U41(tt,x14:S,x15:S) -> U42(isList(x14:S),x15:S), id: 8, possubterms: U41(tt,x14:S,x15:S)->[], tt->[1]) 0.002/0.002 (rule: U42(tt,x16:S) -> U43(isNeList(x16:S)), id: 9, possubterms: U42(tt,x16:S)->[], tt->[1]) 0.002/0.002 (rule: U43(tt) -> tt, id: 10, possubterms: U43(tt)->[], tt->[1]) 0.002/0.002 (rule: U51(tt,x17:S,x18:S) -> U52(isNeList(x17:S),x18:S), id: 11, possubterms: U51(tt,x17:S,x18:S)->[], tt->[1]) 0.002/0.002 (rule: U52(tt,x19:S) -> U53(isList(x19:S)), id: 12, possubterms: U52(tt,x19:S)->[], tt->[1]) 0.002/0.002 (rule: U53(tt) -> tt, id: 13, possubterms: U53(tt)->[], tt->[1]) 0.002/0.002 (rule: U61(tt,x20:S) -> U62(isQid(x20:S)), id: 14, possubterms: U61(tt,x20:S)->[], tt->[1]) 0.002/0.002 (rule: U62(tt) -> tt, id: 15, possubterms: U62(tt)->[], tt->[1]) 0.002/0.002 (rule: U71(tt,x21:S) -> U72(isNePal(x21:S)), id: 16, possubterms: U71(tt,x21:S)->[], tt->[1]) 0.002/0.002 (rule: U72(tt) -> tt, id: 17, possubterms: U72(tt)->[], tt->[1]) 0.002/0.002 (rule: __(__(x22:S,x23:S),x24:S) -> __(x22:S,__(x23:S,x24:S)), id: 18, possubterms: __(__(x22:S,x23:S),x24:S)->[], __(x22:S,x23:S)->[1]) 0.002/0.002 (rule: __(nil,x25:S) -> x25:S, id: 19, possubterms: __(nil,x25:S)->[], nil->[1]) 0.002/0.002 (rule: __(x26:S,nil) -> x26:S, id: 20, possubterms: __(x26:S,nil)->[], nil->[2]) 0.002/0.002 (rule: and(tt,x27:S) -> x27:S, id: 21, possubterms: and(tt,x27:S)->[], tt->[1]) 0.002/0.002 (rule: isList(__(x28:S,x29:S)) -> U21(and(isPalListKind(x28:S),isPalListKind(x29:S)),x28:S,x29:S), id: 22, possubterms: isList(__(x28:S,x29:S))->[]) 0.002/0.002 (rule: isList(nil) -> tt, id: 23, possubterms: isList(nil)->[]) 0.002/0.002 (rule: isList(x30:S) -> U11(isPalListKind(x30:S),x30:S), id: 24, possubterms: isList(x30:S)->[]) 0.002/0.002 (rule: isNeList(__(x31:S,x32:S)) -> U41(and(isPalListKind(x31:S),isPalListKind(x32:S)),x31:S,x32:S), id: 25, possubterms: isNeList(__(x31:S,x32:S))->[]) 0.002/0.002 (rule: isNeList(__(x33:S,x34:S)) -> U51(and(isPalListKind(x33:S),isPalListKind(x34:S)),x33:S,x34:S), id: 26, possubterms: isNeList(__(x33:S,x34:S))->[]) 0.002/0.002 (rule: isNeList(x35:S) -> U31(isPalListKind(x35:S),x35:S), id: 27, possubterms: isNeList(x35:S)->[]) 0.002/0.002 (rule: isNePal(__(x36:S,__(x37:S,x36:S))) -> and(and(isQid(x36:S),isPalListKind(x36:S)),and(isPal(x37:S),isPalListKind(x37:S))), id: 28, possubterms: isNePal(__(x36:S,__(x37:S,x36:S)))->[]) 0.002/0.002 (rule: isNePal(x38:S) -> U61(isPalListKind(x38:S),x38:S), id: 29, possubterms: isNePal(x38:S)->[]) 0.002/0.002 (rule: isPal(nil) -> tt, id: 30, possubterms: isPal(nil)->[]) 0.002/0.002 (rule: isPal(x39:S) -> U71(isPalListKind(x39:S),x39:S), id: 