MAYBE Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Proof: DP Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) active#(__(X,nil())) -> mark#(X) active#(__(nil(),X)) -> mark#(X) active#(U11(tt(),V)) -> isNeList#(V) active#(U11(tt(),V)) -> U12#(isNeList(V)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) active#(U21(tt(),V1,V2)) -> isList#(V1) active#(U21(tt(),V1,V2)) -> U22#(isList(V1),V2) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) active#(U22(tt(),V2)) -> isList#(V2) active#(U22(tt(),V2)) -> U23#(isList(V2)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) active#(U23(tt())) -> mark#(tt()) active#(U31(tt(),V)) -> isQid#(V) active#(U31(tt(),V)) -> U32#(isQid(V)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> isList#(V1) active#(U41(tt(),V1,V2)) -> U42#(isList(V1),V2) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) active#(U42(tt(),V2)) -> isNeList#(V2) active#(U42(tt(),V2)) -> U43#(isNeList(V2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> isNeList#(V1) active#(U51(tt(),V1,V2)) -> U52#(isNeList(V1),V2) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) active#(U52(tt(),V2)) -> isList#(V2) active#(U52(tt(),V2)) -> U53#(isList(V2)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) active#(U53(tt())) -> mark#(tt()) active#(U61(tt(),V)) -> isQid#(V) active#(U61(tt(),V)) -> U62#(isQid(V)) active#(U61(tt(),V)) -> mark#(U62(isQid(V))) active#(U62(tt())) -> mark#(tt()) active#(U71(tt(),V)) -> isNePal#(V) active#(U71(tt(),V)) -> U72#(isNePal(V)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) active#(U72(tt())) -> mark#(tt()) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> isPalListKind#(V) active#(isList(V)) -> U11#(isPalListKind(V),V) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isList(nil())) -> mark#(tt()) active#(isList(__(V1,V2))) -> isPalListKind#(V2) active#(isList(__(V1,V2))) -> isPalListKind#(V1) active#(isList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isList(__(V1,V2))) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isList(__(V1,V2))) -> mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active#(isNeList(V)) -> isPalListKind#(V) active#(isNeList(V)) -> U31#(isPalListKind(V),V) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) active#(isNeList(__(V1,V2))) -> isPalListKind#(V2) active#(isNeList(__(V1,V2))) -> isPalListKind#(V1) active#(isNeList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isNeList(__(V1,V2))) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNeList(__(V1,V2))) -> mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active#(isNeList(__(V1,V2))) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNeList(__(V1,V2))) -> mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active#(isNePal(V)) -> isPalListKind#(V) active#(isNePal(V)) -> U61#(isPalListKind(V),V) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(P) active#(isNePal(__(I,__(P,I)))) -> isPal#(P) active#(isNePal(__(I,__(P,I)))) -> and#(isPal(P),isPalListKind(P)) active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(I) active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPalListKind(I)) active#(isNePal(__(I,__(P,I)))) -> and#(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) active#(isNePal(__(I,__(P,I)))) -> mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active#(isPal(V)) -> isPalListKind#(V) active#(isPal(V)) -> U71#(isPalListKind(V),V) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPal(nil())) -> mark#(tt()) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V2) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V1) active#(isPalListKind(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(e())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) active#(isQid(o())) -> mark#(tt()) active#(isQid(u())) -> mark#(tt()) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> U12#(mark(X)) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> U22#(mark(X1),X2) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) mark#(isList(X)) -> active#(isList(X)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> U23#(mark(X)) mark#(U23(X)) -> active#(U23(mark(X))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> U32#(mark(X)) mark#(U32(X)) -> active#(U32(mark(X))) mark#(isQid(X)) -> active#(isQid(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> U42#(mark(X1),X2) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> U43#(mark(X)) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> U52#(mark(X1),X2) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> U53#(mark(X)) mark#(U53(X)) -> active#(U53(mark(X))) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> U71#(mark(X1),X2) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> U72#(mark(X)) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) mark#(a()) -> active#(a()) mark#(e()) -> active#(e()) mark#(i()) -> active#(i()) mark#(o()) -> active#(o()) mark#(u()) -> active#(u()) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U12#(mark(X)) -> U12#(X) U12#(active(X)) -> U12#(X) isNeList#(mark(X)) -> isNeList#(X) isNeList#(active(X)) -> isNeList#(X) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) isList#(mark(X)) -> isList#(X) isList#(active(X)) -> isList#(X) U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U32#(mark(X)) -> U32#(X) U32#(active(X)) -> U32#(X) isQid#(mark(X)) -> isQid#(X) isQid#(active(X)) -> isQid#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U42#(mark(X1),X2) -> U42#(X1,X2) U42#(X1,mark(X2)) -> U42#(X1,X2) U42#(active(X1),X2) -> U42#(X1,X2) U42#(X1,active(X2)) -> U42#(X1,X2) U43#(mark(X)) -> U43#(X) U43#(active(X)) -> U43#(X) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) U51#(active(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U52#(mark(X1),X2) -> U52#(X1,X2) U52#(X1,mark(X2)) -> U52#(X1,X2) U52#(active(X1),X2) -> U52#(X1,X2) U52#(X1,active(X2)) -> U52#(X1,X2) U53#(mark(X)) -> U53#(X) U53#(active(X)) -> U53#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U71#(X1,mark(X2)) -> U71#(X1,X2) U71#(active(X1),X2) -> U71#(X1,X2) U71#(X1,active(X2)) -> U71#(X1,X2) U72#(mark(X)) -> U72#(X) U72#(active(X)) -> U72#(X) isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) isPalListKind#(mark(X)) -> isPalListKind#(X) isPalListKind#(active(X)) -> isPalListKind#(X) isPal#(mark(X)) -> isPal#(X) isPal#(active(X)) -> isPal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) TDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) active#(__(X,nil())) -> mark#(X) active#(__(nil(),X)) -> mark#(X) active#(U11(tt(),V)) -> isNeList#(V) active#(U11(tt(),V)) -> U12#(isNeList(V)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) active#(U21(tt(),V1,V2)) -> isList#(V1) active#(U21(tt(),V1,V2)) -> U22#(isList(V1),V2) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) active#(U22(tt(),V2)) -> isList#(V2) active#(U22(tt(),V2)) -> U23#(isList(V2)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) active#(U23(tt())) -> mark#(tt()) active#(U31(tt(),V)) -> isQid#(V) active#(U31(tt(),V)) -> U32#(isQid(V)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> isList#(V1) active#(U41(tt(),V1,V2)) -> U42#(isList(V1),V2) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) active#(U42(tt(),V2)) -> isNeList#(V2) active#(U42(tt(),V2)) -> U43#(isNeList(V2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> isNeList#(V1) active#(U51(tt(),V1,V2)) -> U52#(isNeList(V1),V2) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) active#(U52(tt(),V2)) -> isList#(V2) active#(U52(tt(),V2)) -> U53#(isList(V2)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) active#(U53(tt())) -> mark#(tt()) active#(U61(tt(),V)) -> isQid#(V) active#(U61(tt(),V)) -> U62#(isQid(V)) active#(U61(tt(),V)) -> mark#(U62(isQid(V))) active#(U62(tt())) -> mark#(tt()) active#(U71(tt(),V)) -> isNePal#(V) active#(U71(tt(),V)) -> U72#(isNePal(V)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) active#(U72(tt())) -> mark#(tt()) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> isPalListKind#(V) active#(isList(V)) -> U11#(isPalListKind(V),V) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isList(nil())) -> mark#(tt()) active#(isList(__(V1,V2))) -> isPalListKind#(V2) active#(isList(__(V1,V2))) -> isPalListKind#(V1) active#(isList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isList(__(V1,V2))) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isList(__(V1,V2))) -> mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active#(isNeList(V)) -> isPalListKind#(V) active#(isNeList(V)) -> U31#(isPalListKind(V),V) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) active#(isNeList(__(V1,V2))) -> isPalListKind#(V2) active#(isNeList(__(V1,V2))) -> isPalListKind#(V1) active#(isNeList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isNeList(__(V1,V2))) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNeList(__(V1,V2))) -> mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active#(isNeList(__(V1,V2))) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNeList(__(V1,V2))) -> mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active#(isNePal(V)) -> isPalListKind#(V) active#(isNePal(V)) -> U61#(isPalListKind(V),V) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(P) active#(isNePal(__(I,__(P,I)))) -> isPal#(P) active#(isNePal(__(I,__(P,I)))) -> and#(isPal(P),isPalListKind(P)) active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(I) active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPalListKind(I)) active#(isNePal(__(I,__(P,I)))) -> and#(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) active#(isNePal(__(I,__(P,I)))) -> mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active#(isPal(V)) -> isPalListKind#(V) active#(isPal(V)) -> U71#(isPalListKind(V),V) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPal(nil())) -> mark#(tt()) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V2) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V1) active#(isPalListKind(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(e())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) active#(isQid(o())) -> mark#(tt()) active#(isQid(u())) -> mark#(tt()) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> U12#(mark(X)) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> U22#(mark(X1),X2) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) mark#(isList(X)) -> active#(isList(X)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> U23#(mark(X)) mark#(U23(X)) -> active#(U23(mark(X))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> U32#(mark(X)) mark#(U32(X)) -> active#(U32(mark(X))) mark#(isQid(X)) -> active#(isQid(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> U42#(mark(X1),X2) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> U43#(mark(X)) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> U52#(mark(X1),X2) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> U53#(mark(X)) mark#(U53(X)) -> active#(U53(mark(X))) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> U71#(mark(X1),X2) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> U72#(mark(X)) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) mark#(a()) -> active#(a()) mark#(e()) -> active#(e()) mark#(i()) -> active#(i()) mark#(o()) -> active#(o()) mark#(u()) -> active#(u()) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U12#(mark(X)) -> U12#(X) U12#(active(X)) -> U12#(X) isNeList#(mark(X)) -> isNeList#(X) isNeList#(active(X)) -> isNeList#(X) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) isList#(mark(X)) -> isList#(X) isList#(active(X)) -> isList#(X) U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U32#(mark(X)) -> U32#(X) U32#(active(X)) -> U32#(X) isQid#(mark(X)) -> isQid#(X) isQid#(active(X)) -> isQid#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U42#(mark(X1),X2) -> U42#(X1,X2) U42#(X1,mark(X2)) -> U42#(X1,X2) U42#(active(X1),X2) -> U42#(X1,X2) U42#(X1,active(X2)) -> U42#(X1,X2) U43#(mark(X)) -> U43#(X) U43#(active(X)) -> U43#(X) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) U51#(active(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) U52#(mark(X1),X2) -> U52#(X1,X2) U52#(X1,mark(X2)) -> U52#(X1,X2) U52#(active(X1),X2) -> U52#(X1,X2) U52#(X1,active(X2)) -> U52#(X1,X2) U53#(mark(X)) -> U53#(X) U53#(active(X)) -> U53#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U71#(X1,mark(X2)) -> U71#(X1,X2) U71#(active(X1),X2) -> U71#(X1,X2) U71#(X1,active(X2)) -> U71#(X1,X2) U72#(mark(X)) -> U72#(X) U72#(active(X)) -> U72#(X) isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) isPalListKind#(mark(X)) -> isPalListKind#(X) isPalListKind#(active(X)) -> isPalListKind#(X) isPal#(mark(X)) -> isPal#(X) isPal#(active(X)) -> isPal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) graph: ... SCC Processor: #sccs: 26 #rules: 175 #arcs: 7929/59049 DPs: mark#(u()) -> active#(u()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(X,nil())) -> mark#(X) mark#(nil()) -> active#(nil()) active#(__(nil(),X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) mark#(tt()) -> active#(tt()) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(U61(tt(),V)) -> mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isList(nil())) -> mark#(tt()) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) active#(isList(__(V1,V2))) -> mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNeList(__(V1,V2))) -> mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isNeList(__(V1,V2))) -> mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) mark#(a()) -> active#(a()) active#(isNePal(__(I,__(P,I)))) -> mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) mark#(e()) -> active#(e()) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) mark#(i()) -> active#(i()) active#(isPal(nil())) -> mark#(tt()) mark#(o()) -> active#(o()) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(e())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) active#(isQid(o())) -> mark#(tt()) active#(isQid(u())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 1, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 1, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 1, [nil] = 1, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: mark#(u()) = 1 >= 1 = active#(u()) active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = mark#(X2) mark#(__(X1,X2)) = 1 >= 1 = mark#(X1) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(__(X,nil())) = 1 >= 1 = mark#(X) mark#(nil()) = 1 >= 1 = active#(nil()) active#(__(nil(),X)) = 1 >= 1 = mark#(X) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) mark#(tt()) = 1 >= 1 = active#(tt()) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(isQid(X)) = 1 >= 1 = active#(isQid(X)) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) active#(U61(tt(),V)) = 1 >= 1 = mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(U72(tt())) = 1 >= 1 = mark#(tt()) mark#(U61(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U61(X1,X2)) = 1 >= 1 = active#(U61(mark(X1),X2)) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) active#(isList(nil())) = 1 >= 1 = mark#(tt()) mark#(U72(X)) = 1 >= 1 = mark#(X) mark#(U72(X)) = 1 >= 1 = active#(U72(mark(X))) active#(isList(__(V1,V2))) = 