/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) Proof: DP Processor: DPs: a____#(__(X,Y),Z) -> mark#(Z) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) a__U11#(tt(),V) -> a__isNeList#(V) a__U11#(tt(),V) -> a__U12#(a__isNeList(V)) a__U21#(tt(),V1,V2) -> a__isList#(V1) a__U21#(tt(),V1,V2) -> a__U22#(a__isList(V1),V2) a__U22#(tt(),V2) -> a__isList#(V2) a__U22#(tt(),V2) -> a__U23#(a__isList(V2)) a__U31#(tt(),V) -> a__isQid#(V) a__U31#(tt(),V) -> a__U32#(a__isQid(V)) a__U41#(tt(),V1,V2) -> a__isList#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isList(V1),V2) a__U42#(tt(),V2) -> a__isNeList#(V2) a__U42#(tt(),V2) -> a__U43#(a__isNeList(V2)) a__U51#(tt(),V1,V2) -> a__isNeList#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNeList(V1),V2) a__U52#(tt(),V2) -> a__isList#(V2) a__U52#(tt(),V2) -> a__U53#(a__isList(V2)) a__U61#(tt(),V) -> a__isQid#(V) a__U61#(tt(),V) -> a__U62#(a__isQid(V)) a__U71#(tt(),V) -> a__isNePal#(V) a__U71#(tt(),V) -> a__U72#(a__isNePal(V)) a__and#(tt(),X) -> mark#(X) a__isList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isList#(__(V1,V2)) -> a__U21#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList#(V) -> a__isPalListKind#(V) a__isNeList#(V) -> a__U31#(a__isPalListKind(V),V) a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isNeList#(__(V1,V2)) -> a__U41#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal#(V) -> a__isPalListKind#(V) a__isNePal#(V) -> a__U61#(a__isPalListKind(V),V) a__isNePal#(__(I,__(P,I))) -> a__isQid#(I) a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPalListKind(I)) a__isNePal#(__(I,__(P,I))) -> a__and#(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal#(V) -> a__isPalListKind#(V) a__isPal#(V) -> a__U71#(a__isPalListKind(V),V) a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> a__U12#(mark(X)) mark#(isNeList(X)) -> a__isNeList#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> a__U23#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> a__U32#(mark(X)) mark#(isQid(X)) -> a__isQid#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> a__U43#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> a__U53#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> a__U62#(mark(X)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> a__U72#(mark(X)) mark#(isNePal(X)) -> a__isNePal#(X) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isPalListKind(X)) -> a__isPalListKind#(X) mark#(isPal(X)) -> a__isPal#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) TDG Processor: DPs: a____#(__(X,Y),Z) -> mark#(Z) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) a__U11#(tt(),V) -> a__isNeList#(V) a__U11#(tt(),V) -> a__U12#(a__isNeList(V)) a__U21#(tt(),V1,V2) -> a__isList#(V1) a__U21#(tt(),V1,V2) -> a__U22#(a__isList(V1),V2) a__U22#(tt(),V2) -> a__isList#(V2) a__U22#(tt(),V2) -> a__U23#(a__isList(V2)) a__U31#(tt(),V) -> a__isQid#(V) a__U31#(tt(),V) -> a__U32#(a__isQid(V)) a__U41#(tt(),V1,V2) -> a__isList#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isList(V1),V2) a__U42#(tt(),V2) -> a__isNeList#(V2) a__U42#(tt(),V2) -> a__U43#(a__isNeList(V2)) a__U51#(tt(),V1,V2) -> a__isNeList#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNeList(V1),V2) a__U52#(tt(),V2) -> a__isList#(V2) a__U52#(tt(),V2) -> a__U53#(a__isList(V2)) a__U61#(tt(),V) -> a__isQid#(V) a__U61#(tt(),V) -> a__U62#(a__isQid(V)) a__U71#(tt(),V) -> a__isNePal#(V) a__U71#(tt(),V) -> a__U72#(a__isNePal(V)) a__and#(tt(),X) -> mark#(X) a__isList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isList#(__(V1,V2)) -> a__U21#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList#(V) -> a__isPalListKind#(V) a__isNeList#(V) -> a__U31#(a__isPalListKind(V),V) a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isNeList#(__(V1,V2)) -> a__U41#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal#(V) -> a__isPalListKind#(V) a__isNePal#(V) -> a__U61#(a__isPalListKind(V),V) a__isNePal#(__(I,__(P,I))) -> a__isQid#(I) a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPalListKind(I)) a__isNePal#(__(I,__(P,I))) -> a__and#(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal#(V) -> a__isPalListKind#(V) a__isPal#(V) -> a__U71#(a__isPalListKind(V),V) a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