YES Problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Proof: DP Processor: DPs: a____#(__(X,Y),Z) -> mark#(Z) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) a__U11#(tt(),V) -> a__isPalListKind#(V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__U12#(tt(),V) -> a__U13#(a__isNeList(V)) a__U21#(tt(),V1,V2) -> a__isPalListKind#(V1) a__U21#(tt(),V1,V2) -> a__U22#(a__isPalListKind(V1),V1,V2) a__U22#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U22#(tt(),V1,V2) -> a__U23#(a__isPalListKind(V2),V1,V2) a__U23#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U23#(tt(),V1,V2) -> a__U24#(a__isPalListKind(V2),V1,V2) a__U24#(tt(),V1,V2) -> a__isList#(V1) a__U24#(tt(),V1,V2) -> a__U25#(a__isList(V1),V2) a__U25#(tt(),V2) -> a__isList#(V2) a__U25#(tt(),V2) -> a__U26#(a__isList(V2)) a__U31#(tt(),V) -> a__isPalListKind#(V) a__U31#(tt(),V) -> a__U32#(a__isPalListKind(V),V) a__U32#(tt(),V) -> a__isQid#(V) a__U32#(tt(),V) -> a__U33#(a__isQid(V)) a__U41#(tt(),V1,V2) -> a__isPalListKind#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isPalListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isPalListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__isList#(V1) a__U44#(tt(),V1,V2) -> a__U45#(a__isList(V1),V2) a__U45#(tt(),V2) -> a__isNeList#(V2) a__U45#(tt(),V2) -> a__U46#(a__isNeList(V2)) a__U51#(tt(),V1,V2) -> a__isPalListKind#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) -> a__isNeList#(V1) a__U54#(tt(),V1,V2) -> a__U55#(a__isNeList(V1),V2) a__U55#(tt(),V2) -> a__isList#(V2) a__U55#(tt(),V2) -> a__U56#(a__isList(V2)) a__U61#(tt(),V) -> a__isPalListKind#(V) a__U61#(tt(),V) -> a__U62#(a__isPalListKind(V),V) a__U62#(tt(),V) -> a__isQid#(V) a__U62#(tt(),V) -> a__U63#(a__isQid(V)) a__U71#(tt(),I,P) -> a__isPalListKind#(I) a__U71#(tt(),I,P) -> a__U72#(a__isPalListKind(I),P) a__U72#(tt(),P) -> a__isPal#(P) a__U72#(tt(),P) -> a__U73#(a__isPal(P),P) a__U73#(tt(),P) -> a__isPalListKind#(P) a__U73#(tt(),P) -> a__U74#(a__isPalListKind(P)) a__U81#(tt(),V) -> a__isPalListKind#(V) a__U81#(tt(),V) -> a__U82#(a__isPalListKind(V),V) a__U82#(tt(),V) -> a__isNePal#(V) a__U82#(tt(),V) -> a__U83#(a__isNePal(V)) a__U91#(tt(),V2) -> a__isPalListKind#(V2) a__U91#(tt(),V2) -> a__U92#(a__isPalListKind(V2)) a__isList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(V) -> a__isPalListKind#(V) a__isNeList#(V) -> a__U31#(a__isPalListKind(V),V) a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isNeList#(__(V1,V2)) -> a__U41#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__isNePal#(V) -> a__isPalListKind#(V) a__isNePal#(V) -> a__U61#(a__isPalListKind(V),V) a__isNePal#(__(I,__(P,I))) -> a__isQid#(I) a__isNePal#(__(I,__(P,I))) -> a__U71#(a__isQid(I),I,P) a__isPal#(V) -> a__isPalListKind#(V) a__isPal#(V) -> a__U81#(a__isPalListKind(V),V) a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) -> a__U91#(a__isPalListKind(V1),V2) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(isPalListKind(X)) -> a__isPalListKind#(X) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> a__U13#(mark(X)) mark#(isNeList(X)) -> a__isNeList#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> a__U23#(mark(X1),X2,X3) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> a__U24#(mark(X1),X2,X3) mark#(U25(X1,X2)) -> mark#(X1) mark#(U25(X1,X2)) -> a__U25#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(U26(X)) -> mark#(X) mark#(U26(X)) -> a__U26#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> a__U32#(mark(X1),X2) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> a__U33#(mark(X)) mark#(isQid(X)) -> a__isQid#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> a__U42#(mark(X1),X2,X3) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> a__U43#(mark(X1),X2,X3) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> a__U44#(mark(X1),X2,X3) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> a__U45#(mark(X1),X2) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> a__U46#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U53(X1,X2,X3)) -> a__U53#(mark(X1),X2,X3) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> a__U54#(mark(X1),X2,X3) mark#(U55(X1,X2)) -> mark#(X1) mark#(U55(X1,X2)) -> a__U55#(mark(X1),X2) mark#(U56(X)) -> mark#(X) mark#(U56(X)) -> a__U56#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U62(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> a__U62#(mark(X1),X2) mark#(U63(X)) -> mark#(X) mark#(U63(X)) -> a__U63#(mark(X)) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U72(X1,X2)) -> mark#(X1) mark#(U72(X1,X2)) -> a__U72#(mark(X1),X2) mark#(U73(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> a__U73#(mark(X1),X2) mark#(isPal(X)) -> a__isPal#(X) mark#(U74(X)) -> mark#(X) mark#(U74(X)) -> a__U74#(mark(X)) mark#(U81(X1,X2)) -> mark#(X1) mark#(U81(X1,X2)) -> a__U81#(mark(X1),X2) mark#(U82(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> a__U82#(mark(X1),X2) mark#(U83(X)) -> mark#(X) mark#(U83(X)) -> a__U83#(mark(X)) mark#(isNePal(X)) -> a__isNePal#(X) mark#(U91(X1,X2)) -> mark#(X1) mark#(U91(X1,X2)) -> a__U91#(mark(X1),X2) mark#(U92(X)) -> mark#(X) mark#(U92(X)) -> a__U92#(mark(X)) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) TDG Processor: DPs: a____#(__(X,Y),Z) -> mark#(Z) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) a__U11#(tt(),V) -> a__isPalListKind#(V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__U12#(tt(),V) -> a__U13#(a__isNeList(V)) a__U21#(tt(),V1,V2) -> a__isPalListKind#(V1) a__U21#(tt(),V1,V2) -> a__U22#(a__isPalListKind(V1),V1,V2) a__U22#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U22#(tt(),V1,V2) -> a__U23#(a__isPalListKind(V2),V1,V2) a__U23#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U23#(tt(),V1,V2) -> a__U24#(a__isPalListKind(V2),V1,V2) a__U24#(tt(),V1,V2) -> a__isList#(V1) a__U24#(tt(),V1,V2) -> a__U25#(a__isList(V1),V2) a__U25#(tt(),V2) -> a__isList#(V2) a__U25#(tt(),V2) -> a__U26#(a__isList(V2)) a__U31#(tt(),V) -> a__isPalListKind#(V) a__U31#(tt(),V) -> a__U32#(a__isPalListKind(V),V) a__U32#(tt(),V) -> a__isQid#(V) a__U32#(tt(),V) -> a__U33#(a__isQid(V)) a__U41#(tt(),V1,V2) -> a__isPalListKind#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isPalListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isPalListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__isList#(V1) a__U44#(tt(),V1,V2) -> a__U45#(a__isList(V1),V2) a__U45#(tt(),V2) -> a__isNeList#(V2) a__U45#(tt(),V2) -> a__U46#(a__isNeList(V2)) a__U51#(tt(),V1,V2) -> a__isPalListKind#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__isPalListKind#(V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) -> a__isNeList#(V1) a__U54#(tt(),V1,V2) -> a__U55#(a__isNeList(V1),V2) a__U55#(tt(),V2) -> a__isList#(V2) a__U55#(tt(),V2) -> a__U56#(a__isList(V2)) a__U61#(tt(),V) -> a__isPalListKind#(V) a__U61#(tt(),V) -> a__U62#(a__isPalListKind(V),V) a__U62#(tt(),V) -> a__isQid#(V) a__U62#(tt(),V) -> a__U63#(a__isQid(V)) a__U71#(tt(),I,P) -> a__isPalListKind#(I) a__U71#(tt(),I,P) -> a__U72#(a__isPalListKind(I),P) a__U72#(tt(),P) -> a__isPal#(P) a__U72#(tt(),P) -> a__U73#(a__isPal(P),P) a__U73#(tt(),P) -> a__isPalListKind#(P) a__U73#(tt(),P) -> a__U74#(a__isPalListKind(P)) a__U81#(tt(),V) -> a__isPalListKind#(V) a__U81#(tt(),V) -> a__U82#(a__isPalListKind(V),V) a__U82#(tt(),V) -> a__isNePal#(V) a__U82#(tt(),V) -> a__U83#(a__isNePal(V)) a__U91#(tt(),V2) -> a__isPalListKind#(V2) a__U91#(tt(),V2) -> a__U92#(a__isPalListKind(V2)) a__isList#(V) -> a__isPalListKind#(V) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(V) -> a__isPalListKind#(V) a__isNeList#(V) -> a__U31#(a__isPalListKind(V),V) a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1) a__isNeList#(__(V1,V2)) -> a__U41#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__isNePal#(V) -> a__isPalListKind#(V) a__isNePal#(V) -> a__U61#(a__isPalListKind(V),V) a__isNePal#(__(I,__(P,I))) -> a__isQid#(I) a__isNePal#(__(I,__(P,I))) -> a__U71#(a__isQid(I),I,P) a__isPal#(V) -> a__isPalListKind#(V) a__isPal#(V) -> a__U81#(a__isPalListKind(V),V) a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) -> a__U91#(a__isPalListKind(V1),V2) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(isPalListKind(X)) -> a__isPalListKind#(X) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> a__U13#(mark(X)) mark#(isNeList(X)) -> a__isNeList#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> a__U23#(mark(X1),X2,X3) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> a__U24#(mark(X1),X2,X3) mark#(U25(X1,X2)) -> mark#(X1) mark#(U25(X1,X2)) -> a__U25#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(U26(X)) -> mark#(X) mark#(U26(X)) -> a__U26#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> a__U32#(mark(X1),X2) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> a__U33#(mark(X)) mark#(isQid(X)) -> a__isQid#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> a__U42#(mark(X1),X2,X3) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> a__U43#(mark(X1),X2,X3) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> a__U44#(mark(X1),X2,X3) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> a__U45#(mark(X1),X2) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> a__U46#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> a__U52#(mark(X1),X2,X3) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U53(X1,X2,X3)) -> a__U53#(mark(X1),X2,X3) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> a__U54#(mark(X1),X2,X3) mark#(U55(X1,X2)) -> mark#(X1) mark#(U55(X1,X2)) -> a__U55#(mark(X1),X2) mark#(U56(X)) -> mark#(X) mark#(U56(X)) -> a__U56#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U62(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> a__U62#(mark(X1),X2) mark#(U63(X)) -> mark#(X) mark#(U63(X)) -> a__U63#(mark(X)) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> a__U71#(mark(X1),X2,X3) mark#(U72(X1,X2)) -> mark#(X1) mark#(U72(X1,X2)) -> a__U72#(mark(X1),X2) mark#(U73(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> a__U73#(mark(X1),X2) mark#(isPal(X)) -> a__isPal#(X) mark#(U74(X)) -> mark#(X) mark#(U74(X)) -> a__U74#(mark(X)) mark#(U81(X1,X2)) -> mark#(X1) mark#(U81(X1,X2)) -> a__U81#(mark(X1),X2) mark#(U82(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> a__U82#(mark(X1),X2) mark#(U83(X)) -> mark#(X) mark#(U83(X)) -> a__U83#(mark(X)) mark#(isNePal(X)) -> a__isNePal#(X) mark#(U91(X1,X2)) -> mark#(X1) mark#(U91(X1,X2)) -> a__U91#(mark(X1),X2) mark#(U92(X)) -> mark#(X) mark#(U92(X)) -> a__U92#(mark(X)) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) graph: ... SCC Processor: #sccs: 4 #rules: 79 #arcs: 3712/25281 DPs: mark#(U92(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) -> mark#(Z) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U63(X)) -> mark#(X) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> mark#(X1) mark#(U74(X)) -> mark#(X) mark#(U81(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> mark#(X1) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [a____#](x0, x1) = x0 + x1, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = x0 + 1, [U83](x0) = x0, [U82](x0, x1) = x0 + x1, [U81](x0, x1) = x0 + x1, [U74](x0) = x0, [isPal](x0) = x0 + 1, [U73](x0, x1) = x0, [U72](x0, x1) = x0 + x1, [U71](x0, x1, x2) = x0 + x2, [U63](x0) = x0 + 1, [U62](x0, x1) = x0 + x1, [U61](x0, x1) = x0 + x1, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x0 + x1 + x2, [U52](x0, x1, x2) = x0 + x1 + x2, [U51](x0, x1, x2) = x0 + x1 + x2, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x0 + x1 + x2, [U41](x0, x1, x2) = x0 + x1 + x2, [isQid](x0) = x0, [U33](x0) = x0, [U32](x0, x1) = x0 + x1, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [isList](x0) = x0 + 1, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2, [U22](x0, x1, x2) = x0 + x1 + x2, [U21](x0, x1, x2) = x0 + x1 + x2, [isNeList](x0) = x0 + 1, [U13](x0) = x0, [isPalListKind](x0) = 1, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = x0 + 1, [a__U82](x0, x1) = x0 + x1, [a__U81](x0, x1) = x0 + x1, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = x0 + 1, [a__U72](x0, x1) = x0 + x1, [a__U71](x0, x1, x2) = x0 + x2, [a__U63](x0) = x0 + 1, [a__U62](x0, x1) = x0 + x1, [a__U61](x0, x1) = x0 + x1, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x0 + x1 + x2, [a__U52](x0, x1, x2) = x0 + x1 + x2, [a__U51](x0, x1, x2) = x0 + x1 + x2, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x0 + x1 + x2, [a__U41](x0, x1, x2) = x0 + x1 + x2, [a__U33](x0) = x0, [a__isQid](x0) = x0, [a__U32](x0, x1) = x0 + x1, [a__U31](x0, x1) = x0 + x1, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2, [a__U22](x0, x1, x2) = x0 + x1 + x2, [a__U21](x0, x1, x2) = x0 + x1 + x2, [a__U13](x0) = x0, [a__isNeList](x0) = x0 + 1, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 1, [a__U11](x0, x1) = x0 + x1, [tt] = 1, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(__(X1,X2)) = X1 + X2 >= X2 = mark#(X2) mark#(__(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) = X + Y + Z >= Z = mark#(Z) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U62(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U63(X)) = X + 1 >= X = mark#(X) mark#(U71(X1,X2,X3)) = X1 + X3 >= X1 = mark#(X1) mark#(U72(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U73(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U74(X)) = X >= X = mark#(X) mark#(U81(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U82(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U83(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____#(__(X,Y),Z) = X + Y + Z >= Y = mark#(Y) a____#(__(X,Y),Z) = X + Y + Z >= Y + Z = a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) = X + Y + Z >= X = mark#(X) a____#(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) = X >= X = mark#(X) a____#(nil(),X) = X >= X = mark#(X) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__U11(tt(),V) = V + 1 >= V + 1 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V + 1 >= V + 1 = a__U13(a__isNeList(V)) a__U13(tt()) = 1 >= 1 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 + 1 >= V2 + 1 = a__U26(a__isList(V2)) a__U26(tt()) = 1 >= 1 = tt() a__U31(tt(),V) = V + 1 >= V + 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = V + 1 >= V = a__U33(a__isQid(V)) a__U33(tt()) = 1 >= 1 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 + 1 >= V2 + 1 = a__U46(a__isNeList(V2)) a__U46(tt()) = 1 >= 1 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 + 1 >= V2 + 1 = a__U56(a__isList(V2)) a__U56(tt()) = 1 >= 1 = tt() a__U61(tt(),V) = V + 1 >= V + 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = V + 1 >= V + 1 = a__U63(a__isQid(V)) a__U63(tt()) = 2 >= 1 = tt() a__U71(tt(),I,P) = P + 1 >= P + 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = P + 1 >= P + 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 1 >= 1 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 1 >= 1 = tt() a__U81(tt(),V) = V + 1 >= V + 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = V + 1 >= V + 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 1 >= 1 = tt() a__U91(tt(),V2) = 1 >= 1 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 1 >= 1 = tt() a__isList(V) = V + 1 >= V + 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 1 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V + 1 >= V + 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V + 1 >= V + 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 1 >= I + P = a__U71(a__isQid(I),I,P) a__isPal(V) = V + 1 >= V + 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 1 = tt() a__isPalListKind(a()) = 1 >= 1 = tt() a__isPalListKind(e()) = 1 >= 1 = tt() a__isPalListKind(i()) = 1 >= 1 = tt() a__isPalListKind(nil()) = 1 >= 1 = tt() a__isPalListKind(o()) = 1 >= 1 = tt() a__isPalListKind(u()) = 1 >= 1 = tt() a__isPalListKind(__(V1,V2)) = 1 >= 1 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 1 >= 1 = tt() a__isQid(e()) = 1 >= 1 = tt() a__isQid(i()) = 1 >= 1 = tt() a__isQid(o()) = 1 >= 1 = tt() a__isQid(u()) = 1 >= 1 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 1 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X + 1 >= X + 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 + X2 >= X1 + X2 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 + X2 >= X1 + X2 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 + X2 >= X1 + X2 = a__U62(mark(X1),X2) mark(U63(X)) = X + 1 >= X + 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X1 + X3 >= X1 + X3 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X1 + X2 >= X1 + X2 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = X + 1 >= X + 1 = a__isPal(X) mark(U74(X)) = X >= X = a__U74(mark(X)) mark(U81(X1,X2)) = X1 + X2 >= X1 + X2 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X1 + X2 >= X1 + X2 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = X + 1 >= X + 1 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 1 >= 1 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 1 >= 1 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U21(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = X1 + X2 >= X1 + X2 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = X >= X = isQid(X) a__U41(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 + X2 >= X1 + X2 = U61(X1,X2) a__U62(X1,X2) = X1 + X2 >= X1 + X2 = U62(X1,X2) a__U63(X) = X + 1 >= X + 1 = U63(X) a__U71(X1,X2,X3) = X1 + X3 >= X1 + X3 = U71(X1,X2,X3) a__U72(X1,X2) = X1 + X2 >= X1 + X2 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = X + 1 >= X + 1 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 + X2 >= X1 + X2 = U81(X1,X2) a__U82(X1,X2) = X1 + X2 >= X1 + X2 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = X + 1 >= X + 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) -> mark#(Z) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> mark#(X1) mark#(U74(X)) -> mark#(X) mark#(U81(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> mark#(X1) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 1, [a____#](x0, x1) = x0 + x1 + 1, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [isPal](x0) = 0, [U73](x0, x1) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x0, [U63](x0) = 0, [U62](x0, x1) = x0, [U61](x0, x1) = x0, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = 0, [U25](x0, x1) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [isNeList](x0) = 0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = x0, [a__U81](x0, x1) = x0, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 0, [a__U72](x0, x1) = x0, [a__U71](x0, x1, x2) = x0, [a__U63](x0) = 0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = x0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = x0, [a__U51](x0, x1, x2) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = x0, [a__U23](x0, x1, x2) = x0, [a__U22](x0, x1, x2) = x0, [a__U21](x0, x1, x2) = x0, [a__U13](x0) = x0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = x0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: mark#(U92(X)) = X + 1 >= X + 1 = mark#(X) mark#(__(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = mark#(X2) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) = X + Y + Z + 1 >= Z + 1 = mark#(Z) mark#(U11(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U12(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U13(X)) = X + 1 >= X + 1 = mark#(X) mark#(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U25(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U26(X)) = X + 1 >= X + 1 = mark#(X) mark#(U31(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U32(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U33(X)) = X + 1 >= X + 1 = mark#(X) mark#(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U45(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U46(X)) = X + 1 >= X + 1 = mark#(X) mark#(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U55(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U56(X)) = X + 1 >= X + 1 = mark#(X) mark#(U61(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U62(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U72(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U73(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U74(X)) = X + 1 >= X + 1 = mark#(X) mark#(U81(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U82(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U83(X)) = X + 1 >= X + 1 = mark#(X) mark#(U91(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) a____#(__(X,Y),Z) = X + Y + Z + 1 >= Y + 1 = mark#(Y) a____#(__(X,Y),Z) = X + Y + Z + 1 >= Y + Z + 1 = a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) = X + Y + Z + 1 >= X + 1 = mark#(X) a____#(__(X,Y),Z) = X + Y + Z + 1 >= X + Y + Z + 1 = a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) = X + 2 >= X + 1 = mark#(X) a____#(nil(),X) = X + 2 >= X + 1 = mark#(X) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 >= X1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 >= X1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 >= X1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 >= X1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 >= X1 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X1 >= X1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X1 >= X1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X1 >= X1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 >= X1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 >= X1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 >= X1 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 >= X1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X1 >= X1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X1 >= X1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = X >= X = a__U74(mark(X)) mark(U81(X1,X2)) = X1 >= X1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X1 >= X1 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = X1 >= X1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 >= X1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 >= X1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 >= X1 = U24(X1,X2,X3) a__U25(X1,X2) = X1 >= X1 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X1 >= X1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X1 >= X1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 >= X1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = X1 >= X1 = U71(X1,X2,X3) a__U72(X1,X2) = X1 >= X1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 >= X1 = U81(X1,X2) a__U82(X1,X2) = X1 >= X1 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) -> mark#(Z) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> mark#(X1) mark#(U74(X)) -> mark#(X) mark#(U81(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> mark#(X1) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [a____#](x0, x1) = x0 + x1, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = x0, [U83](x0) = x0, [U82](x0, x1) = x0 + x1, [U81](x0, x1) = x0 + x1, [U74](x0) = x0, [isPal](x0) = x0, [U73](x0, x1) = x0, [U72](x0, x1) = x0 + x1, [U71](x0, x1, x2) = x0 + x2, [U63](x0) = x0, [U62](x0, x1) = x0 + x1, [U61](x0, x1) = x0 + x1, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x0 + x1 + x2, [U52](x0, x1, x2) = x0 + x1 + x2, [U51](x0, x1, x2) = x0 + x1 + x2, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x0 + x1 + x2, [U41](x0, x1, x2) = x0 + x1 + x2, [isQid](x0) = x0, [U33](x0) = x0, [U32](x0, x1) = x0 + x1, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2, [U22](x0, x1, x2) = x0 + x1 + x2, [U21](x0, x1, x2) = x0 + x1 + x2, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = x0, [a__U82](x0, x1) = x0 + x1, [a__U81](x0, x1) = x0 + x1, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = x0, [a__U72](x0, x1) = x0 + x1, [a__U71](x0, x1, x2) = x0 + x2, [a__U63](x0) = x0, [a__U62](x0, x1) = x0 + x1, [a__U61](x0, x1) = x0 + x1, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x0 + x1 + x2, [a__U52](x0, x1, x2) = x0 + x1 + x2, [a__U51](x0, x1, x2) = x0 + x1 + x2, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x0 + x1 + x2, [a__U41](x0, x1, x2) = x0 + x1 + x2, [a__U33](x0) = x0, [a__isQid](x0) = x0, [a__U32](x0, x1) = x0 + x1, [a__U31](x0, x1) = x0 + x1, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2, [a__U22](x0, x1, x2) = x0 + x1 + x2, [a__U21](x0, x1, x2) = x0 + x1 + x2, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) 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 = a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) = X + Y + Z + 1 >= Z = mark#(Z) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U62(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U71(X1,X2,X3)) = X1 + X3 >= X1 = mark#(X1) mark#(U72(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U73(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U74(X)) = X >= X = mark#(X) mark#(U81(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U82(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U83(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____#(__(X,Y),Z) = X + Y + Z + 1 >= Y = mark#(Y) a____#(__(X,Y),Z) = X + Y + Z + 1 >= Y + Z = a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) = X + Y + Z + 