1 >= 1 = mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) active#(isNeList(__(V1,V2))) = 1 >= 1 = mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) active#(isNeList(__(V1,V2))) = 1 >= 1 = mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPal(X)) = 1 >= 1 = active#(isPal(X)) active#(isNePal(V)) = 1 >= 1 = mark#(U61(isPalListKind(V),V)) mark#(a()) = 1 >= 1 = active#(a()) active#(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) mark#(e()) = 1 >= 0 = active#(e()) active#(isPal(V)) = 1 >= 1 = mark#(U71(isPalListKind(V),V)) mark#(i()) = 1 >= 1 = active#(i()) active#(isPal(nil())) = 1 >= 1 = mark#(tt()) mark#(o()) = 1 >= 1 = active#(o()) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 1 >= 1 = mark#(tt()) active#(isQid(e())) = 1 >= 1 = mark#(tt()) active#(isQid(i())) = 1 >= 1 = mark#(tt()) active#(isQid(o())) = 1 >= 1 = mark#(tt()) active#(isQid(u())) = 1 >= 1 = mark#(tt()) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: mark#(u()) -> active#(u()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(X,nil())) -> mark#(X) mark#(nil()) -> active#(nil()) active#(__(nil(),X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) mark#(tt()) -> active#(tt()) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(U61(tt(),V)) -> mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isList(nil())) -> mark#(tt()) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) active#(isList(__(V1,V2))) -> mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNeList(__(V1,V2))) -> mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isNeList(__(V1,V2))) -> mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) mark#(a()) -> active#(a()) active#(isNePal(__(I,__(P,I)))) -> mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) mark#(i()) -> active#(i()) active#(isPal(nil())) -> mark#(tt()) mark#(o()) -> active#(o()) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(e())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) active#(isQid(o())) -> mark#(tt()) active#(isQid(u())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x0 + x1, [U62](x0) = x0, [U61](x0, x1) = x0 + x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x0 + x1, [U23](x0) = x0, [U22](x0, x1) = x0 + x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0 + x1 + x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: mark#(u()) = 0 >= 0 = active#(u()) active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X2 = mark#(X2) mark#(__(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(__(X,nil())) = X >= X = mark#(X) mark#(nil()) = 0 >= 0 = active#(nil()) active#(__(nil(),X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V >= V = mark#(U12(isNeList(V))) mark#(tt()) = 0 >= 0 = active#(tt()) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U22(tt(),V2)) = V2 >= V2 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = V >= V = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(isQid(X)) = X >= X = active#(isQid(X)) active#(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) active#(U61(tt(),V)) = V >= V = mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = V >= V = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(U72(tt())) = 0 >= 0 = mark#(tt()) mark#(U61(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U61(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U61(mark(X1),X2)) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U71(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U71(mark(X1),X2)) active#(isList(nil())) = 0 >= 0 = mark#(tt()) mark#(U72(X)) = X >= X = mark#(X) mark#(U72(X)) = X >= X = active#(U72(mark(X))) active#(isList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isNePal(X)) = X >= X = active#(isNePal(X)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) active#(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) active#(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPal(X)) = X >= X = active#(isPal(X)) active#(isNePal(V)) = V >= V = mark#(U61(isPalListKind(V),V)) mark#(a()) = 0 >= 0 = active#(a()) active#(isNePal(__(I,__(P,I)))) = 2I + P >= I + P = mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active#(isPal(V)) = V >= V = mark#(U71(isPalListKind(V),V)) mark#(i()) = 0 >= 0 = active#(i()) active#(isPal(nil())) = 0 >= 0 = mark#(tt()) mark#(o()) = 0 >= 0 = active#(o()) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 0 >= 0 = mark#(tt()) active#(isQid(e())) = 1 >= 0 = mark#(tt()) active#(isQid(i())) = 0 >= 0 = mark#(tt()) active#(isQid(o())) = 0 >= 0 = mark#(tt()) active#(isQid(u())) = 0 >= 0 = mark#(tt()) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= V2 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= V = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= V = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= V = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= V = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P >= I + P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= V = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = X >= X = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = X1 + X2 >= X1 + X2 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = X1 + X2 >= X1 + X2 = active(U71(mark(X1),X2)) mark(U72(X)) = X >= X = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = X >= X = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) U31(mark(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(active(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,active(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = X1 + X2 >= X1 + X2 = U61(X1,X2) U61(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U61(X1,X2) U61(active(X1),X2) = X1 + X2 >= X1 + X2 = U61(X1,X2) U61(X1,active(X2)) = X1 + X2 >= X1 + X2 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = X1 + X2 >= X1 + X2 = U71(X1,X2) U71(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U71(X1,X2) U71(active(X1),X2) = X1 + X2 >= X1 + X2 = U71(X1,X2) U71(X1,active(X2)) = X1 + X2 >= X1 + X2 = U71(X1,X2) U72(mark(X)) = X >= X = U72(X) U72(active(X)) = X >= X = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = X >= X = isPal(X) isPal(active(X)) = X >= X = isPal(X) problem: DPs: mark#(u()) -> active#(u()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(X,nil())) -> mark#(X) mark#(nil()) -> active#(nil()) active#(__(nil(),X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) mark#(tt()) -> active#(tt()) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(U61(tt(),V)) -> mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isList(nil())) -> mark#(tt()) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) active#(isList(__(V1,V2))) -> mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNeList(__(V1,V2))) -> mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isNeList(__(V1,V2))) -> mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) mark#(a()) -> active#(a()) active#(isNePal(__(I,__(P,I)))) -> mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) mark#(i()) -> active#(i()) active#(isPal(nil())) -> mark#(tt()) mark#(o()) -> active#(o()) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) active#(isQid(o())) -> mark#(tt()) active#(isQid(u())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x0 + x1, [U62](x0) = x0, [U61](x0, x1) = x0 + x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x0 + x1, [U23](x0) = x0, [U22](x0, x1) = x0 + x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0 + x1 + x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(u()) = 1 >= 1 = active#(u()) active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X2 = mark#(X2) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(__(X,nil())) = X + 1 >= X = mark#(X) mark#(nil()) = 0 >= 0 = active#(nil()) active#(__(nil(),X)) = X + 1 >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V >= V = mark#(U12(isNeList(V))) mark#(tt()) = 0 >= 0 = active#(tt()) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U22(tt(),V2)) = V2 >= V2 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = V >= V = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(isQid(X)) = X >= X = active#(isQid(X)) active#(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) active#(U61(tt(),V)) = V >= V = mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = V >= V = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(U72(tt())) = 0 >= 0 = mark#(tt()) mark#(U61(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U61(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U61(mark(X1),X2)) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U71(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U71(mark(X1),X2)) active#(isList(nil())) = 0 >= 0 = mark#(tt()) mark#(U72(X)) = X >= X = mark#(X) mark#(U72(X)) = X >= X = active#(U72(mark(X))) active#(isList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isNePal(X)) = X >= X = active#(isNePal(X)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) active#(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) active#(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) mark#(isPal(X)) = X >= X = active#(isPal(X)) active#(isNePal(V)) = V >= V = mark#(U61(isPalListKind(V),V)) mark#(a()) = 0 >= 0 = active#(a()) active#(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= I + P = mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active#(isPal(V)) = V >= V = mark#(U71(isPalListKind(V),V)) mark#(i()) = 0 >= 0 = active#(i()) active#(isPal(nil())) = 0 >= 0 = mark#(tt()) mark#(o()) = 0 >= 0 = active#(o()) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 0 >= 0 = mark#(tt()) active#(isQid(i())) = 0 >= 0 = mark#(tt()) active#(isQid(o())) = 0 >= 0 = mark#(tt()) active#(isQid(u())) = 1 >= 0 = mark#(tt()) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= V2 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= V = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= V = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= V = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= V = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= I + P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= V = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 1 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = X >= X = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = X1 + X2 >= X1 + X2 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = X1 + X2 >= X1 + X2 = active(U71(mark(X1),X2)) mark(U72(X)) = X >= X = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = X >= X = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) U31(mark(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(active(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,active(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = X1 + X2 >= X1 + X2 = U61(X1,X2) U61(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U61(X1,X2) U61(active(X1),X2) = X1 + X2 >= X1 + X2 = U61(X1,X2) U61(X1,active(X2)) = X1 + X2 >= X1 + X2 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = X1 + X2 >= X1 + X2 = U71(X1,X2) U71(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U71(X1,X2) U71(active(X1),X2) = X1 + X2 >= X1 + X2 = U71(X1,X2) U71(X1,active(X2)) = X1 + X2 >= X1 + X2 = U71(X1,X2) U72(mark(X)) = X >= X = U72(X) U72(active(X)) = X >= X = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = X >= X = isPal(X) isPal(active(X)) = X >= X = isPal(X) problem: DPs: mark#(u()) -> active#(u()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) mark#(tt()) -> active#(tt()) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(U61(tt(),V)) -> mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isList(nil())) -> mark#(tt()) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) mark#(a()) -> active#(a()) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) mark#(i()) -> active#(i()) active#(isPal(nil())) -> mark#(tt()) mark#(o()) -> active#(o()) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) active#(isQid(o())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 1, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 1, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 1, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 1, [nil] = 1, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = 1 orientation: mark#(u()) = 1 >= 1 = active#(u()) active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(nil()) = 1 >= 1 = active#(nil()) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) mark#(tt()) = 1 >= 1 = active#(tt()) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(isQid(X)) = 1 >= 1 = active#(isQid(X)) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) active#(U61(tt(),V)) = 1 >= 1 = mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(U72(tt())) = 1 >= 1 = mark#(tt()) mark#(U61(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U61(X1,X2)) = 1 >= 1 = active#(U61(mark(X1),X2)) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) active#(isList(nil())) = 1 >= 1 = mark#(tt()) mark#(U72(X)) = 1 >= 1 = mark#(X) mark#(U72(X)) = 1 >= 1 = active#(U72(mark(X))) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) mark#(isPal(X)) = 1 >= 1 = active#(isPal(X)) active#(isNePal(V)) = 1 >= 1 = mark#(U61(isPalListKind(V),V)) mark#(a()) = 1 >= 0 = active#(a()) active#(isPal(V)) = 1 >= 1 = mark#(U71(isPalListKind(V),V)) mark#(i()) = 1 >= 0 = active#(i()) active#(isPal(nil())) = 1 >= 1 = mark#(tt()) mark#(o()) = 1 >= 1 = active#(o()) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 1 >= 1 = mark#(tt()) active#(isQid(i())) = 1 >= 1 = mark#(tt()) active#(isQid(o())) = 1 >= 1 = mark#(tt()) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = 1 >= 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X)) = 1 >= 1 = active(U12(mark(X))) mark(isNeList(X)) = 1 >= 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = 1 >= 1 = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X)) = 1 >= 1 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 1 >= 1 = active(U42(mark(X1),X2)) mark(U43(X)) = 1 >= 1 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 1 >= 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 1 >= 1 = active(U52(mark(X1),X2)) mark(U53(X)) = 1 >= 1 = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = 1 >= 1 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 1 >= 1 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 1 >= 0 = active(a()) mark(e()) = 1 >= 0 = active(e()) mark(i()) = 1 >= 0 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: mark#(u()) -> active#(u()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) mark#(tt()) -> active#(tt()) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(U61(tt(),V)) -> mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isList(nil())) -> mark#(tt()) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPal(nil())) -> mark#(tt()) mark#(o()) -> active#(o()) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) active#(isQid(o())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 1, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 1, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: mark#(u()) = 1 >= 1 = active#(u()) active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(nil()) = 1 >= 0 = active#(nil()) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) mark#(tt()) = 1 >= 0 = active#(tt()) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(isQid(X)) = 1 >= 1 = active#(isQid(X)) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) active#(U61(tt(),V)) = 1 >= 1 = mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(U72(tt())) = 1 >= 1 = mark#(tt()) mark#(U61(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U61(X1,X2)) = 1 >= 1 = active#(U61(mark(X1),X2)) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) active#(isList(nil())) = 1 >= 1 = mark#(tt()) mark#(U72(X)) = 1 >= 1 = mark#(X) mark#(U72(X)) = 1 >= 1 = active#(U72(mark(X))) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) mark#(isPal(X)) = 1 >= 1 = active#(isPal(X)) active#(isNePal(V)) = 1 >= 1 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = 1 >= 1 = mark#(U71(isPalListKind(V),V)) active#(isPal(nil())) = 1 >= 1 = mark#(tt()) mark#(o()) = 1 >= 0 = active#(o()) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 1 >= 1 = mark#(tt()) active#(isQid(i())) = 1 >= 1 = mark#(tt()) active#(isQid(o())) = 1 >= 1 = mark#(tt()) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: mark#(u()) -> active#(u()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(U61(tt(),V)) -> mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isList(nil())) -> mark#(tt()) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPal(nil())) -> mark#(tt()) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) active#(isQid(o())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 1, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 1, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = 1 orientation: mark#(u()) = 1 >= 0 = active#(u()) active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(isQid(X)) = 1 >= 1 = active#(isQid(X)) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) active#(U61(tt(),V)) = 1 >= 1 = mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(U72(tt())) = 1 >= 1 = mark#(tt()) mark#(U61(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U61(X1,X2)) = 1 >= 1 = active#(U61(mark(X1),X2)) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) active#(isList(nil())) = 1 >= 1 = mark#(tt()) mark#(U72(X)) = 1 >= 1 = mark#(X) mark#(U72(X)) = 1 >= 1 = active#(U72(mark(X))) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) mark#(isPal(X)) = 1 >= 1 = active#(isPal(X)) active#(isNePal(V)) = 1 >= 1 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = 1 >= 1 = mark#(U71(isPalListKind(V),V)) active#(isPal(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 1 >= 1 = mark#(tt()) active#(isQid(i())) = 1 >= 1 = mark#(tt()) active#(isQid(o())) = 1 >= 1 = mark#(tt()) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = 1 >= 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 0 = active(nil()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 0 = active(tt()) mark(U12(X)) = 1 >= 1 = active(U12(mark(X))) mark(isNeList(X)) = 1 >= 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = 1 >= 1 = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X)) = 1 >= 1 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 1 >= 1 = active(U42(mark(X1),X2)) mark(U43(X)) = 1 >= 1 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 1 >= 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 1 >= 1 = active(U52(mark(X1),X2)) mark(U53(X)) = 1 >= 1 = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = 1 >= 1 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 1 >= 1 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 1 >= 0 = active(a()) mark(e()) = 1 >= 0 = active(e()) mark(i()) = 1 >= 0 = active(i()) mark(o()) = 1 >= 0 = active(o()) mark(u()) = 1 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(U61(tt(),V)) -> mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isList(nil())) -> mark#(tt()) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPal(nil())) -> mark#(tt()) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) active#(isQid(o())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0 + 1, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x0 + x1 + 1, [U62](x0) = x0, [U61](x0, x1) = x0 + x1 + 1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x0 + x1, [U23](x0) = x0, [U22](x0, x1) = x0 + x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0 + x1 + x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V >= V = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U22(tt(),V2)) = V2 >= V2 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = V >= V = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(isQid(X)) = X >= X = active#(isQid(X)) active#(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) active#(U61(tt(),V)) = V + 1 >= V = mark#(U62(isQid(V))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = V + 1 >= V + 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(U72(tt())) = 0 >= 0 = mark#(tt()) mark#(U61(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U61(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U61(mark(X1),X2)) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U71(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U71(mark(X1),X2)) active#(isList(nil())) = 0 >= 0 = mark#(tt()) mark#(U72(X)) = X >= X = mark#(X) mark#(U72(X)) = X >= X = active#(U72(mark(X))) mark#(isNePal(X)) = X + 1 >= X + 1 = active#(isNePal(X)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) mark#(isPal(X)) = X + 1 >= X + 1 = active#(isPal(X)) active#(isNePal(V)) = V + 1 >= V + 1 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = V + 1 >= V + 1 = mark#(U71(isPalListKind(V),V)) active#(isPal(nil())) = 1 >= 0 = mark#(tt()) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 0 >= 0 = mark#(tt()) active#(isQid(i())) = 0 >= 0 = mark#(tt()) active#(isQid(o())) = 1 >= 0 = mark#(tt()) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= V2 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= V = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= V = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V + 1 >= V + 1 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= V + 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= I + P + 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= V + 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = X >= X = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U71(mark(X1),X2)) mark(U72(X)) = X >= X = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = X + 1 >= X + 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) U31(mark(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(active(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,active(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(X1,X2) U61(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(X1,X2) U61(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(X1,X2) U61(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U71(X1,X2) U71(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U71(X1,X2) U71(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U71(X1,X2) U71(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U71(X1,X2) U72(mark(X)) = X >= X = U72(X) U72(active(X)) = X >= X = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = X + 1 >= X + 1 = isPal(X) isPal(active(X)) = X + 1 >= X + 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isList(nil())) -> mark#(tt()) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = x0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0 + x1, [U23](x0) = x0, [U22](x0, x1) = x0 + x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0 + x1 + x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V >= V = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U22(tt(),V2)) = V2 >= V2 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = V >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(isQid(X)) = 0 >= 0 = active#(isQid(X)) active#(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 0 >= 0 = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(U72(tt())) = 0 >= 0 = mark#(tt()) mark#(U61(X1,X2)) = 0 >= 0 = active#(U61(mark(X1),X2)) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 0 >= 0 = active#(U71(mark(X1),X2)) active#(isList(nil())) = 1 >= 0 = mark#(tt()) mark#(U72(X)) = X >= X = mark#(X) mark#(U72(X)) = X >= X = active#(U72(mark(X))) mark#(isNePal(X)) = 0 >= 0 = active#(isNePal(X)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) mark#(isPal(X)) = 0 >= 0 = active#(isPal(X)) active#(isNePal(V)) = 0 >= 0 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = 0 >= 0 = mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 0 >= 0 = mark#(tt()) active#(isQid(i())) = 0 >= 0 = mark#(tt()) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= V2 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = X >= X = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) U31(mark(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(active(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,active(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = X >= X = U72(X) U72(active(X)) = X >= X = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 1, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(isQid(X)) = 1 >= 1 = active#(isQid(X)) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(U72(tt())) = 1 >= 1 = mark#(tt()) mark#(U61(X1,X2)) = 1 >= 0 = active#(U61(mark(X1),X2)) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) mark#(U72(X)) = 1 >= 1 = mark#(X) mark#(U72(X)) = 1 >= 1 = active#(U72(mark(X))) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) mark#(isPal(X)) = 1 >= 1 = active#(isPal(X)) active#(isNePal(V)) = 1 >= 1 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = 1 >= 1 = mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 1 >= 1 = mark#(tt()) active#(isQid(i())) = 1 >= 1 = mark#(tt()) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) -> mark#(tt()) active#(isQid(i())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 1, [isPal](x0) = x0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x0 + x1, [U23](x0) = x0, [U22](x0, x1) = x0 + x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0 + x1 + x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V >= V = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U22(tt(),V2)) = V2 >= V2 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = V >= V = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(isQid(X)) = X >= X = active#(isQid(X)) active#(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = V >= V = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(U72(tt())) = 0 >= 0 = mark#(tt()) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = X2 >= X2 = active#(U71(mark(X1),X2)) mark#(U72(X)) = X >= X = mark#(X) mark#(U72(X)) = X >= X = active#(U72(mark(X))) mark#(isNePal(X)) = X >= X = active#(isNePal(X)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) mark#(isPal(X)) = X >= X = active#(isPal(X)) active#(isNePal(V)) = V >= V = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = V >= V = mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(a())) = 1 >= 0 = mark#(tt()) active#(isQid(i())) = 0 >= 0 = mark#(tt()) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= V2 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= V = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= V = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= V = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= V = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P >= I + P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= V = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = X >= X = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = X2 >= X2 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = X2 >= X2 = active(U71(mark(X1),X2)) mark(U72(X)) = X >= X = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = X >= X = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) U31(mark(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(active(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,active(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = X2 >= X2 = U61(X1,X2) U61(X1,mark(X2)) = X2 >= X2 = U61(X1,X2) U61(active(X1),X2) = X2 >= X2 = U61(X1,X2) U61(X1,active(X2)) = X2 >= X2 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = X2 >= X2 = U71(X1,X2) U71(X1,mark(X2)) = X2 >= X2 = U71(X1,X2) U71(active(X1),X2) = X2 >= X2 = U71(X1,X2) U71(X1,active(X2)) = X2 >= X2 = U71(X1,X2) U72(mark(X)) = X >= X = U72(X) U72(active(X)) = X >= X = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = X >= X = isPal(X) isPal(active(X)) = X >= X = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(i())) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 0, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = x0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x0 + x1, [U23](x0) = x0, [U22](x0, x1) = x0 + x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0 + x1 + x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V >= V = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U22(tt(),V2)) = V2 >= V2 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = V >= V = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(isQid(X)) = X >= X = active#(isQid(X)) active#(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = V >= V = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(U72(tt())) = 0 >= 0 = mark#(tt()) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = X2 >= X2 = active#(U71(mark(X1),X2)) mark#(U72(X)) = X >= X = mark#(X) mark#(U72(X)) = X >= X = active#(U72(mark(X))) mark#(isNePal(X)) = X >= X = active#(isNePal(X)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) mark#(isPal(X)) = X >= X = active#(isPal(X)) active#(isNePal(V)) = V >= V = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = V >= V = mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active#(isQid(i())) = 1 >= 0 = mark#(tt()) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= V2 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= V = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= V = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= V = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= V = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P >= I + P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= V = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 1 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = X >= X = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = X2 >= X2 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = X2 >= X2 = active(U71(mark(X1),X2)) mark(U72(X)) = X >= X = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = X >= X = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) U31(mark(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(active(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,active(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = X2 >= X2 = U61(X1,X2) U61(X1,mark(X2)) = X2 >= X2 = U61(X1,X2) U61(active(X1),X2) = X2 >= X2 = U61(X1,X2) U61(X1,active(X2)) = X2 >= X2 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = X2 >= X2 = U71(X1,X2) U71(X1,mark(X2)) = X2 >= X2 = U71(X1,X2) U71(active(X1),X2) = X2 >= X2 = U71(X1,X2) U71(X1,active(X2)) = X2 >= X2 = U71(X1,X2) U72(mark(X)) = X >= X = U72(X) U72(active(X)) = X >= X = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = X >= X = isPal(X) isPal(active(X)) = X >= X = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 1, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = 1, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(isQid(X)) = 1 >= 0 = active#(isQid(X)) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(U72(tt())) = 1 >= 1 = mark#(tt()) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) mark#(U72(X)) = 1 >= 1 = mark#(X) mark#(U72(X)) = 1 >= 1 = active#(U72(mark(X))) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) mark#(isPal(X)) = 1 >= 1 = active#(isPal(X)) active#(isNePal(V)) = 1 >= 1 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = 1 >= 1 = mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = 1 >= 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X)) = 1 >= 1 = active(U12(mark(X))) mark(isNeList(X)) = 1 >= 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = 1 >= 1 = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X)) = 1 >= 1 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 1 >= 1 = active(U42(mark(X1),X2)) mark(U43(X)) = 1 >= 1 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 1 >= 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 1 >= 1 = active(U52(mark(X1),X2)) mark(U53(X)) = 1 >= 1 = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = 1 >= 1 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 1 >= 1 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U23(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(U72(tt())) -> mark#(tt()) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X)) -> mark#(X) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0 + 1, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0 + 1, [isNePal](x0) = x0, [U71](x0, x1) = x1 + 1, [U62](x0) = x0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0 + x1, [U23](x0) = x0 + 1, [U22](x0, x1) = x0 + x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x0 + x1 + x2 + 1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V >= V = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U22(tt(),V2)) = V2 + 1 >= V2 + 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active#(U21(mark(X1),X2,X3)) active#(U23(tt())) = 1 >= 0 = mark#(tt()) mark#(U22(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = V >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U23(X)) = X + 1 >= X = mark#(X) mark#(U23(X)) = X + 1 >= X + 1 = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = V + 1 >= V + 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(U72(tt())) = 1 >= 0 = mark#(tt()) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U71(mark(X1),X2)) mark#(U72(X)) = X + 1 >= X = mark#(X) mark#(U72(X)) = X + 1 >= X + 1 = active#(U72(mark(X))) mark#(isNePal(X)) = X >= X = active#(isNePal(X)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) mark#(isPal(X)) = X + 1 >= X + 1 = active#(isPal(X)) active#(isNePal(V)) = V >= 0 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = V + 1 >= V + 1 = mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X = mark(X) active(__(nil(),X)) = X + 2 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V + 1 >= V + 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= P + 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= V + 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 2 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = X + 1 >= X + 1 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = X2 + 1 >= X2 + 1 = active(U71(mark(X1),X2)) mark(U72(X)) = X + 1 >= X + 1 = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = X + 1 >= X + 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = X + 1 >= X + 1 = U23(X) U23(active(X)) = X + 1 >= X + 1 = U23(X) U31(mark(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(active(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,active(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = X2 + 1 >= X2 + 1 = U71(X1,X2) U71(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U71(X1,X2) U71(active(X1),X2) = X2 + 1 >= X2 + 1 = U71(X1,X2) U71(X1,active(X2)) = X2 + 1 >= X2 + 1 = U71(X1,X2) U72(mark(X)) = X + 1 >= X + 1 = U72(X) U72(active(X)) = X + 1 >= X + 1 = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = X + 1 >= X + 1 = isPal(X) isPal(active(X)) = X + 1 >= X + 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U23(X)) -> active#(U23(mark(X))) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 1, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 1, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U23(X)) = 1 >= 0 = active#(U23(mark(X))) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) mark#(U72(X)) = 1 >= 1 = active#(U72(mark(X))) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) mark#(isPal(X)) = 1 >= 1 = active#(isPal(X)) active#(isNePal(V)) = 1 >= 1 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = 1 >= 1 = mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) mark#(U72(X)) = 1 >= 0 = active#(U72(mark(X))) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) mark#(isPal(X)) = 1 >= 1 = active#(isPal(X)) active#(isNePal(V)) = 1 >= 1 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = 1 >= 1 = mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPal(V)) -> mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 0, [a] = 0, [isPal](x0) = x0 + 1, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0, [U71](x0, x1) = 0, [U62](x0) = x0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= X1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 0 >= 0 = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 0 >= 0 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 0 >= 0 = active#(isNeList(X)) active#(U22(tt(),V2)) = 0 >= 0 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 0 >= 0 = active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = 0 >= 0 = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 0 >= 0 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = 0 >= 0 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 >= X1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 0 >= 0 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 >= X1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 >= X1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 >= X1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 0 >= 0 = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = 0 >= 0 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 0 >= 0 = active#(U71(mark(X1),X2)) mark#(isNePal(X)) = X >= X = active#(isNePal(X)) active#(isNeList(V)) = 0 >= 0 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) mark#(isPal(X)) = X + 1 >= X + 1 = active#(isPal(X)) active#(isNePal(V)) = V >= 0 = mark#(U61(isPalListKind(V),V)) active#(isPal(V)) = V + 1 >= 0 = mark#(U71(isPalListKind(V),V)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= P + 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 >= X1 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 >= X1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 >= X1 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = X + 1 >= X + 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = 0 >= 0 = isNeList(X) isNeList(active(X)) = 0 >= 0 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 0 >= 0 = isList(X) isList(active(X)) = 0 >= 0 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 >= X1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 >= X1 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 >= X1 = U42(X1,X2) U42(X1,mark(X2)) = X1 >= X1 = U42(X1,X2) U42(active(X1),X2) = X1 >= X1 = U42(X1,X2) U42(X1,active(X2)) = X1 >= X1 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 >= X1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 >= X1 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 >= X1 = U52(X1,X2) U52(X1,mark(X2)) = X1 >= X1 = U52(X1,X2) U52(active(X1),X2) = X1 >= X1 = U52(X1,X2) U52(X1,active(X2)) = X1 >= X1 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = X + 1 >= X + 1 = isPal(X) isPal(active(X)) = X + 1 >= X + 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) mark#(isPal(X)) = 1 >= 0 = active#(isPal(X)) active#(isNePal(V)) = 1 >= 1 = mark#(U61(isPalListKind(V),V)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = 0, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= X1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 0 >= 0 = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 0 >= 0 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 0 >= 0 = active#(isNeList(X)) active#(U22(tt(),V2)) = 0 >= 0 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 0 >= 0 = active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = 0 >= 0 = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 0 >= 0 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = 0 >= 0 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 >= X1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 0 >= 0 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 >= X1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 >= X1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 >= X1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 0 >= 0 = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = 0 >= 0 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 0 >= 0 = active#(U71(mark(X1),X2)) mark#(isNePal(X)) = X + 1 >= X + 1 = active#(isNePal(X)) active#(isNeList(V)) = 0 >= 0 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) active#(isNePal(V)) = V + 1 >= V = mark#(U61(isPalListKind(V),V)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= V = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 >= X1 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 >= X1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 >= X1 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = X2 >= X2 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = 0 >= 0 = isNeList(X) isNeList(active(X)) = 0 >= 0 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 0 >= 0 = isList(X) isList(active(X)) = 0 >= 0 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 >= X1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 >= X1 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 >= X1 = U42(X1,X2) U42(X1,mark(X2)) = X1 >= X1 = U42(X1,X2) U42(active(X1),X2) = X1 >= X1 = U42(X1,X2) U42(X1,active(X2)) = X1 >= X1 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 >= X1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 >= X1 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 >= X1 = U52(X1,X2) U52(X1,mark(X2)) = X1 >= X1 = U52(X1,X2) U52(active(X1),X2) = X1 >= X1 = U52(X1,X2) U52(X1,active(X2)) = X1 >= X1 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = X2 >= X2 = U61(X1,X2) U61(X1,mark(X2)) = X2 >= X2 = U61(X1,X2) U61(active(X1),X2) = X2 >= X2 = U61(X1,X2) U61(X1,active(X2)) = X2 >= X2 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 1 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) mark#(isNePal(X)) = 1 >= 0 = active#(isNePal(X)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = 0, [U62](x0) = x0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V >= V = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) active#(U21(tt(),V1,V2)) = 1 >= 0 = mark#(U22(isList(V1),V2)) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U22(tt(),V2)) = 0 >= 0 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 1 = active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 0 >= 0 = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 0 >= 0 = active#(U71(mark(X1),X2)) active#(isNeList(V)) = V >= 0 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 3 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 1 = mark#(U23(isList(V2))) mark#(U21(X1,X2,X3)) = 1 >= 0 = active#(U21(mark(X1),X2,X3)) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U22(tt(),V2)) -> mark#(U23(isList(V2))) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 1, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0, [U71](x0, x1) = 0, [U62](x0) = x0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 1, [isList](x0) = x0, [U21](x0, x1, x2) = 1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V >= V = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U22(tt(),V2)) = 1 >= 0 = mark#(U23(isList(V2))) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 0 >= 0 = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 0 >= 0 = active#(U71(mark(X1),X2)) active#(isNeList(V)) = V >= 0 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 >= X1 + X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) mark#(U22(X1,X2)) = 1 >= 0 = active#(U22(mark(X1),X2)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 1 = mark#(U72(isNePal(V))) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U71(tt(),V)) -> mark#(U72(isNePal(V))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = 1, [U62](x0) = x0, [U61](x0, x1) = 1, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= X1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 0 >= 0 = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = 0 >= 0 = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = 0 >= 0 = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 0 >= 0 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = 0 >= 0 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 >= X1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 0 >= 0 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 >= X1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 >= X1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 >= X1 = active#(U52(mark(X1),X2)) active#(U71(tt(),V)) = 1 >= 0 = mark#(U72(isNePal(V))) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = active#(U62(mark(X))) active#(isList(V)) = 0 >= 0 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 1 = active#(U71(mark(X1),X2)) active#(isNeList(V)) = 0 >= 0 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 1 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 >= X1 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 >= X1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 >= X1 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = 0 >= 0 = isNeList(X) isNeList(active(X)) = 0 >= 0 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 0 >= 0 = isList(X) isList(active(X)) = 0 >= 0 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 >= X1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 >= X1 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 >= X1 = U42(X1,X2) U42(X1,mark(X2)) = X1 >= X1 = U42(X1,X2) U42(active(X1),X2) = X1 >= X1 = U42(X1,X2) U42(X1,active(X2)) = X1 >= X1 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 >= X1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 >= X1 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 >= X1 = U52(X1,X2) U52(X1,mark(X2)) = X1 >= X1 = U52(X1,X2) U52(active(X1),X2) = X1 >= X1 = U52(X1,X2) U52(X1,active(X2)) = X1 >= X1 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = 1 >= 1 = mark#(U12(isNeList(V))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 1 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) mark#(U71(X1,X2)) = 