> a__U12#(mark(X)) mark#(isNeList(X)) -> a__isNeList#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> a__U23#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> a__U32#(mark(X)) mark#(isQid(X)) -> a__isQid#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> a__U43#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> a__U53#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> a__U62#(mark(X)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> a__U72#(mark(X)) mark#(isNePal(X)) -> a__isNePal#(X) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isPalListKind(X)) -> a__isPalListKind#(X) mark#(isPal(X)) -> a__isPal#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) graph: ... SCC Processor: #sccs: 1 #rules: 71 #arcs: 1314/8649 DPs: a__isPal#(V) -> a__isPalListKind#(V) a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__and#(tt(),X) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) -> mark#(Z) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U11#(tt(),V) -> a__isNeList#(V) a__isNeList#(V) -> a__isPalListKind#(V) a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isNeList#(__(V1,V2)) -> a__U41#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U41#(tt(),V1,V2) -> a__isList#(V1) a__isList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isList#(__(V1,V2)) -> a__U21#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U21#(tt(),V1,V2) -> a__isList#(V1) a__U21#(tt(),V1,V2) -> a__U22#(a__isList(V1),V2) a__U22#(tt(),V2) -> a__isList#(V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isList(V1),V2) a__U42#(tt(),V2) -> a__isNeList#(V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNeList#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNeList(V1),V2) a__U52#(tt(),V2) -> a__isList#(V2) mark#(U12(X)) -> mark#(X) mark#(isNeList(X)) -> a__isNeList#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2) a__U71#(tt(),V) -> a__isNePal#(V) a__isNePal#(V) -> a__isPalListKind#(V) a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPalListKind(I)) a__isNePal#(__(I,__(P,I))) -> a__and#(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) mark#(U72(X)) -> mark#(X) mark#(isNePal(X)) -> a__isNePal#(X) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isPalListKind(X)) -> a__isPalListKind#(X) mark#(isPal(X)) -> a__isPal#(X) a__isPal#(V) -> a__U71#(a__isPalListKind(V),V) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=3 usable rules: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) interpretation: [1 0 1] [a__U51](x0, x1, x2) = [0 0 0]x0 [0 0 0] , [1 0 1] [U51](x0, x1, x2) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [0], [1 0 1] [a__U41](x0, x1, x2) = [0 0 0]x0 [0 0 0] , [1 0 1] [a__U21](x0, x1, x2) = [0 0 0]x0 [0 0 0] , [1 0 1] [U62](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 1] [1] [a____](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0] [0 0 1] [0 1 1] [0], [0] [nil] = [0] [0], [1 0 1] [a__U42](x0, x1) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 1] [a__U61](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [u] = [0] [0], [1 0 0] [1 0 1] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [a__U21#](x0, x1, x2) = [1 0 0]x0, [0] [a] = [0] [0], [1 0 1] [a__U52](x0, x1) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U43](x0) = [0 0 0]x0 [0 0 1] , [a__U11#](x0, x1) = [1 0 0]x0, [0] [a__isPalListKind](x0) = [0] [0], [0] [i] = [0] [0], [1 0 1] [a__U62](x0) = [0 0 0]x0 [0 0 0] , [0] [isPalListKind](x0) = [0] [0], [a__U22#](x0, x1) = [1 0 0]x0, [1 0 1] [U31](x0, x1) = [0 0 0]x0 [0 0 0] , [1 0 1] [a__U11](x0, x1) = [0 0 0]x0 [0 0 0] , [0] [e] = [0] [0], [a__isList#](x0) = [0], [1 0 1] [a__U22](x0, x1) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 1] [1] [__](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0] [0 0 1] [0 1 1] [0], [0] [isNeList](x0) = [0] [0], [1 0 1] [a__U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [a__U53](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U72](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [U53](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U43](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 0 1] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [a__U32](x0) = [0 0 0]x0 [0 0 