1 >= X = mark#(X) a____#(__(X,Y),Z) = X + Y + Z + 1 >= X + Y + Z + 1 = a____#(mark(X),a____(mark(Y),mark(Z))) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= V = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = V >= V = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = V >= V = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = V >= V = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = P >= P = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = P >= P = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = V >= V = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = V >= V = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= V = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V >= V = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 2 >= I + P = a__U71(a__isQid(I),I,P) a__isPal(V) = V >= V = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 + X2 >= X1 + X2 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 + X2 >= X1 + X2 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 + X2 >= X1 + X2 = a__U62(mark(X1),X2) mark(U63(X)) = X >= X = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X1 + X3 >= X1 + X3 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X1 + X2 >= X1 + X2 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = X >= X = a__isPal(X) mark(U74(X)) = X >= X = a__U74(mark(X)) mark(U81(X1,X2)) = X1 + X2 >= X1 + X2 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X1 + X2 >= X1 + X2 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = X1 + X2 >= X1 + X2 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = X >= X = isQid(X) a__U41(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 + X2 >= X1 + X2 = U61(X1,X2) a__U62(X1,X2) = X1 + X2 >= X1 + X2 = U62(X1,X2) a__U63(X) = X >= X = U63(X) a__U71(X1,X2,X3) = X1 + X3 >= X1 + X3 = U71(X1,X2,X3) a__U72(X1,X2) = X1 + X2 >= X1 + X2 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = X >= X = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 + X2 >= X1 + X2 = U81(X1,X2) a__U82(X1,X2) = X1 + X2 >= X1 + X2 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = X >= X = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> mark#(X1) mark#(U74(X)) -> mark#(X) mark#(U81(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> mark#(X1) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 0, [a____#](x0, x1) = x0, [U92](x0) = x0, [U91](x0, x1) = 1, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 1, [U55](x0, x1) = 1, [U54](x0, x1, x2) = 1, [U53](x0, x1, x2) = 1, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = x0 + x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1 + 1, [U44](x0, x1, x2) = x2 + 1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x0 + x2 + 1, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = x0 + x1, [U26](x0) = 0, [isList](x0) = x0 + 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0 + 1, [U13](x0) = 1, [isPalListKind](x0) = 1, [U12](x0, x1) = 1, [U11](x0, x1) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = 1, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 1, [a__U55](x0, x1) = 1, [a__U54](x0, x1, x2) = 1, [a__U53](x0, x1, x2) = 1, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x1 + 1, [a__U44](x0, x1, x2) = x2 + 1, [a__U43](x0, x1, x2) = x2 + 1, [a__U42](x0, x1, x2) = x2 + 1, [a__U41](x0, x1, x2) = x0 + x2 + 1, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = x0 + x1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = 1, [a__isNeList](x0) = x0 + 1, [a__U12](x0, x1) = 1, [a__isPalListKind](x0) = 1, [a__U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = 0 >= 0 = mark#(X) mark#(U11(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U12(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U13(X)) = 0 >= 0 = mark#(X) mark#(U21(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U22(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U23(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U24(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U25(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U26(X)) = 0 >= 0 = mark#(X) mark#(U31(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U32(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U33(X)) = 0 >= 0 = mark#(X) mark#(U41(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U42(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U43(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U44(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U45(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U46(X)) = 0 >= 0 = mark#(X) mark#(U51(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U52(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U53(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U54(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U55(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U56(X)) = 0 >= 0 = mark#(X) mark#(U61(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U62(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U71(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U72(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U73(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U74(X)) = 0 >= 0 = mark#(X) mark#(U81(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U82(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U83(X)) = 0 >= 0 = mark#(X) mark#(U91(X1,X2)) = 0 >= 0 = mark#(X1) a____#(__(X,Y),Z) = X + Y + 1 >= X = a____#(mark(X),a____(mark(Y),mark(Z))) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = 1 >= 1 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 1 >= 1 = a__U13(a__isNeList(V)) a__U13(tt()) = 1 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 + 1 >= V2 + 1 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 1 >= 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 1 >= 1 = a__U56(a__isList(V2)) a__U56(tt()) = 1 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 1 >= 1 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V + 1 >= V + 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 2 >= V2 + 2 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 2 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 1 >= 0 = tt() a__isPalListKind(e()) = 1 >= 0 = tt() a__isPalListKind(i()) = 1 >= 0 = tt() a__isPalListKind(nil()) = 1 >= 0 = tt() a__isPalListKind(o()) = 1 >= 0 = tt() a__isPalListKind(u()) = 1 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 1 >= 1 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 1 = a__isPalListKind(X) mark(U13(X)) = 1 >= 1 = a__U13(mark(X)) mark(isNeList(X)) = X + 1 >= X + 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X1 + X3 + 1 >= X1 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X2 + 1 >= X2 + 1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 1 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 1 >= 1 = U12(X1,X2) a__isPalListKind(X) = 1 >= 1 = isPalListKind(X) a__U13(X) = 1 >= 1 = U13(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X1 + X3 + 1 >= X1 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X3 + 1 >= X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X3 + 1 >= X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X3 + 1 >= X3 + 1 = U44(X1,X2,X3) a__U45(X1,X2) = X2 + 1 >= X2 + 1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 1 >= 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 1 >= 1 = U54(X1,X2,X3) a__U55(X1,X2) = 1 >= 1 = U55(X1,X2) a__U56(X) = 1 >= 1 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = 1 >= 1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> mark#(X1) mark#(U74(X)) -> mark#(X) mark#(U81(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> mark#(X1) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [isPal](x0) = 0, [U73](x0, x1) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x0, [U63](x0) = 0, [U62](x0, x1) = x0, [U61](x0, x1) = x0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x0 + x1 + x2, [U52](x0, x1, x2) = x0 + x1 + x2, [U51](x0, x1, x2) = x0 + x1 + x2, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x0 + x1 + x2, [U41](x0, x1, x2) = x0 + x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2, [U22](x0, x1, x2) = x0 + x1 + x2, [U21](x0, x1, x2) = x0 + x1 + x2, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = x0, [a__U81](x0, x1) = x0, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 0, [a__U72](x0, x1) = x0, [a__U71](x0, x1, x2) = x0, [a__U63](x0) = 0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x0 + x1 + x2, [a__U52](x0, x1, x2) = x0 + x1 + x2, [a__U51](x0, x1, x2) = x0 + x1 + x2, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x0 + x1 + x2, [a__U41](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2, [a__U22](x0, x1, x2) = x0 + x1 + x2, [a__U21](x0, x1, x2) = x0 + x1 + x2, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U71(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U72(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U73(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U74(X)) = X >= X = mark#(X) mark#(U81(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U82(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U83(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 >= X1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X1 >= X1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X1 >= X1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = X >= X = a__U74(mark(X)) mark(U81(X1,X2)) = X1 >= X1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X1 >= X1 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = X1 >= X1 = U71(X1,X2,X3) a__U72(X1,X2) = X1 >= X1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 >= X1 = U81(X1,X2) a__U82(X1,X2) = X1 >= X1 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2,X3)) -> mark#(X1) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> mark#(X1) mark#(U74(X)) -> mark#(X) mark#(U81(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> mark#(X1) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [isPal](x0) = 0, [U73](x0, x1) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x0, [U63](x0) = 0, [U62](x0, x1) = x0, [U61](x0, x1) = x0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x0 + x1 + x2, [U52](x0, x1, x2) = x0 + x1 + x2 + 1, [U51](x0, x1, x2) = x0 + x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x0 + x1 + x2, [U41](x0, x1, x2) = x1 + x2, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2, [U22](x0, x1, x2) = x0 + x1 + x2, [U21](x0, x1, x2) = x0 + x1 + x2, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = x0, [a__U81](x0, x1) = x0, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 0, [a__U72](x0, x1) = x0, [a__U71](x0, x1, x2) = x0, [a__U63](x0) = 0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x0 + x1 + x2, [a__U52](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U51](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x0 + x1 + x2, [a__U41](x0, x1, x2) = x1 + x2, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2, [a__U22](x0, x1, x2) = x0 + x1 + x2, [a__U21](x0, x1, x2) = x0 + x1 + x2, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U71(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U72(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U73(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U74(X)) = X >= X = mark#(X) mark#(U81(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U82(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U83(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 >= X1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X1 >= X1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X1 >= X1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = X >= X = a__U74(mark(X)) mark(U81(X1,X2)) = X1 >= X1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X1 >= X1 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = X1 >= X1 = U71(X1,X2,X3) a__U72(X1,X2) = X1 >= X1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 >= X1 = U81(X1,X2) a__U82(X1,X2) = X1 >= X1 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> mark#(X1) mark#(U74(X)) -> mark#(X) mark#(U81(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> mark#(X1) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = x0, [U83](x0) = x0, [U82](x0, x1) = x0 + x1, [U81](x0, x1) = x0 + x1, [U74](x0) = x0, [isPal](x0) = x0, [U73](x0, x1) = x0, [U72](x0, x1) = x0 + x1, [U71](x0, x1, x2) = x0 + x2 + 1, [U63](x0) = 0, [U62](x0, x1) = x0, [U61](x0, x1) = x0, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = 0, [U25](x0, x1) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [isNeList](x0) = 