1 >= 0 = active#(U71(mark(X1),X2)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),V)) -> mark#(U12(isNeList(V))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) active#(U62(tt())) -> mark#(tt()) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = 1, [U71](x0, x1) = 0, [U62](x0) = x0 + 1, [U61](x0, x1) = 1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1 + 1, [U51](x0, x1, x2) = x0 + x1 + x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x0 + x1 + x2 + 1, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0 + 1, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0 + x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U11(mark(X1),X2)) active#(U11(tt(),V)) = V + 1 >= V = mark#(U12(isNeList(V))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X + 1 >= X + 1 = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 + 1 >= V2 + 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active#(U51(mark(X1),X2,X3)) active#(U62(tt())) = 1 >= 0 = mark#(tt()) mark#(U52(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U52(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) mark#(U62(X)) = X + 1 >= X = mark#(X) mark#(U62(X)) = X + 1 >= X + 1 = active#(U62(mark(X))) active#(isList(V)) = V + 1 >= V + 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= 0 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V + 1 >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X + 1 >= X + 1 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = X + 1 >= X + 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X + 1 >= X + 1 = isList(X) isList(active(X)) = X + 1 >= X + 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U52(X1,X2) U52(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U52(X1,X2) U52(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U52(X1,X2) U52(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = X + 1 >= X + 1 = U62(X) U62(active(X)) = X + 1 >= X + 1 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) mark#(U62(X)) = 1 >= 0 = active#(U62(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(i())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 1, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = X2 >= X2 = active#(U11(mark(X1),X2)) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V2 >= V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X3 >= X3 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = X2 >= X2 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = X >= X = active#(isPalListKind(X)) active#(isPalListKind(a())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(i())) = 1 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= V2 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= I + P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X3 >= X3 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 >= X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 >= X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X3 >= X3 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X3 >= X3 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X3 >= X3 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X3 >= X3 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X3 >= X3 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X3 >= X3 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 >= X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 >= X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,mark(X2)) = X2 >= X2 = U52(X1,X2) U52(active(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,active(X2)) = X2 >= X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 1, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) mark#(U11(X1,X2)) = 1 >= 0 = active#(U11(mark(X1),X2)) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) active#(isPalListKind(a())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(e())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(u())) = 1 >= 1 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(a())) -> mark#(tt()) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 1, [isPal](x0) = 0, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V2 >= V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X3 >= X3 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = X2 >= X2 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = X >= X = active#(isPalListKind(X)) active#(isPalListKind(a())) = 1 >= 0 = mark#(tt()) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P >= I + P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 >= X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 >= X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 >= X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 >= X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,mark(X2)) = X2 >= X2 = U52(X1,X2) U52(active(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,active(X2)) = X2 >= X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(o())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 1, [i] = 1, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V2 >= V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X3 >= X3 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = X2 >= X2 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = X >= X = active#(isPalListKind(X)) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(o())) = 1 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P >= I + P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 >= X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 >= X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 >= X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 >= X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,mark(X2)) = X2 >= X2 = U52(X1,X2) U52(active(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,active(X2)) = X2 >= X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(nil())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = x0, [isList](x0) = x0, [U21](x0, x1, x2) = x1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V2 >= V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X3 >= X3 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = X2 >= X2 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = X >= X = active#(isPalListKind(X)) active#(isPalListKind(e())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(nil())) = 1 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 >= V1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= V1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= I + P + 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X2 >= X2 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 >= X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 >= X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X2 >= X2 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X2 >= X2 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X2 >= X2 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X2 >= X2 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X2 >= X2 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X2 >= X2 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 >= X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 >= X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,mark(X2)) = X2 >= X2 = U52(X1,X2) U52(active(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,active(X2)) = X2 >= X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(e())) -> mark#(tt()) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 1, [i] = 0, [e] = 1, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = 0, [U62](x0) = 1, [U61](x0, x1) = 1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V2 >= V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X3 >= X3 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = X2 >= X2 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = X >= X = active#(isPalListKind(X)) active#(isPalListKind(e())) = 1 >= 0 = mark#(tt()) active#(isPalListKind(u())) = 0 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= I + P + 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 >= X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 >= X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 >= X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 >= X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,mark(X2)) = X2 >= X2 = U52(X1,X2) U52(active(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,active(X2)) = X2 >= X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(u())) -> mark#(tt()) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = x0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V2 >= V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X3 >= X3 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = X2 >= X2 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = X >= X = active#(isPalListKind(X)) active#(isPalListKind(u())) = 1 >= 0 = mark#(tt()) active#(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P >= I + P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 1 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 >= X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 >= X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 >= X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 >= X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,mark(X2)) = X2 >= X2 = U52(X1,X2) U52(active(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,active(X2)) = X2 >= X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [isPal](x0) = x0 + 1, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 1, [isNePal](x0) = x0, [U71](x0, x1) = 1, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2 + 1, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) active#(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 = mark#(U42(isList(V1),V2)) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V2 >= V2 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X3 >= X3 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = X2 >= X2 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= 0 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X = mark(X) active(__(nil(),X)) = X + 2 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= P + 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 2 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 >= X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 >= X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = X + 1 >= X + 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 >= X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 >= X3 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,mark(X2)) = X2 >= X2 = U52(X1,X2) U52(active(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,active(X2)) = X2 >= X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = X + 1 >= X + 1 = isPal(X) isPal(active(X)) = X + 1 >= X + 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 0, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = 1, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V1,V2)) = 1 >= 1 = mark#(U52(isNeList(V1),V2)) mark#(U41(X1,X2,X3)) = 1 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 1 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = 1 >= 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X)) = 1 >= 1 = active(U12(mark(X))) mark(isNeList(X)) = 1 >= 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = 1 >= 1 = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X)) = 1 >= 1 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 1 >= 1 = active(U42(mark(X1),X2)) mark(U43(X)) = 1 >= 1 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 1 >= 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 1 >= 1 = active(U52(mark(X1),X2)) mark(U53(X)) = 1 >= 1 = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = 1 >= 1 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 1 >= 1 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2)) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = 1, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x1 + x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0 + x1, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = x0, [U21](x0, x1, x2) = x2 + 1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = V >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V1,V2)) = V1 + V2 + 1 >= V2 = mark#(U52(isNeList(V1),V2)) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = X2 >= X2 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 0 >= 0 = active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) = 0 >= 0 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 1 >= V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= V2 + 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 >= X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X3 + 1 >= X3 + 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X3 + 1 >= X3 + 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X3 + 1 >= X3 + 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X3 + 1 >= X3 + 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X3 + 1 >= X3 + 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X3 + 1 >= X3 + 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(active(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,active(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,mark(X2)) = X2 >= X2 = U52(X1,X2) U52(active(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,active(X2)) = X2 >= X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 1, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 0, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 0, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U51(X1,X2,X3)) = 1 >= 0 = active#(U51(mark(X1),X2,X3)) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 1 = active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) = 1 >= 1 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1, [U72](x0) = 1, [isNePal](x0) = x0 + 1, [U71](x0, x1) = 1, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = x0, [U21](x0, x1, x2) = 1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U52(tt(),V2)) = V2 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U52(X1,X2)) = X2 >= X2 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = X >= X = active#(isPalListKind(X)) active#(isPalListKind(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark#(and(isPalListKind(V1),isPalListKind(V2))) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X = mark(X) active(__(nil(),X)) = X + 2 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= V2 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V2 + 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 3 >= I + P + 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 1 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 >= X2 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,mark(X2)) = X2 >= X2 = U52(X1,X2) U52(active(X1),X2) = X2 >= X2 = U52(X1,X2) U52(X1,active(X2)) = X2 >= X2 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 1, [U61](x0, x1) = 1, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 0, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 0, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) active#(U52(tt(),V2)) = 