1] , [a__isPalListKind#](x0) = [0], [1 0 0] [U72](x0) = [0 0 0]x0 [0 0 1] , [a__isNePal#](x0) = [1 0 1]x0, [1 0 1] [a__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [a__U31](x0, x1) = [0 0 0]x0 [0 0 0] , [1 0 0] [U32](x0) = [0 0 0]x0 [0 0 1] , [a__U71#](x0, x1) = [1 0 1]x1, [a__and#](x0, x1) = [1 0 0]x1, [1 0 1] [1 0 1] [a__U71](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [a__U41#](x0, x1, x2) = [1 0 0]x0, [1 0 1] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U23](x0) = [0 0 0]x0 [0 0 1] , [0] [a__isList](x0) = [0] [0], [0] [a__isQid](x0) = [0] [0], [1 0 1] [U52](x0, x1) = [0 0 0]x0 [0 0 0] , [1 0 1] [U21](x0, x1, x2) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 1] [U71](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [mark#](x0) = [1 0 0]x0, [0] [a__isNeList](x0) = [0] [0], [1 0 1] [U12](x0) = [0 0 0]x0 [0 0 0] , [a__isNeList#](x0) = [0], [a____#](x0, x1) = [1 0 0]x0 + [1 0 1]x1, [a__U52#](x0, x1) = [1 0 0]x0, [1 0 1] [U42](x0, x1) = [0 0 0]x0 [0 0 0] , [a__U42#](x0, x1) = [1 0 0]x0, [1 0 1] [1 0 1] [U61](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 1] [U41](x0, x1, x2) = [0 0 0]x0 [0 0 0] , [a__U51#](x0, x1, x2) = [1 0 0]x0, [1 0 1] [U11](x0, x1) = [0 0 0]x0 [0 0 0] , [1 0 1] [U22](x0, x1) = [0 0 0]x0 [0 0 0] , [0] [isList](x0) = [0] [0], [0] [isQid](x0) = [0] [0], [a__isPal#](x0) = [1 0 1]x0, [0] [o] = [0] [0], [1 0 1] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U23](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [mark](x0) = [0 0 0]x0 [0 0 0] orientation: a__isPal#(V) = [1 0 1]V >= [0] = a__isPalListKind#(V) a__isPalListKind#(__(V1,V2)) = [0] >= [0] = a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) = [0] >= [0] = a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__and#(tt(),X) = [1 0 0]X >= [1 0 0]X = mark#(X) mark#(__(X1,X2)) = [1 0 1]X1 + [1 0 1]X2 + [1] >= [1 0 0]X2 = mark#(X2) mark#(__(X1,X2)) = [1 0 1]X1 + [1 0 1]X2 + [1] >= [1 0 0]X1 = mark#(X1) mark#(__(X1,X2)) = [1 0 1]X1 + [1 0 1]X2 + [1] >= [1 0 1]X1 + [1 0 1]X2 = a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) = [1 0 1]X + [1 0 1]Y + [1 0 1]Z + [1] >= [1 0 0]Z = mark#(Z) mark#(U11(X1,X2)) = [1 0 1]X1 >= [1 0 0]X1 = mark#(X1) mark#(U11(X1,X2)) = [1 0 1]X1 >= [1 0 1]X1 = a__U11#(mark(X1),X2) a__U11#(tt(),V) = [0] >= [0] = a__isNeList#(V) a__isNeList#(V) = [0] >= [0] = a__isPalListKind#(V) a__isNeList#(__(V1,V2)) = [0] >= [0] = a__isPalListKind#(V1) a__isNeList#(__(V1,V2)) = [0] >= [0] = a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isNeList#(__(V1,V2)) = [0] >= [0] = a__U41#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U41#(tt(),V1,V2) = [0] >= [0] = a__isList#(V1) a__isList#(V) = [0] >= [0] = a__isPalListKind#(V) a__isList#(V) = [0] >= [0] = a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) = [0] >= [0] = a__isPalListKind#(V1) a__isList#(__(V1,V2)) = [0] >= [0] = a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isList#(__(V1,V2)) = [0] >= [0] = a__U21#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U21#(tt(),V1,V2) = [0] >= [0] = a__isList#(V1) a__U21#(tt(),V1,V2) = [0] >= [0] = a__U22#(a__isList(V1),V2) a__U22#(tt(),V2) = [0] >= [0] = a__isList#(V2) a__U41#(tt(),V1,V2) = [0] >= [0] = a__U42#(a__isList(V1),V2) a__U42#(tt(),V2) = [0] >= [0] = a__isNeList#(V2) a__isNeList#(__(V1,V2)) = [0] >= [0] = a__U51#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) = [0] >= [0] = a__isNeList#(V1) a__U51#(tt(),V1,V2) = [0] >= [0] = a__U52#(a__isNeList(V1),V2) a__U52#(tt(),V2) = [0] >= [0] = a__isList#(V2) mark#(U12(X)) = [1 0 1]X >= [1 0 0]X = mark#(X) mark#(isNeList(X)) = [0] >= [0] = a__isNeList#(X) mark#(U21(X1,X2,X3)) = [1 0 1]X1 >= [1 0 0]X1 = mark#(X1) mark#(U21(X1,X2,X3)) = [1 0 1]X1 >= [1 0 1]X1 = a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2)) = [1 0 1]X1 >= [1 0 0]X1 = mark#(X1) mark#(U22(X1,X2)) = [1 0 1]X1 >= [1 0 1]X1 = a__U22#(mark(X1),X2) mark#(isList(X)) = [0] >= [0] = a__isList#(X) mark#(U23(X)) = [1 0 0]X >= [1 0 0]X = mark#(X) mark#(U31(X1,X2)) = [1 0 1]X1 >= [1 0 0]X1 = mark#(X1) mark#(U32(X)) = [1 0 0]X >= [1 0 0]X = mark#(X) mark#(U41(X1,X2,X3)) = [1 0 1]X1 >= [1 0 0]X1 = mark#(X1) mark#(U41(X1,X2,X3)) = [1 0 1]X1 >= [1 0 1]X1 = a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) = [1 