31, possubterms: isPal(x39:S)->[]) 0.002/0.002 (rule: isPalListKind(__(x40:S,x41:S)) -> and(isPalListKind(x40:S),isPalListKind(x41:S)), id: 32, possubterms: isPalListKind(__(x40:S,x41:S))->[]) 0.002/0.002 (rule: isPalListKind(a) -> tt, id: 33, possubterms: isPalListKind(a)->[]) 0.002/0.002 (rule: isPalListKind(e) -> tt, id: 34, possubterms: isPalListKind(e)->[]) 0.002/0.002 (rule: isPalListKind(i) -> tt, id: 35, possubterms: isPalListKind(i)->[]) 0.002/0.002 (rule: isPalListKind(nil) -> tt, id: 36, possubterms: isPalListKind(nil)->[]) 0.002/0.002 (rule: isPalListKind(o) -> tt, id: 37, possubterms: isPalListKind(o)->[]) 0.002/0.002 (rule: isPalListKind(u) -> tt, id: 38, possubterms: isPalListKind(u)->[]) 0.002/0.002 (rule: isQid(a) -> tt, id: 39, possubterms: isQid(a)->[]) 0.002/0.002 (rule: isQid(e) -> tt, id: 40, possubterms: isQid(e)->[]) 0.002/0.002 (rule: isQid(i) -> tt, id: 41, possubterms: isQid(i)->[]) 0.002/0.002 (rule: isQid(o) -> tt, id: 42, possubterms: isQid(o)->[]) 0.002/0.002 (rule: isQid(u) -> tt, id: 43, possubterms: isQid(u)->[]) 0.002/0.002 0.002/0.002 -> Unifications: 0.002/0.002 (R18 unifies with R18 at p: [1], l: __(__(x22:S,x23:S),x24:S), lp: __(x22:S,x23:S), sig: {x22:S -> __(X:S,Y:S),x23:S -> Z:S}, l': __(__(X:S,Y:S),Z:S), r: __(x22:S,__(x23:S,x24:S)), r': __(X:S,__(Y:S,Z:S))) 0.002/0.002 (R18 unifies with R19 at p: [1], l: __(__(x22:S,x23:S),x24:S), lp: __(x22:S,x23:S), sig: {x22:S -> nil,x23:S -> X:S}, l': __(nil,X:S), r: __(x22:S,__(x23:S,x24:S)), r': X:S) 0.002/0.002 (R18 unifies with R20 at p: [1], l: __(__(x22:S,x23:S),x24:S), lp: __(x22:S,x23:S), sig: {x22:S -> X:S,x23:S -> nil}, l': __(X:S,nil), r: __(x22:S,__(x23:S,x24:S)), r': X:S) 0.002/0.002 (R20 unifies with R18 at p: [], l: __(x26:S,nil), lp: __(x26:S,nil), sig: {Z:S -> nil,x26:S -> __(X:S,Y:S)}, l': __(__(X:S,Y:S),Z:S), r: x26:S, r': __(X:S,__(Y:S,Z:S))) 0.002/0.002 (R20 unifies with R19 at p: [], l: __(x26:S,nil), lp: __(x26:S,nil), sig: {X:S -> nil,x26:S -> nil}, l': __(nil,X:S), r: x26:S, r': X:S) 0.002/0.002 (R24 unifies with R22 at p: [], l: isList(x30:S), lp: isList(x30:S), sig: {x30:S -> __(V1:S,V2:S)}, l': isList(__(V1:S,V2:S)), r: U11(isPalListKind(x30:S),x30:S), r': U21(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S)) 0.002/0.002 (R24 unifies with R23 at p: [], l: isList(x30:S), lp: isList(x30:S), sig: {x30:S -> nil}, l': isList(nil), r: U11(isPalListKind(x30:S),x30:S), r': tt) 0.002/0.002 (R26 unifies with R25 at p: [], l: isNeList(__(x33:S,x34:S)), lp: isNeList(__(x33:S,x34:S)), sig: {x33:S -> V1:S,x34:S -> V2:S}, l': isNeList(__(V1:S,V2:S)), r: U51(and(isPalListKind(x33:S),isPalListKind(x34:S)),x33:S,x34:S), r': U41(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S)) 0.002/0.002 (R27 unifies with R25 at p: [], l: isNeList(x35:S), lp: isNeList(x35:S), sig: {x35:S -> __(V1:S,V2:S)}, l': isNeList(__(V1:S,V2:S)), r: U31(isPalListKind(x35:S),x35:S), r': U41(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S)) 0.002/0.002 (R27 unifies with R26 at p: [], l: isNeList(x35:S), lp: isNeList(x35:S), sig: {x35:S -> __(V1:S,V2:S)}, l': isNeList(__(V1:S,V2:S)), r: U31(isPalListKind(x35:S),x35:S), r': U51(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S)) 0.002/0.002 (R29 unifies with R28 at p: [], l: isNePal(x38:S), lp: isNePal(x38:S), sig: {x38:S -> __(I:S,__(P:S,I:S))}, l': isNePal(__(I:S,__(P:S,I:S))), r: U61(isPalListKind(x38:S),x38:S), r': and(and(isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S)))) 0.002/0.002 (R31 unifies with R30 at p: [], l: isPal(x39:S), lp: isPal(x39:S), sig: {x39:S -> nil}, l': isPal(nil), r: U71(isPalListKind(x39:S),x39: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 => Trivial, Overlay, NW0, N3 0.002/0.002 <__(__(X:S,__(Y:S,Z:S)),Z:S),__(__(X:S,Y:S),__(Z:S,Z:S))> => Not trivial, Not overlay, NW0, N4 0.002/0.002 => Not trivial, 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 <__(X:S,__(Y:S,nil)),__(X:S,Y:S)> => Not trivial, Overlay, NW0, N8 0.002/0.002 <__(X:S,Z:S),__(nil,__(X:S,Z:S))> => Not trivial, Not overlay, NW0, N9 0.002/0.002 => Not trivial, Overlay, NW0, N10 0.002/0.002 => Not trivial, Overlay, NW0, N11 0.002/0.002 <__(X:S,Z:S),__(X:S,__(nil,Z:S))> => Not trivial, Not overlay, NW0, N12 0.002/0.002 0.002/0.002 -> Problem conclusions: 0.002/0.002 Not 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, 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: U51(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 0.002/0.002 Nodes: [0] 0.002/0.002 Edges: [] 0.002/0.002 ID: 0 => ('U51(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S)', D0) 0.002/0.002 t: U31(isPalListKind(__(V1:S,V2:S)),__(V1:S,V2:S)) 0.002/0.002 Nodes: [0,1] 0.002/0.002 Edges: [(0,1)] 0.002/0.002 ID: 0 => ('U31(isPalListKind(__(V1:S,V2:S)),__(V1:S,V2:S))', D0) 0.002/0.002 ID: 1 => ('U31(and(isPalListKind(V1:S),isPalListKind(V2:S)),__(V1:S,V2:S))', D1, R32, P[1], S{x40:S -> V1:S, x41:S -> V2:S}), NR: 'and(isPalListKind(V1:S),isPalListKind(V2:S))' 0.002/0.002 U51(and(isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) ->* no union *<- U31(isPalListKind(__(V1:S,V2:S)),__(V1:S,V2: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 11816maxresident)k 0.002/0.002 0inputs+0outputs (0major+1146minor)pagefaults 0swaps