1 >= 1 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U52(X1,X2)) = 1 >= 1 = active#(U52(mark(X1),X2)) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(isPalListKind(X)) = 1 >= 0 = active#(isPalListKind(X)) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) active#(U52(tt(),V2)) -> mark#(U53(isList(V2))) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 0, [i] = 1, [e] = 1, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = 1, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0 + x1, [U23](x0) = 0, [U22](x0, x1) = 1, [isList](x0) = x0, [U21](x0, x1, x2) = x1 + 1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = V >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) active#(U52(tt(),V2)) = V2 + 1 >= V2 = mark#(U53(isList(V2))) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U52(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U52(mark(X1),X2)) mark#(U53(X)) = X >= X = mark#(X) mark#(U53(X)) = X >= X = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= V2 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= V1 + 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V2 + 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 + 1 >= X2 + 1 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(active(X1),X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) U31(X1,active(X2)) = X1 + X2 >= X1 + X2 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 + 1 >= X2 + 1 = U52(X1,X2) U52(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U52(X1,X2) U52(active(X1),X2) = X2 + 1 >= X2 + 1 = U52(X1,X2) U52(X1,active(X2)) = X2 + 1 >= X2 + 1 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = 1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = 1, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U52(X1,X2)) = 1 >= 0 = active#(U52(mark(X1),X2)) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(and(tt(),X)) = 1 >= 1 = mark#(X) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = 1 >= 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X)) = 1 >= 1 = active(U12(mark(X))) mark(isNeList(X)) = 1 >= 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = 1 >= 1 = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X)) = 1 >= 1 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 1 >= 1 = active(U42(mark(X1),X2)) mark(U43(X)) = 1 >= 1 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 1 >= 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 1 >= 1 = active(U52(mark(X1),X2)) mark(U53(X)) = 1 >= 1 = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = 1 >= 1 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 1 >= 1 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) active#(U53(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = x0 + 1, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) active#(U53(tt())) = 1 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U53(X)) = X + 1 >= X = mark#(X) mark#(U53(X)) = X + 1 >= X + 1 = active#(U53(mark(X))) active#(and(tt(),X)) = X >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= 0 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 >= X1 + X2 = active#(and(mark(X1),X2)) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V2 + 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 + 1 >= X2 + 1 = active(U52(mark(X1),X2)) mark(U53(X)) = X + 1 >= X + 1 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 + 1 >= X2 + 1 = U52(X1,X2) U52(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U52(X1,X2) U52(active(X1),X2) = X2 + 1 >= X2 + 1 = U52(X1,X2) U52(X1,active(X2)) = X2 + 1 >= X2 + 1 = U52(X1,X2) U53(mark(X)) = X + 1 >= X + 1 = U53(X) U53(active(X)) = X + 1 >= X + 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U53(X)) -> active#(U53(mark(X))) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1 + 1, [U72](x0) = 0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 1, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2 + 1, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) mark#(U53(X)) = 0 >= 0 = active#(U53(mark(X))) active#(and(tt(),X)) = X + 1 >= X = mark#(X) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(and(mark(X1),X2)) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X = mark(X) active(__(nil(),X)) = X + 2 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X + 1 >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 3 >= I + P + 3 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 1 >= 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2) and(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2) and(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U53(X)) -> active#(U53(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = 0, [U72](x0) = 1, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 1, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U53(X)) = 1 >= 1 = active#(U53(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) mark#(and(X1,X2)) = 1 >= 0 = active#(and(mark(X1),X2)) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U53(X)) -> active#(U53(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = 0, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 0, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = 1, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = 1 >= 1 = mark#(U43(isNeList(V2))) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = active#(U42(mark(X1),X2)) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) mark#(U53(X)) = 1 >= 0 = active#(U53(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = 1 >= 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X)) = 1 >= 1 = active(U12(mark(X))) mark(isNeList(X)) = 1 >= 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = 1 >= 1 = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X)) = 1 >= 1 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 1 >= 1 = active(U42(mark(X1),X2)) mark(U43(X)) = 1 >= 1 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 1 >= 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 1 >= 1 = active(U52(mark(X1),X2)) mark(U53(X)) = 1 >= 1 = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = 1 >= 1 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 1 >= 1 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2))) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x1, [U72](x0) = x0 + 1, [isNePal](x0) = x0, [U71](x0, x1) = x1 + 1, [U62](x0) = 1, [U61](x0, x1) = x0, [U53](x0) = 1, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0 + x1, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = x1 + x2, [U32](x0) = x0, [isQid](x0) = 1, [U31](x0, x1) = x0, [U23](x0) = 1, [U22](x0, x1) = x0, [isList](x0) = x0, [U21](x0, x1, x2) = x1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 1, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U42(tt(),V2)) = V2 + 1 >= V2 = mark#(U43(isNeList(V2))) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U42(mark(X1),X2)) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= V = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 >= V1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 + 1 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + 1 >= V1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = V + 1 >= V + 1 = mark(U72(isNePal(V))) active(U72(tt())) = 2 >= 1 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= V1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= V = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= V = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P >= P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= V + 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 2 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 >= V2 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = X2 >= X2 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 >= X1 + X2 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X1 >= X1 = active(U52(mark(X1),X2)) mark(U53(X)) = 1 >= 1 = active(U53(mark(X))) mark(U61(X1,X2)) = X1 >= X1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = X2 + 1 >= X2 + 1 = active(U71(mark(X1),X2)) mark(U72(X)) = X + 1 >= X + 1 = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X2 >= X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = X + 1 >= X + 1 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = X2 >= X2 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X2 >= X2 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X2 >= X2 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X2 >= X2 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X2 >= X2 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X2 >= X2 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 >= X1 + X2 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 + X2 >= X1 + X2 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 + X2 >= X1 + X2 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 + X2 >= X1 + X2 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 + X2 >= X1 + X2 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 + X2 >= X1 + X2 = U51(X1,X2,X3) U52(mark(X1),X2) = X1 >= X1 = U52(X1,X2) U52(X1,mark(X2)) = X1 >= X1 = U52(X1,X2) U52(active(X1),X2) = X1 >= X1 = U52(X1,X2) U52(X1,active(X2)) = X1 >= X1 = U52(X1,X2) U53(mark(X)) = 1 >= 1 = U53(X) U53(active(X)) = 1 >= 1 = U53(X) U61(mark(X1),X2) = X1 >= X1 = U61(X1,X2) U61(X1,mark(X2)) = X1 >= X1 = U61(X1,X2) U61(active(X1),X2) = X1 >= X1 = U61(X1,X2) U61(X1,active(X2)) = X1 >= X1 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = X2 + 1 >= X2 + 1 = U71(X1,X2) U71(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U71(X1,X2) U71(active(X1),X2) = X2 + 1 >= X2 + 1 = U71(X1,X2) U71(X1,active(X2)) = X2 + 1 >= X2 + 1 = U71(X1,X2) U72(mark(X)) = X + 1 >= X + 1 = U72(X) U72(active(X)) = X + 1 >= X + 1 = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,mark(X2)) = X2 >= X2 = and(X1,X2) and(active(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,active(X2)) = X2 >= X2 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = X + 1 >= X + 1 = isPal(X) isPal(active(X)) = X + 1 >= X + 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2)) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = 0, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 0, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 1 = mark#(tt()) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) mark#(U32(X)) = 1 >= 1 = mark#(X) mark#(U32(X)) = 1 >= 1 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 0 = active#(U42(mark(X1),X2)) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,mark(X2)) = 0 >= 0 = U42(X1,X2) U42(active(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,active(X2)) = 0 >= 0 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U42(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = 1, [isPalListKind](x0) = 0, [and](x0, x1) = x1, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = x0, [U42](x0, x1) = x0 + x1 + 1, [U41](x0, x1, x2) = x1 + x2 + 1, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X >= X = active#(isList(X)) active#(U32(tt())) = 0 >= 0 = mark#(tt()) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) mark#(U32(X)) = X >= X = mark#(X) mark#(U32(X)) = X >= X = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) active#(isList(V)) = V >= V = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V >= 0 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X = mark(X) active(__(nil(),X)) = X + 2 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 + 1 >= V2 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X)) = X >= X = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = X2 >= X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X)) = X >= X = U32(X) U32(active(X)) = X >= X = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) U42(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U42(X1,X2) U42(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U42(X1,X2) U42(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U42(X1,X2) U42(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,mark(X2)) = X2 >= X2 = and(X1,X2) and(active(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,active(X2)) = X2 >= X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) active#(U32(tt())) -> mark#(tt()) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x1, [U72](x0) = 0, [isNePal](x0) = 1, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = x0, [U42](x0, x1) = x1 + 1, [U41](x0, x1, x2) = x2 + 1, [U32](x0) = x0 + 1, [isQid](x0) = 0, [U31](x0, x1) = x0 + 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0 + 1, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0 + 1, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X + 1 >= X + 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = X + 1 >= X + 1 = active#(isList(X)) active#(U32(tt())) = 1 >= 0 = mark#(tt()) mark#(U31(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U31(mark(X1),X2)) mark#(U32(X)) = X + 1 >= X = mark#(X) mark#(U32(X)) = X + 1 >= X + 1 = active#(U32(mark(X))) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) active#(isList(V)) = V + 1 >= V + 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = V + 1 >= 1 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V + 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V2 + 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = X2 + 1 >= X2 + 1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X + 1 >= X + 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X + 1 >= X + 1 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + 1 >= X1 + 1 = active(U31(mark(X1),X2)) mark(U32(X)) = X + 1 >= X + 1 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X2 + 1 >= X2 + 1 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = X2 >= X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(active(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,active(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X + 1 >= X + 1 = isNeList(X) isNeList(active(X)) = X + 1 >= X + 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X + 1 >= X + 1 = isList(X) isList(active(X)) = X + 1 >= X + 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = U31(X1,X2) U31(X1,mark(X2)) = X1 + 1 >= X1 + 1 = U31(X1,X2) U31(active(X1),X2) = X1 + 1 >= X1 + 1 = U31(X1,X2) U31(X1,active(X2)) = X1 + 1 >= X1 + 1 = U31(X1,X2) U32(mark(X)) = X + 1 >= X + 1 = U32(X) U32(active(X)) = X + 1 >= X + 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U42(mark(X1),X2) = X2 + 1 >= X2 + 1 = U42(X1,X2) U42(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U42(X1,X2) U42(active(X1),X2) = X2 + 1 >= X2 + 1 = U42(X1,X2) U42(X1,active(X2)) = X2 + 1 >= X2 + 1 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,mark(X2)) = X2 >= X2 = and(X1,X2) and(active(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,active(X2)) = X2 >= X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X)) -> active#(U32(mark(X))) active#(U43(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and( isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and( isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and( isPalListKind(V1), isPalListKind (V2)), V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 1, [and](x0, x1) = 0, [U72](x0) = 1, [isNePal](x0) = 0, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 0, [U43](x0) = 1, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 0, [U32](x0) = 0, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 1 = active#(isList(X)) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) mark#(U32(X)) = 1 >= 0 = active#(U32(mark(X))) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) active#(isList(V)) = 1 >= 1 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 0 >= 0 = U32(X) U32(active(X)) = 0 >= 0 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,mark(X2)) = 0 >= 0 = U42(X1,X2) U42(active(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,active(X2)) = 0 >= 0 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,mark(X2)) = 1 >= 1 = U52(X1,X2) U52(active(X1),X2) = 1 >= 1 = U52(X1,X2) U52(X1,active(X2)) = 1 >= 1 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,mark(X2)) = 1 >= 1 = U71(X1,X2) U71(active(X1),X2) = 1 >= 1 = U71(X1,X2) U71(X1,active(X2)) = 1 >= 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U43(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(isList(V)) -> mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark(U51(and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = 0, [and](x0, x1) = x1, [U72](x0) = 0, [isNePal](x0) = 1, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = x0, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 0, [U32](x0) = 0, [isQid](x0) = 1, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0 + 1, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = 0 >= 0 = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(isList(X)) = X + 1 >= X + 1 = active#(isList(X)) mark#(U31(X1,X2)) = 0 >= 0 = active#(U31(mark(X1),X2)) active#(U43(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X)) = X >= X = mark#(X) mark#(U43(X)) = X >= X = active#(U43(mark(X))) active#(isList(V)) = V + 1 >= 0 = mark#(U11(isPalListKind(V),V)) active#(isNeList(V)) = 0 >= 0 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 1 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X + 1 >= X + 1 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = X2 >= X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = X >= X = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = 0 >= 0 = isNeList(X) isNeList(active(X)) = 0 >= 0 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X + 1 >= X + 1 = isList(X) isList(active(X)) = X + 1 >= X + 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X)) = 0 >= 0 = U32(X) U32(active(X)) = 0 >= 0 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,mark(X2)) = 0 >= 0 = U42(X1,X2) U42(active(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,active(X2)) = 0 >= 0 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,mark(X2)) = X2 >= X2 = and(X1,X2) and(active(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,active(X2)) = X2 >= X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = X >= X = isPal(X) isPal(active(X)) = X >= X = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(isList(X)) -> active#(isList(X)) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U43(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark(U51(and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = 0, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = 1, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 0, [U32](x0) = 1, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 0, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = 1, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(isList(X)) = 1 >= 0 = active#(isList(X)) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U43(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(U43(X)) = 1 >= 1 = active#(U43(mark(X))) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = 1 >= 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X)) = 1 >= 1 = active(U12(mark(X))) mark(isNeList(X)) = 1 >= 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isList(X)) = 1 >= 1 = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X)) = 1 >= 1 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 1 >= 1 = active(U42(mark(X1),X2)) mark(U43(X)) = 1 >= 1 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 1 >= 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 1 >= 1 = active(U52(mark(X1),X2)) mark(U53(X)) = 1 >= 1 = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 1 >= 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = 1 >= 1 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 1 >= 1 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 0 >= 0 = isList(X) isList(active(X)) = 0 >= 0 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,mark(X2)) = 0 >= 0 = U42(X1,X2) U42(active(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,active(X2)) = 0 >= 0 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U43(tt())) -> mark#(tt()) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> active#(U43(mark(X))) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark(U51(and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [isPal](x0) = 0, [isPalListKind](x0) = 1, [and](x0, x1) = x1, [U72](x0) = 0, [isNePal](x0) = x0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = x0, [U43](x0) = x0 + 1, [U42](x0, x1) = x1 + 1, [U41](x0, x1, x2) = x2 + 1, [U32](x0) = 0, [isQid](x0) = 1, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0, [U21](x0, x1, x2) = 0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X >= X = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(U31(X1,X2)) = 0 >= 0 = active#(U31(mark(X1),X2)) active#(U43(tt())) = 1 >= 0 = mark#(tt()) mark#(U43(X)) = X + 1 >= X = mark#(X) mark#(U43(X)) = X + 1 >= X + 1 = active#(U43(mark(X))) active#(isNeList(V)) = V >= 0 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X = mark(X) active(__(nil(),X)) = X + 2 >= X = mark(X) active(U11(tt(),V)) = V >= V = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V2 + 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 1 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 1 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X2 >= X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X >= X = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = X2 + 1 >= X2 + 1 = active(U42(mark(X1),X2)) mark(U43(X)) = X + 1 >= X + 1 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X1 >= X1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(and(X1,X2)) = X2 >= X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 1 >= 1 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,mark(X2)) = X2 >= X2 = U11(X1,X2) U11(active(X1),X2) = X2 >= X2 = U11(X1,X2) U11(X1,active(X2)) = X2 >= X2 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X)) = 0 >= 0 = U32(X) U32(active(X)) = 0 >= 0 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) U42(mark(X1),X2) = X2 + 1 >= X2 + 1 = U42(X1,X2) U42(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U42(X1,X2) U42(active(X1),X2) = X2 + 1 >= X2 + 1 = U42(X1,X2) U42(X1,active(X2)) = X2 + 1 >= X2 + 1 = U42(X1,X2) U43(mark(X)) = X + 1 >= X + 1 = U43(X) U43(active(X)) = X + 1 >= X + 1 = U43(X) U51(mark(X1),X2,X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X1 >= X1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X1 >= X1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X1 >= X1 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) and(mark(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,mark(X2)) = X2 >= X2 = and(X1,X2) and(active(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,active(X2)) = X2 >= X2 = and(X1,X2) isPalListKind(mark(X)) = 1 >= 1 = isPalListKind(X) isPalListKind(active(X)) = 1 >= 1 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U43(X)) -> active#(U43(mark(X))) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark(U51( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and( and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and( isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = 0, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = 0, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 0, [U32](x0) = 0, [isQid](x0) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 0, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isQid(V))) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) mark#(U43(X)) = 1 >= 0 = active#(U43(mark(X))) active#(isNeList(V)) = 1 >= 1 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 0 >= 0 = isList(X) isList(active(X)) = 0 >= 0 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X)) = 0 >= 0 = U32(X) U32(active(X)) = 0 >= 0 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,mark(X2)) = 0 >= 0 = U42(X1,X2) U42(active(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,active(X2)) = 0 >= 0 = U42(X1,X2) U43(mark(X)) = 0 >= 0 = U43(X) U43(active(X)) = 0 >= 0 = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21 (and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41 (and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark(U51 (and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and (and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and (isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x1, [U72](x0) = 0, [isNePal](x0) = 1, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 1, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = x0, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 0, [isQid](x0) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = x0, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 0 >= 0 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isQid(V))) mark#(U31(X1,X2)) = 0 >= 0 = active#(U31(mark(X1),X2)) active#(isNeList(V)) = 1 >= 0 = mark#(U31(isPalListKind(V),V)) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = 1 >= 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 1 >= 1 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 1 >= 1 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 1 >= 1 = active(U42(mark(X1),X2)) mark(U43(X)) = X >= X = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 1 >= 1 = active(isNePal(X)) mark(and(X1,X2)) = X2 >= X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 1 >= 1 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 1 >= 1 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 1 >= 1 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 1 >= 1 = isList(X) isList(active(X)) = 1 >= 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X)) = 0 >= 0 = U32(X) U32(active(X)) = 0 >= 0 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = X >= X = U43(X) U43(active(X)) = X >= X = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) and(mark(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,mark(X2)) = X2 >= X2 = and(X1,X2) and(active(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,active(X2)) = X2 >= X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) active#(U31(tt(),V)) -> mark#(U32(isQid(V))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21 (and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41 (and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark(U51 (and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and (and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and (isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x1, [U72](x0) = 1, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x1 + 1, [U62](x0) = x0, [U61](x0, x1) = x1 + 1, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = 1, [isQid](x0) = 1, [U31](x0, x1) = x0 + 1, [U23](x0) = 1, [U22](x0, x1) = x0, [isList](x0) = x0 + 1, [U21](x0, x1, x2) = x0 + x1, [U12](x0) = x0, [isNeList](x0) = x0 + 1, [U11](x0, x1) = x1 + 1, [tt] = 1, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = X >= X = mark#(X) mark#(U12(X)) = X >= X = active#(U12(mark(X))) mark#(isNeList(X)) = X + 1 >= X + 1 = active#(isNeList(X)) active#(U31(tt(),V)) = 2 >= 1 = mark#(U32(isQid(V))) mark#(U31(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U31(mark(X1),X2)) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X = mark(X) active(__(nil(),X)) = X + 2 >= X = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + 1 >= V1 + 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = V + 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 2 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V2 + 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= V + 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 3 >= P = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= V + 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 2 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 + 1 >= V2 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X2 + 1 >= X2 + 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNeList(X)) = X + 1 >= X + 1 = active(isNeList(X)) mark(U21(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isList(X)) = X + 1 >= X + 1 = active(isList(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(U31(X1,X2)) = X1 + 1 >= X1 + 1 = active(U31(mark(X1),X2)) mark(U32(X)) = 1 >= 1 = active(U32(mark(X))) mark(isQid(X)) = 1 >= 1 = active(isQid(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 1 >= 1 = active(U42(mark(X1),X2)) mark(U43(X)) = 1 >= 1 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = X2 + 1 >= X2 + 1 = active(U52(mark(X1),X2)) mark(U53(X)) = X >= X = active(U53(mark(X))) mark(U61(X1,X2)) = X2 + 1 >= X2 + 1 = active(U61(mark(X1),X2)) mark(U62(X)) = X >= X = active(U62(mark(X))) mark(U71(X1,X2)) = X2 + 1 >= X2 + 1 = active(U71(mark(X1),X2)) mark(U72(X)) = 1 >= 1 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X2 >= X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = X >= X = active(isPalListKind(X)) mark(isPal(X)) = X + 1 >= X + 1 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 1 >= 1 = active(i()) mark(o()) = 1 >= 1 = active(o()) mark(u()) = 1 >= 1 = active(u()) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) U11(mark(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(active(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,active(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNeList(mark(X)) = X + 1 >= X + 1 = isNeList(X) isNeList(active(X)) = X + 1 >= X + 1 = isNeList(X) U21(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = X1 + X2 >= X1 + X2 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = X1 + X2 >= X1 + X2 = U21(X1,X2,X3) U21(active(X1),X2,X3) = X1 + X2 >= X1 + X2 = U21(X1,X2,X3) U21(X1,active(X2),X3) = X1 + X2 >= X1 + X2 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = X1 + X2 >= X1 + X2 = U21(X1,X2,X3) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isList(mark(X)) = X + 1 >= X + 1 = isList(X) isList(active(X)) = X + 1 >= X + 1 = isList(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = U31(X1,X2) U31(X1,mark(X2)) = X1 + 1 >= X1 + 1 = U31(X1,X2) U31(active(X1),X2) = X1 + 1 >= X1 + 1 = U31(X1,X2) U31(X1,active(X2)) = X1 + 1 >= X1 + 1 = U31(X1,X2) U32(mark(X)) = 1 >= 1 = U32(X) U32(active(X)) = 1 >= 1 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,mark(X2)) = 1 >= 1 = U42(X1,X2) U42(active(X1),X2) = 1 >= 1 = U42(X1,X2) U42(X1,active(X2)) = 1 >= 1 = U42(X1,X2) U43(mark(X)) = 1 >= 1 = U43(X) U43(active(X)) = 1 >= 1 = U43(X) U51(mark(X1),X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) U52(mark(X1),X2) = X2 + 1 >= X2 + 1 = U52(X1,X2) U52(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U52(X1,X2) U52(active(X1),X2) = X2 + 1 >= X2 + 1 = U52(X1,X2) U52(X1,active(X2)) = X2 + 1 >= X2 + 1 = U52(X1,X2) U53(mark(X)) = X >= X = U53(X) U53(active(X)) = X >= X = U53(X) U61(mark(X1),X2) = X2 + 1 >= X2 + 1 = U61(X1,X2) U61(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U61(X1,X2) U61(active(X1),X2) = X2 + 1 >= X2 + 1 = U61(X1,X2) U61(X1,active(X2)) = X2 + 1 >= X2 + 1 = U61(X1,X2) U62(mark(X)) = X >= X = U62(X) U62(active(X)) = X >= X = U62(X) U71(mark(X1),X2) = X2 + 1 >= X2 + 1 = U71(X1,X2) U71(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U71(X1,X2) U71(active(X1),X2) = X2 + 1 >= X2 + 1 = U71(X1,X2) U71(X1,active(X2)) = X2 + 1 >= X2 + 1 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,mark(X2)) = X2 >= X2 = and(X1,X2) and(active(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,active(X2)) = X2 >= X2 = and(X1,X2) isPalListKind(mark(X)) = X >= X = isPalListKind(X) isPalListKind(active(X)) = X >= X = isPalListKind(X) isPal(mark(X)) = X + 1 >= X + 1 = isPal(X) isPal(active(X)) = X + 1 >= X + 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21 ( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41 ( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark(U51 ( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and ( and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and ( isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = 0, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 1, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 1, [U43](x0) = 0, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 0, [U32](x0) = 0, [isQid](x0) = 1, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 0, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 1 = active#(isNeList(X)) mark#(U31(X1,X2)) = 1 >= 0 = active#(U31(mark(X1),X2)) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 1 >= 1 = isNeList(X) isNeList(active(X)) = 1 >= 1 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 0 >= 0 = isList(X) isList(active(X)) = 0 >= 0 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X)) = 0 >= 0 = U32(X) U32(active(X)) = 0 >= 0 = U32(X) isQid(mark(X)) = 1 >= 1 = isQid(X) isQid(active(X)) = 1 >= 1 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,mark(X2)) = 0 >= 0 = U42(X1,X2) U42(active(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,active(X2)) = 0 >= 0 = U42(X1,X2) U43(mark(X)) = 0 >= 0 = U43(X) U43(active(X)) = 0 >= 0 = U43(X) U51(mark(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 1 >= 1 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 1 >= 1 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 1 >= 1 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNeList(X)) -> active#(isNeList(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark( U21 ( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark( U41 ( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark( U51 ( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark( and ( and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark( and ( isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 0, [and](x0, x1) = 0, [U72](x0) = 0, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = 0, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 1, [U32](x0) = 0, [isQid](x0) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 0, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 1 = mark#(tt()) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(U12(X)) = 1 >= 1 = active#(U12(mark(X))) mark#(isNeList(X)) = 1 >= 0 = active#(isNeList(X)) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 0 >= 0 = isNeList(X) isNeList(active(X)) = 0 >= 0 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 0 >= 0 = isList(X) isList(active(X)) = 0 >= 0 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X)) = 0 >= 0 = U32(X) U32(active(X)) = 0 >= 0 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,mark(X2)) = 0 >= 0 = U42(X1,X2) U42(active(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,active(X2)) = 0 >= 0 = U42(X1,X2) U43(mark(X)) = 0 >= 0 = U43(X) U43(active(X)) = 0 >= 0 = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark (U21 (and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark (U41 (and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark (U51 (and (isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark (and (and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark (and (isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 1, [isPal](x0) = 1, [isPalListKind](x0) = 0, [and](x0, x1) = x1, [U72](x0) = 0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = 0, [U62](x0) = 1, [U61](x0, x1) = 1, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = x2, [U43](x0) = 0, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 0, [U32](x0) = 0, [isQid](x0) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = x0 + 1, [U21](x0, x1, x2) = 0, [U12](x0) = x0 + 1, [isNeList](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active#(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = active#(__(mark(X1),mark(X2))) active#(U12(tt())) = 1 >= 0 = mark#(tt()) mark#(U12(X)) = X + 1 >= X = mark#(X) mark#(U12(X)) = X + 1 >= X + 1 = active#(U12(mark(X))) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 2 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 >= V2 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X1,X2)) = X2 + 1 >= X2 + 1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X + 1 >= X + 1 = active(U12(mark(X))) mark(isNeList(X)) = X >= X = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = X + 1 >= X + 1 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = X3 >= X3 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 1 >= 1 = active(U61(mark(X1),X2)) mark(U62(X)) = 1 >= 1 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(X)) mark(and(X1,X2)) = X2 >= X2 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 1 >= 1 = active(isPal(X)) mark(a()) = 1 >= 1 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(active(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,active(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U12(mark(X)) = X + 1 >= X + 1 = U12(X) U12(active(X)) = X + 1 >= X + 1 = U12(X) isNeList(mark(X)) = X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = X + 1 >= X + 1 = isList(X) isList(active(X)) = X + 1 >= X + 1 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X)) = 0 >= 0 = U32(X) U32(active(X)) = 0 >= 0 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,mark(X2)) = 0 >= 0 = U42(X1,X2) U42(active(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,active(X2)) = 0 >= 0 = U42(X1,X2) U43(mark(X)) = 0 >= 0 = U43(X) U43(active(X)) = 0 >= 0 = U43(X) U51(mark(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = X3 >= X3 = U51(X1,X2,X3) U51(active(X1),X2,X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,active(X2),X3) = X3 >= X3 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = X3 >= X3 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,mark(X2)) = 1 >= 1 = U61(X1,X2) U61(active(X1),X2) = 1 >= 1 = U61(X1,X2) U61(X1,active(X2)) = 1 >= 1 = U61(X1,X2) U62(mark(X)) = 1 >= 1 = U62(X) U62(active(X)) = 1 >= 1 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 0 >= 0 = U72(X) U72(active(X)) = 0 >= 0 = U72(X) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) and(mark(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,mark(X2)) = X2 >= X2 = and(X1,X2) and(active(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,active(X2)) = X2 >= X2 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 1 >= 1 = isPal(X) isPal(active(X)) = 1 >= 1 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U12(X)) -> active#(U12(mark(X))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark (U21 (and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark (U41 (and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark (U51 (and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark (and (and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark (and (isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = 0, [U72](x0) = 1, [isNePal](x0) = 0, [U71](x0, x1) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U53](x0) = 0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [U43](x0) = 0, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 0, [U32](x0) = 0, [isQid](x0) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 0, [U21](x0, x1, x2) = 0, [U12](x0) = 1, [isNeList](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 0 orientation: active#(__(__(X,Y),Z)) = 0 >= 0 = mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) = 0 >= 0 = active#(__(mark(X1),mark(X2))) mark#(U12(X)) = 1 >= 0 = active#(U12(mark(X))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 0 >= 0 = active(U12(mark(X))) mark(isNeList(X)) = 0 >= 0 = active(isNeList(X)) mark(U21(X1,X2,X3)) = 0 >= 0 = active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isList(X)) = 0 >= 0 = active(isList(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X)) = 0 >= 0 = active(U32(mark(X))) mark(isQid(X)) = 0 >= 0 = active(isQid(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) = 0 >= 0 = active(U42(mark(X1),X2)) mark(U43(X)) = 0 >= 0 = active(U43(mark(X))) mark(U51(X1,X2,X3)) = 0 >= 0 = active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) = 0 >= 0 = active(U52(mark(X1),X2)) mark(U53(X)) = 0 >= 0 = active(U53(mark(X))) mark(U61(X1,X2)) = 0 >= 0 = active(U61(mark(X1),X2)) mark(U62(X)) = 0 >= 0 = active(U62(mark(X))) mark(U71(X1,X2)) = 0 >= 0 = active(U71(mark(X1),X2)) mark(U72(X)) = 0 >= 0 = active(U72(mark(X))) mark(isNePal(X)) = 0 >= 0 = active(isNePal(X)) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(isPalListKind(X)) = 0 >= 0 = active(isPalListKind(X)) mark(isPal(X)) = 0 >= 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 0 >= 0 = __(X1,X2) __(X1,mark(X2)) = 0 >= 0 = __(X1,X2) __(active(X1),X2) = 0 >= 0 = __(X1,X2) __(X1,active(X2)) = 0 >= 0 = __(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X)) = 1 >= 1 = U12(X) U12(active(X)) = 1 >= 1 = U12(X) isNeList(mark(X)) = 0 >= 0 = isNeList(X) isNeList(active(X)) = 0 >= 0 = isNeList(X) U21(mark(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,mark(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,mark(X3)) = 0 >= 0 = U21(X1,X2,X3) U21(active(X1),X2,X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,active(X2),X3) = 0 >= 0 = U21(X1,X2,X3) U21(X1,X2,active(X3)) = 0 >= 0 = U21(X1,X2,X3) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isList(mark(X)) = 0 >= 0 = isList(X) isList(active(X)) = 0 >= 0 = isList(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X)) = 0 >= 0 = U32(X) U32(active(X)) = 0 >= 0 = U32(X) isQid(mark(X)) = 0 >= 0 = isQid(X) isQid(active(X)) = 0 >= 0 = isQid(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,mark(X2)) = 0 >= 0 = U42(X1,X2) U42(active(X1),X2) = 0 >= 0 = U42(X1,X2) U42(X1,active(X2)) = 0 >= 0 = U42(X1,X2) U43(mark(X)) = 0 >= 0 = U43(X) U43(active(X)) = 0 >= 0 = U43(X) U51(mark(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,mark(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,mark(X3)) = 0 >= 0 = U51(X1,X2,X3) U51(active(X1),X2,X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,active(X2),X3) = 0 >= 0 = U51(X1,X2,X3) U51(X1,X2,active(X3)) = 0 >= 0 = U51(X1,X2,X3) U52(mark(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,mark(X2)) = 0 >= 0 = U52(X1,X2) U52(active(X1),X2) = 0 >= 0 = U52(X1,X2) U52(X1,active(X2)) = 0 >= 0 = U52(X1,X2) U53(mark(X)) = 0 >= 0 = U53(X) U53(active(X)) = 0 >= 0 = U53(X) U61(mark(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,mark(X2)) = 0 >= 0 = U61(X1,X2) U61(active(X1),X2) = 0 >= 0 = U61(X1,X2) U61(X1,active(X2)) = 0 >= 0 = U61(X1,X2) U62(mark(X)) = 0 >= 0 = U62(X) U62(active(X)) = 0 >= 0 = U62(X) U71(mark(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,mark(X2)) = 0 >= 0 = U71(X1,X2) U71(active(X1),X2) = 0 >= 0 = U71(X1,X2) U71(X1,active(X2)) = 0 >= 0 = U71(X1,X2) U72(mark(X)) = 1 >= 1 = U72(X) U72(active(X)) = 1 >= 1 = U72(X) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isPalListKind(mark(X)) = 0 >= 0 = isPalListKind(X) isPalListKind(active(X)) = 0 >= 0 = isPalListKind(X) isPal(mark(X)) = 0 >= 0 = isPal(X) isPal(active(X)) = 0 >= 0 = isPal(X) problem: DPs: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark (U21 ( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark (U41 ( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNeList(__(V1,V2))) -> mark (U51 ( and ( isPalListKind(V1), isPalListKind (V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark (and ( and(isQid(I),isPalListKind(I)), and (isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark (and ( isPalListKind(V1), isPalListKind (V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: isNeList#(mark(X)) -> isNeList#(X) isNeList#(active(X)) -> isNeList#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U12#(mark(X)) -> U12#(X) U12#(active(X)) -> U12#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: isList#(mark(X)) -> isList#(X) isList#(active(X)) -> isList#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: isQid#(mark(X)) -> isQid#(X) isQid#(active(X)) -> isQid#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U32#(mark(X)) -> U32#(X) U32#(active(X)) -> U32#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U42#(mark(X1),X2) -> U42#(X1,X2) U42#(X1,mark(X2)) -> U42#(X1,X2) U42#(active(X1),X2) -> U42#(X1,X2) U42#(X1,active(X2)) -> U42#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U43#(mark(X)) -> U43#(X) U43#(active(X)) -> U43#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U52#(mark(X1),X2) -> U52#(X1,X2) U52#(X1,mark(X2)) -> U52#(X1,X2) U52#(active(X1),X2) -> U52#(X1,X2) U52#(X1,active(X2)) -> U52#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U53#(mark(X)) -> U53#(X) U53#(active(X)) -> U53#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U72#(mark(X)) -> U72#(X) U72#(active(X)) -> U72#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: isPalListKind#(mark(X)) -> isPalListKind#(X) isPalListKind#(active(X)) -> isPalListKind#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3) U51#(active(X1),X2,X3) -> U51#(X1,X2,X3) U51#(X1,active(X2),X3) -> U51#(X1,X2,X3) U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: isPal#(mark(X)) -> isPal#(X) isPal#(active(X)) -> isPal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open DPs: U71#(mark(X1),X2) -> U71#(X1,X2) U71#(X1,mark(X2)) -> U71#(X1,X2) U71#(active(X1),X2) -> U71#(X1,X2) U71#(X1,active(X2)) -> U71#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2)) -> active(U42(mark(X1),X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2) -> U42(X1,X2) U42(X1,mark(X2)) -> U42(X1,X2) U42(active(X1),X2) -> U42(X1,X2) U42(X1,active(X2)) -> U42(X1,X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,mark(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) U51(active(X1),X2,X3) -> U51(X1,X2,X3) U51(X1,active(X2),X3) -> U51(X1,X2,X3) U51(X1,X2,active(X3)) -> U51(X1,X2,X3) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Open