0 1]X1 >= [1 0 0]X1 = mark#(X1) mark#(U42(X1,X2)) = [1 0 1]X1 >= [1 0 1]X1 = a__U42#(mark(X1),X2) mark#(U43(X)) = [1 0 0]X >= [1 0 0]X = mark#(X) mark#(U51(X1,X2,X3)) = [1 0 1]X1 >= [1 0 0]X1 = mark#(X1) mark#(U51(X1,X2,X3)) = [1 0 1]X1 >= [1 0 1]X1 = a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) = [1 0 1]X1 >= [1 0 0]X1 = mark#(X1) mark#(U52(X1,X2)) = [1 0 1]X1 >= [1 0 1]X1 = a__U52#(mark(X1),X2) mark#(U53(X)) = [1 0 1]X >= [1 0 0]X = mark#(X) mark#(U61(X1,X2)) = [1 0 1]X1 + [1 0 1]X2 >= [1 0 0]X1 = mark#(X1) mark#(U62(X)) = [1 0 1]X >= [1 0 0]X = mark#(X) mark#(U71(X1,X2)) = [1 0 1]X1 + [1 0 1]X2 >= [1 0 0]X1 = mark#(X1) mark#(U71(X1,X2)) = [1 0 1]X1 + [1 0 1]X2 >= [1 0 1]X2 = a__U71#(mark(X1),X2) a__U71#(tt(),V) = [1 0 1]V >= [1 0 1]V = a__isNePal#(V) a__isNePal#(V) = [1 0 1]V >= [0] = a__isPalListKind#(V) a__isNePal#(__(I,__(P,I))) = [2 2 5]I + [1 0 4]P + [2] >= [0] = a__and#(a__isQid(I),isPalListKind(I)) a__isNePal#(__(I,__(P,I))) = [2 2 5]I + [1 0 4]P + [2] >= [1 0 1]P = a__and#(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) mark#(U72(X)) = [1 0 0]X >= [1 0 0]X = mark#(X) mark#(isNePal(X)) = [1 0 1]X >= [1 0 1]X = a__isNePal#(X) mark#(and(X1,X2)) = [1 0 0]X1 + [1 0 1]X2 >= [1 0 0]X1 = mark#(X1) mark#(and(X1,X2)) = [1 0 0]X1 + [1 0 1]X2 >= [1 0 0]X2 = a__and#(mark(X1),X2) mark#(isPalListKind(X)) = [0] >= [0] = a__isPalListKind#(X) mark#(isPal(X)) = [1 0 1]X >= [1 0 1]X = a__isPal#(X) a__isPal#(V) = [1 0 1]V >= [1 0 1]V = a__U71#(a__isPalListKind(V),V) a____#(__(X,Y),Z) = [1 0 1]X + [1 0 1]Y + [1 0 1]Z + [1] >= [1 0 0]Y = mark#(Y) a____#(__(X,Y),Z) = [1 0 1]X + [1 0 1]Y + [1 0 1]Z + [1] >= [1 0 1]Y + [1 0 1]Z = a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) = [1 0 1]X + [1 0 1]Y + [1 0 1]Z + [1] >= [1 0 0]X = mark#(X) a____#(__(X,Y),Z) = [1 0 1]X + [1 0 1]Y + [1 0 1]Z + [1] >= [1 0 1]X + [1 0 1]Y + [1 0 1]Z + [1] = a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) = [1 0 0]X >= [1 0 0]X = mark#(X) a____#(nil(),X) = [1 0 1]X >= [1 0 0]X = mark#(X) [1 0 2] [1 1 2] [1 0 1] [2] [1 0 1] [1 0 1] [1 0 1] [2] a____(__(X,Y),Z) = [0 0 1]X + [0 1 1]Y + [0 0 0]Z + [0] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] = a____(mark(X),a____(mark(Y),mark(Z))) [0 0 1] [0 1 1] [0 1 1] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 0 1] [1] [1 0 1] a____(X,nil()) = [0 0 1]X + [0] >= [0 0 0]X = mark(X) [0 0 1] [0] [0 0 0] [1 0 1] [1] [1 0 1] a____(nil(),X) = [0 0 0]X + [0] >= [0 0 0]X = mark(X) [0 1 1] [0] [0 0 0] [0] [0] a__U11(tt(),V) = [0] >= [0] = a__U12(a__isNeList(V)) [0] [0] [0] [0] a__U12(tt()) = [0] >= [0] = tt() [0] [0] [0] [0] a__U21(tt(),V1,V2) = [0] >= [0] = a__U22(a__isList(V1),V2) [0] [0] [0] [0] a__U22(tt(),V2) = [0] >= [0] = a__U23(a__isList(V2)) [0] [0] [0] [0] a__U23(tt()) = [0] >= [0] = tt() [0] [0] [0] [0] a__U31(tt(),V) = [0] >= [0] = a__U32(a__isQid(V)) [0] [0] [0] [0] a__U32(tt()) = [0] >= [0] = tt() [0] [0] [0] [0] a__U41(tt(),V1,V2) = [0] >= [0] = a__U42(a__isList(V1),V2) [0] [0] [0] [0] a__U42(tt(),V2) = [0] >= [0] = a__U43(a__isNeList(V2)) [0] [0] [0] [0] a__U43(tt()) = [0] >= [0] = tt() [0] [0] [0] [0] a__U51(tt(),V1,V2) = [0] >= [0] = a__U52(a__isNeList(V1),V2) [0] [0] [0] [0] a__U52(tt(),V2) = [0] >= [0] = a__U53(a__isList(V2)) [0] [0] [0] [0] a__U53(tt()) = [0] >= [0] = tt() [0] [0] [1 0 1] [0] a__U61(tt(),V) = [0 0 0]V >= [0] = a__U62(a__isQid(V)) [0 0 0] [0] [0] [0] a__U62(tt()) = [0] >= [0] = tt() [0] [0] [1 0 1] [1 0 1] a__U71(tt(),V) = [0 0 0]V >= [0 0 0]V = a__U72(a__isNePal(V)) [0 0 0] [0 0 0] [0] [0] a__U72(tt()) = [0] >= [0] = tt() [0] [0] [1 0 1] [1 0 1] a__and(tt(),X) = [0 0 0]X >= [0 0 0]X = mark(X) [0 0 0] [0 0 0] [0] [0] a__isList(V) = [0] >= [0] = a__U11(a__isPalListKind(V),V) [0] [0] [0] [0] a__isList(nil()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isList(__(V1,V2)) = [0] >= [0] = a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) [0] [0] [0] [0] a__isNeList(V) = [0] >= [0] = a__U31(a__isPalListKind(V),V) [0] [0] [0] [0] a__isNeList(__(V1,V2)) = [0] >= [0] = a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) [0] [0] [0] [0] a__isNeList(__(V1,V2)) = [0] >= [0] = a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) [0] [0] [1 0 1] [1 0 1] a__isNePal(V) = [0 0 0]V >= [0 0 0]V = a__U61(a__isPalListKind(V),V) [0 0 0] [0 0 0] [2 2 5] [1 0 4] [2] [1 0 1] a__isNePal(__(I,__(P,I))) = [0 0 0]I + [0 0 0]P + [0] >= [0 0 0]P = a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) [0 0 0] [0 0 0] [0] [0 0 0] [1 0 1] [1 0 1] a__isPal(V) = [0 0 0]V >= [0 0 0]V = a__U71(a__isPalListKind(V),V) [0 0 0] [0 0 0] [0] [0] a__isPal(nil()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isPalListKind(a()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isPalListKind(e()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isPalListKind(i()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isPalListKind(nil()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isPalListKind(o()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isPalListKind(u()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isPalListKind(__(V1,V2)) = [0] >= [0] = a__and(a__isPalListKind(V1),isPalListKind(V2)) [0] [0] [0] [0] a__isQid(a()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isQid(e()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isQid(i()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isQid(o()) = [0] >= [0] = tt() [0] [0] [0] [0] a__isQid(u()) = [0] >= [0] = tt() [0] [0] [1 0 2] [1 1 2] [1] [1 0 1] [1 0 1] [1] mark(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = a____(mark(X1),mark(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] mark(U11(X1,X2)) = [0 0 0]X1 >= [0 0 0]X1 = a__U11(mark(X1),X2) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U12(X)) = [0 0 0]X >= [0 0 0]X = a__U12(mark(X)) [0 0 0] [0 0 0] [0] [0] mark(isNeList(X)) = [0] >= [0] = a__isNeList(X) [0] [0] [1 0 1] [1 0 1] mark(U21(X1,X2,X3)) = [0 0 0]X1 >= [0 0 0]X1 = a__U21(mark(X1),X2,X3) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U22(X1,X2)) = [0 0 0]X1 >= [0 0 0]X1 = a__U22(mark(X1),X2) [0 0 0] [0 0 0] [0] [0] mark(isList(X)) = [0] >= [0] = a__isList(X) [0] [0] [1 0 1] [1 0 1] mark(U23(X)) = [0 0 0]X >= [0 0 0]X = a__U23(mark(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U31(X1,X2)) = [0 0 0]X1 >= [0 0 0]X1 = a__U31(mark(X1),X2) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U32(X)) = [0 0 0]X >= [0 0 0]X = a__U32(mark(X)) [0 0 0] [0 0 0] [0] [0] mark(isQid(X)) = [0] >= [0] = a__isQid(X) [0] [0] [1 0 1] [1 0 1] mark(U41(X1,X2,X3)) = [0 0 0]X1 >= [0 0 0]X1 = a__U41(mark(X1),X2,X3) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U42(X1,X2)) = [0 0 0]X1 >= [0 0 0]X1 = a__U42(mark(X1),X2) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U43(X)) = [0 0 0]X >= [0 0 0]X = a__U43(mark(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U51(X1,X2,X3)) = [0 0 0]X1 >= [0 0 0]X1 = a__U51(mark(X1),X2,X3) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U52(X1,X2)) = [0 0 0]X1 >= [0 0 0]X1 = a__U52(mark(X1),X2) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U53(X)) = [0 0 0]X >= [0 0 0]X = a__U53(mark(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] mark(U61(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = a__U61(mark(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U62(X)) = [0 0 0]X >= [0 0 0]X = a__U62(mark(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] mark(U71(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = a__U71(mark(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U72(X)) = [0 0 0]X >= [0 0 0]X = a__U72(mark(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(isNePal(X)) = [0 0 0]X >= [0 0 0]X = a__isNePal(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = a__and(mark(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] mark(isPalListKind(X)) = [0] >= [0] = a__isPalListKind(X) [0] [0] [1 0 1] [1 0 1] mark(isPal(X)) = [0 0 0]X >= [0 0 0]X = a__isPal(X) [0 0 0] [0 0 0] [0] [0] mark(nil()) = [0] >= [0] = nil() [0] [0] [0] [0] mark(tt()) = [0] >= [0] = tt() [0] [0] [0] [0] mark(a()) = [0] >= [0] = a() [0] [0] [0] [0] mark(e()) = [0] >= [0] = e() [0] [0] [0] [0] mark(i()) = [0] >= [0] = i() [0] [0] [0] [0] mark(o()) = [0] >= [0] = o() [0] [0] [0] [0] mark(u()) = [0] >= [0] = u() [0] [0] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] a____(X1,X2) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 0 1] [0 1 1] [0] [0 0 1] [0 1 1] [0] [1 0 1] [1 0 1] a__U11(X1,X2) = [0 0 0]X1 >= [0 0 0]X1 = U11(X1,X2) [0 0 0] [0 0 0] [1 0 1] [1 0 1] a__U12(X) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [0] [0] a__isNeList(X) = [0] >= [0] = isNeList(X) [0] [0] [1 0 1] [1 0 1] a__U21(X1,X2,X3) = [0 0 0]X1 >= [0 0 0]X1 = U21(X1,X2,X3) [0 0 0] [0 0 0] [1 0 1] [1 0 1] a__U22(X1,X2) = [0 0 0]X1 >= [0 0 0]X1 = U22(X1,X2) [0 0 0] [0 0 0] [0] [0] a__isList(X) = [0] >= [0] = isList(X) [0] [0] [1 0 0] [1 0 0] a__U23(X) = [0 0 0]X >= [0 0 0]X = U23(X) [0 0 1] [0 0 1] [1 0 1] [1 0 1] a__U31(X1,X2) = [0 0 0]X1 >= [0 0 0]X1 = U31(X1,X2) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U32(X) = [0 0 0]X >= [0 0 0]X = U32(X) [0 0 1] [0 0 1] [0] [0] a__isQid(X) = [0] >= [0] = isQid(X) [0] [0] [1 0 1] [1 0 1] a__U41(X1,X2,X3) = [0 0 0]X1 >= [0 0 0]X1 = U41(X1,X2,X3) [0 0 0] [0 0 0] [1 0 1] [1 0 1] a__U42(X1,X2) = [0 0 0]X1 >= [0 0 0]X1 = U42(X1,X2) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U43(X) = [0 0 0]X >= [0 0 0]X = U43(X) [0 0 1] [0 0 1] [1 0 1] [1 0 1] a__U51(X1,X2,X3) = [0 0 0]X1 >= [0 0 0]X1 = U51(X1,X2,X3) [0 0 0] [0 0 0] [1 0 1] [1 0 1] a__U52(X1,X2) = [0 0 0]X1 >= [0 0 0]X1 = U52(X1,X2) [0 0 0] [0 0 0] [1 0 1] [1 0 1] a__U53(X) = [0 0 0]X >= [0 0 0]X = U53(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] a__U61(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U61(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] a__U62(X) = [0 0 0]X >= [0 0 0]X = U62(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] a__U71(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U71(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U72(X) = [0 0 0]X >= [0 0 0]X = U72(X) [0 0 1] [0 0 1] [1 0 1] [1 0 1] a__isNePal(X) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 1] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [0] [0] a__isPalListKind(X) = [0] >= [0] = isPalListKind(X) [0] [0] [1 0 1] [1 0 1] a__isPal(X) = [0 0 0]X >= [0 0 0]X = isPal(X) [0 0 0] [0 0 0] problem: DPs: a__isPal#(V) -> a__isPalListKind#(V) a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__and#(tt(),X) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U11#(tt(),V) -> a__isNeList#(V) a__isNeList#(V) -> a__isPalListKind#(V) a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isNeList#(__(V1,V2)) -> a__U41#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U41#(tt(),V1,V2) -> a__isList#(V1) a__isList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isList#(__(V1,V2)) -> a__U21#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U21#(tt(),V1,V2) -> a__isList#(V1) a__U21#(tt(),V1,V2) -> a__U22#(a__isList(V1),V2) a__U22#(tt(),V2) -> a__isList#(V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isList(V1),V2) a__U42#(tt(),V2) -> a__isNeList#(V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNeList#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNeList(V1),V2) a__U52#(tt(),V2) -> a__isList#(V2) mark#(U12(X)) -> mark#(X) mark#(isNeList(X)) -> a__isNeList#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2) a__U71#(tt(),V) -> a__isNePal#(V) a__isNePal#(V) -> a__isPalListKind#(V) mark#(U72(X)) -> mark#(X) mark#(isNePal(X)) -> a__isNePal#(X) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isPalListKind(X)) -> a__isPalListKind#(X) mark#(isPal(X)) -> a__isPal#(X) a__isPal#(V) -> a__U71#(a__isPalListKind(V),V) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) Restore Modifier: DPs: a__isPal#(V) -> a__isPalListKind#(V) a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__and#(tt(),X) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U11#(tt(),V) -> a__isNeList#(V) a__isNeList#(V) -> a__isPalListKind#(V) a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isNeList#(__(V1,V2)) -> a__U41#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U41#(tt(),V1,V2) -> a__isList#(V1) a__isList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isList#(__(V1,V2)) -> a__U21#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U21#(tt(),V1,V2) -> a__isList#(V1) a__U21#(tt(),V1,V2) -> a__U22#(a__isList(V1),V2) a__U22#(tt(),V2) -> a__isList#(V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isList(V1),V2) a__U42#(tt(),V2) -> a__isNeList#(V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNeList#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNeList(V1),V2) a__U52#(tt(),V2) -> a__isList#(V2) mark#(U12(X)) -> mark#(X) mark#(isNeList(X)) -> a__isNeList#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2) a__U71#(tt(),V) -> a__isNePal#(V) a__isNePal#(V) -> a__isPalListKind#(V) mark#(U72(X)) -> mark#(X) mark#(isNePal(X)) -> a__isNePal#(X) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isPalListKind(X)) -> a__isPalListKind#(X) mark#(isPal(X)) -> a__isPal#(X) a__isPal#(V) -> a__U71#(a__isPalListKind(V),V) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) SCC Processor: #sccs: 2 #rules: 60 #arcs: 1028/3844 DPs: a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=1 usable rules: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) interpretation: [a__U51](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [tt] = 0, [a__U41](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [U62](x0) = 1, [a____](x0, x1) = 2x0 + x1 + 1, [nil] = 7, [a__U42](x0, x1) = 0, [a__U61](x0, x1) = 1, [u] = 1, [a__and](x0, x1) = x1 + 2, [a] = 0, [a__U52](x0, x1) = 0, [a__U43](x0) = 0, [a__isPalListKind](x0) = 2x0, [i] = 1, [a__U62](x0) = 1, [isPalListKind](x0) = 2x0, [U31](x0, x1) = 0, [a__U11](x0, x1) = 0, [e] = 2, [a__U22](x0, x1) = 0, [__](x0, x1) = 2x0 + x1 + 1, [isNeList](x0) = 0, [a__U12](x0) = 0, [a__U53](x0) = 0, [a__U72](x0) = 0, [U53](x0) = 0, [U43](x0) = 0, [and](x0, x1) = x1 + 2, [a__U32](x0) = 0, [U72](x0) = 0, [a__isPal](x0) = 1, [a__U31](x0, x1) = 0, [U32](x0) = 0, [a__U71](x0, x1) = 1, [a__isNePal](x0) = 6x0 + 1, [isNePal](x0) = 6x0 + 1, [a__U23](x0) = 0, [a__isList](x0) = 0, [a__isQid](x0) = x0, [U52](x0, x1) = 0, [U21](x0, x1, x2) = 0, [U71](x0, x1) = 1, [a__isNeList](x0) = 0, [U12](x0) = 0, [a____#](x0, x1) = 2x0 + x1, [U42](x0, x1) = 0, [U61](x0, x1) = 1, [U41](x0, x1, x2) = 0, [U11](x0, x1) = 0, [U22](x0, x1) = 0, [isList](x0) = 0, [isQid](x0) = x0, [o] = 1, [isPal](x0) = 1, [U23](x0) = 0, [mark](x0) = x0 orientation: a____#(__(X,Y),Z) = 4X + 2Y + Z + 2 >= 2X + 2Y + Z + 1 = a____#(mark(X),a____(mark(Y),mark(Z))) a____(__(X,Y),Z) = 4X + 2Y + Z + 3 >= 2X + 2Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 2X + 8 >= X = mark(X) a____(nil(),X) = X + 15 >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isNeList(V)) a__U12(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isList(V1),V2) a__U22(tt(),V2) = 0 >= 0 = a__U23(a__isList(V2)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isQid(V)) a__U32(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isList(V1),V2) a__U42(tt(),V2) = 0 >= 0 = a__U43(a__isNeList(V2)) a__U43(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) = 0 >= 0 = a__U53(a__isList(V2)) a__U53(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isQid(V)) a__U62(tt()) = 1 >= 0 = tt() a__U71(tt(),V) = 1 >= 0 = a__U72(a__isNePal(V)) a__U72(tt()) = 0 >= 0 = tt() a__and(tt(),X) = X + 2 >= X = mark(X) a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) = 6V + 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 18I + 12P + 13 >= 2P + 4 = a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) = 1 >= 1 = a__U71(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 4 >= 0 = tt() a__isPalListKind(i()) = 2 >= 0 = tt() a__isPalListKind(nil()) = 14 >= 0 = tt() a__isPalListKind(o()) = 2 >= 0 = tt() a__isPalListKind(u()) = 2 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 4V1 + 2V2 + 2 >= 2V2 + 2 = a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 2 >= 0 = tt() a__isQid(i()) = 1 >= 0 = tt() a__isQid(o()) = 1 >= 0 = tt() a__isQid(u()) = 1 >= 0 = tt() mark(__(X1,X2)) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X)) = 0 >= 0 = a__U12(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 0 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X)) = 0 >= 0 = a__U32(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) = 0 >= 0 = a__U42(mark(X1),X2) mark(U43(X)) = 0 >= 0 = a__U43(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) = 0 >= 0 = a__U52(mark(X1),X2) mark(U53(X)) = 0 >= 0 = a__U53(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 1 = a__U62(mark(X)) mark(U71(X1,X2)) = 1 >= 1 = a__U71(mark(X1),X2) mark(U72(X)) = 0 >= 0 = a__U72(mark(X)) mark(isNePal(X)) = 6X + 1 >= 6X + 1 = a__isNePal(X) mark(and(X1,X2)) = X2 + 2 >= X2 + 2 = a__and(mark(X1),X2) mark(isPalListKind(X)) = 2X >= 2X = a__isPalListKind(X) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(nil()) = 7 >= 7 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 2 >= 2 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X) = 0 >= 0 = U12(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X) = 0 >= 0 = U32(X) a__isQid(X) = X >= X = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2) = 0 >= 0 = U42(X1,X2) a__U43(X) = 0 >= 0 = U43(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2) = 0 >= 0 = U52(X1,X2) a__U53(X) = 0 >= 0 = U53(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X) = 1 >= 1 = U62(X) a__U71(X1,X2) = 1 >= 1 = U71(X1,X2) a__U72(X) = 0 >= 0 = U72(X) a__isNePal(X) = 6X + 1 >= 6X + 1 = isNePal(X) a__and(X1,X2) = X2 + 2 >= X2 + 2 = and(X1,X2) a__isPalListKind(X) = 2X >= 2X = isPalListKind(X) a__isPal(X) = 1 >= 1 = isPal(X) problem: DPs: TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) Qed DPs: a__isPal#(V) -> a__isPalListKind#(V) a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__and#(tt(),X) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U11#(tt(),V) -> a__isNeList#(V) a__isNeList#(V) -> a__isPalListKind#(V) a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isNeList#(__(V1,V2)) -> a__U41#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U41#(tt(),V1,V2) -> a__isList#(V1) a__isList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2)) a__isList#(__(V1,V2)) -> a__U21#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U21#(tt(),V1,V2) -> a__isList#(V1) a__U21#(tt(),V1,V2) -> a__U22#(a__isList(V1),V2) a__U22#(tt(),V2) -> a__isList#(V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isList(V1),V2) a__U42#(tt(),V2) -> a__isNeList#(V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNeList#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNeList(V1),V2) a__U52#(tt(),V2) -> a__isList#(V2) mark#(U12(X)) -> mark#(X) mark#(isNeList(X)) -> a__isNeList#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2) a__U71#(tt(),V) -> a__isNePal#(V) a__isNePal#(V) -> a__isPalListKind#(V) mark#(U72(X)) -> mark#(X) mark#(isNePal(X)) -> a__isNePal#(X) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isPalListKind(X)) -> a__isPalListKind#(X) mark#(isPal(X)) -> a__isPal#(X) a__isPal#(V) -> a__U71#(a__isPalListKind(V),V) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) Subterm Criterion Processor: simple projection: pi(a__U53) = [0,0,0] pi(isPalListKind) = [0,0] pi(isPal) = [0,0] pi(and) = [0,1] pi(U42) = [0,0,1,1,1] pi(U52) = [0,0,1,1] pi(U53) = [0,0] pi(mark#) = [0,0] pi(a__U11#) = 1 pi(a__isNeList#) = 0 pi(a__U21#) = [1,2] pi(a__isList#) = 0 pi(a__U22#) = 1 pi(a__U41#) = [1,2] pi(a__U42#) = 1 pi(a__U51#) = [1,2,2,2] pi(a__U52#) = 1 pi(a__U71#) = 1 pi(a__isNePal#) = 0 pi(a__and#) = [1,1] pi(a__isPalListKind#) = 0 pi(a__isPal#) = 0 problem: DPs: a__isPal#(V) -> a__isPalListKind#(V) a__and#(tt(),X) -> mark#(X) a__U11#(tt(),V) -> a__isNeList#(V) a__isNeList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U22#(tt(),V2) -> a__isList#(V2) a__U42#(tt(),V2) -> a__isNeList#(V2) a__U52#(tt(),V2) -> a__isList#(V2) a__U71#(tt(),V) -> a__isNePal#(V) a__isNePal#(V) -> a__isPalListKind#(V) a__isPal#(V) -> a__U71#(a__isPalListKind(V),V) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isNeList(V)) a__U12(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2) a__U22(tt(),V2) -> a__U23(a__isList(V2)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isQid(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNeList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2) a__U52(tt(),V2) -> a__U53(a__isList(V2)) a__U53(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isQid(V)) a__U62(tt()) -> tt() a__U71(tt(),V) -> a__U72(a__isNePal(V)) a__U72(tt()) -> tt() a__and(tt(),X) -> mark(X) a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) a__isPal(V) -> a__U71(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2) -> U22(X1,X2) a__isList(X) -> isList(X) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) a__and(X1,X2) -> and(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__isPal(X) -> isPal(X) SCC Processor: #sccs: 0 #rules: 0 #arcs: 699/144