0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = x0, [a__U82](x0, x1) = x0 + x1, [a__U81](x0, x1) = x0 + x1, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = x0, [a__U72](x0, x1) = x0 + x1, [a__U71](x0, x1, x2) = x0 + x2 + 1, [a__U63](x0) = 0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = x0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = x0, [a__U23](x0, x1, x2) = x0, [a__U22](x0, x1, x2) = x0, [a__U21](x0, x1, x2) = x0, [a__U13](x0) = x0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = x0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U53(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U71(X1,X2,X3)) = X1 + X3 + 1 >= X1 = mark#(X1) mark#(U72(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U73(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U74(X)) = X >= X = mark#(X) mark#(U81(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U82(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U83(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = P + 1 >= P = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = P >= P = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = V >= V = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = V >= V = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 2 >= P + 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = V >= V = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 >= X1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 >= X1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 >= X1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 >= X1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 >= X1 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 >= X1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 >= X1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 >= X1 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 >= X1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X1 + X3 + 1 >= X1 + X3 + 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X1 + X2 >= X1 + X2 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = X >= X = a__isPal(X) mark(U74(X)) = X >= X = a__U74(mark(X)) mark(U81(X1,X2)) = X1 + X2 >= X1 + X2 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X1 + X2 >= X1 + X2 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = X1 >= X1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 >= X1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 >= X1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 >= X1 = U24(X1,X2,X3) a__U25(X1,X2) = X1 >= X1 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 >= X1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = X1 + X3 + 1 >= X1 + X3 + 1 = U71(X1,X2,X3) a__U72(X1,X2) = X1 + X2 >= X1 + X2 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = X >= X = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 + X2 >= X1 + X2 = U81(X1,X2) a__U82(X1,X2) = X1 + X2 >= X1 + X2 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = X >= X = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U72(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> mark#(X1) mark#(U74(X)) -> mark#(X) mark#(U81(X1,X2)) -> mark#(X1) mark#(U82(X1,X2)) -> mark#(X1) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 1, [U83](x0) = x0, [U82](x0, x1) = x0 + 1, [U81](x0, x1) = x0 + 1, [U74](x0) = x0, [isPal](x0) = 1, [U73](x0, x1) = x0, [U72](x0, x1) = x0 + 1, [U71](x0, x1, x2) = 1, [U63](x0) = 0, [U62](x0, x1) = x0, [U61](x0, x1) = x0, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = 0, [U25](x0, x1) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [isNeList](x0) = 0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = x0 + 1, [a__U81](x0, x1) = x0 + 1, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 1, [a__U72](x0, x1) = x0 + 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = x0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = x0, [a__U23](x0, x1, x2) = x0, [a__U22](x0, x1, x2) = x0, [a__U21](x0, x1, x2) = x0, [a__U13](x0) = x0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = x0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U53(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U72(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U73(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U74(X)) = X >= X = mark#(X) mark#(U81(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U82(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U83(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 >= X1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 >= X1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 >= X1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 >= X1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 >= X1 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 >= X1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 >= X1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 >= X1 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 >= X1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X1 + 1 >= X1 + 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = X >= X = a__U74(mark(X)) mark(U81(X1,X2)) = X1 + 1 >= X1 + 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X1 + 1 >= X1 + 1 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = X1 >= X1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 >= X1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 >= X1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 >= X1 = U24(X1,X2,X3) a__U25(X1,X2) = X1 >= X1 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 >= X1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = X1 + 1 >= X1 + 1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 + 1 >= X1 + 1 = U81(X1,X2) a__U82(X1,X2) = X1 + 1 >= X1 + 1 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U73(X1,X2)) -> mark#(X1) mark#(U74(X)) -> mark#(X) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = x0, [U83](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0 + 1, [isPal](x0) = x0, [U73](x0, x1) = x0 + 1, [U72](x0, x1) = x1 + 1, [U71](x0, x1, x2) = x2 + 1, [U63](x0) = 0, [U62](x0, x1) = x0, [U61](x0, x1) = x0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x0 + x1 + x2, [U52](x0, x1, x2) = x1 + x2, [U51](x0, x1, x2) = x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x0 + x1 + x2, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2, [U22](x0, x1, x2) = x0 + x1 + x2, [U21](x0, x1, x2) = x0 + x1 + x2, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = x0, [a__U82](x0, x1) = x1, [a__U81](x0, x1) = x1, [a__U74](x0) = x0 + 1, [a__U73](x0, x1) = x0 + 1, [a__isPal](x0) = x0, [a__U72](x0, x1) = x1 + 1, [a__U71](x0, x1, x2) = x2 + 1, [a__U63](x0) = 0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x0 + x1 + x2, [a__U52](x0, x1, x2) = x1 + x2, [a__U51](x0, x1, x2) = x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x0 + x1 + x2, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0 + x1, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2, [a__U22](x0, x1, x2) = x0 + x1 + x2, [a__U21](x0, x1, x2) = x0 + x1 + x2, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U73(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U74(X)) = X + 1 >= X = mark#(X) mark#(U83(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = P + 1 >= P + 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = P + 1 >= P + 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 1 >= 1 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 1 >= 0 = tt() a__U81(tt(),V) = V >= V = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = V >= V = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= V = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 2 >= P + 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = V >= V = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 >= X1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X2 + 1 >= X2 + 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 + 1 >= X1 + 1 = a__U73(mark(X1),X2) mark(isPal(X)) = X >= X = a__isPal(X) mark(U74(X)) = X + 1 >= X + 1 = a__U74(mark(X)) mark(U81(X1,X2)) = X2 >= X2 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X2 >= X2 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 >= X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = X3 + 1 >= X3 + 1 = U71(X1,X2,X3) a__U72(X1,X2) = X2 + 1 >= X2 + 1 = U72(X1,X2) a__U73(X1,X2) = X1 + 1 >= X1 + 1 = U73(X1,X2) a__isPal(X) = X >= X = isPal(X) a__U74(X) = X + 1 >= X + 1 = U74(X) a__U81(X1,X2) = X2 >= X2 = U81(X1,X2) a__U82(X1,X2) = X2 >= X2 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = X >= X = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U83(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = x0, [U83](x0) = x0 + 1, [U82](x0, x1) = x1 + 1, [U81](x0, x1) = x1 + 1, [U74](x0) = 0, [isPal](x0) = x0 + 1, [U73](x0, x1) = 0, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 0, [U62](x0, x1) = x0, [U61](x0, x1) = x0 + x1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = 0, [U25](x0, x1) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [isNeList](x0) = 0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0 + 1, [a__isNePal](x0) = x0, [a__U82](x0, x1) = x1 + 1, [a__U81](x0, x1) = x1 + 1, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = x0 + 1, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0 + x1, [a__U56](x0) = x0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = x0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = x0, [a__U23](x0, x1, x2) = x0, [a__U22](x0, x1, x2) = x0, [a__U21](x0, x1, x2) = x0, [a__U13](x0) = x0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = x0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U53(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U62(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U83(X)) = X + 1 >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = V >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = V + 1 >= V + 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = V + 1 >= V + 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 1 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V >= V = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 2 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = V + 1 >= V + 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 2 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 >= X1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 >= X1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 >= X1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 >= X1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 >= X1 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 >= X1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 >= X1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 >= X1 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 + X2 >= X1 + X2 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 >= X1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = X + 1 >= X + 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = X2 + 1 >= X2 + 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X2 + 1 >= X2 + 1 = a__U82(mark(X1),X2) mark(U83(X)) = X + 1 >= X + 1 = a__U83(mark(X)) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = X1 >= X1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 >= X1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 >= X1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 >= X1 = U24(X1,X2,X3) a__U25(X1,X2) = X1 >= X1 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 >= X1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 + X2 >= X1 + X2 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = X + 1 >= X + 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = X2 + 1 >= X2 + 1 = U81(X1,X2) a__U82(X1,X2) = X2 + 1 >= X2 + 1 = U82(X1,X2) a__U83(X) = X + 1 >= X + 1 = U83(X) a__isNePal(X) = X >= X = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X1,X2)) -> mark#(X1) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 1, [U83](x0) = x0, [U82](x0, x1) = 1, [U81](x0, x1) = 1, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = x0, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = 0, [U25](x0, x1) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [isNeList](x0) = 0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 1, [a__U81](x0, x1) = 1, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0 + 1, [a__U56](x0) = x0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = x0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = x0, [a__U23](x0, x1, x2) = x0, [a__U22](x0, x1, x2) = x0, [a__U21](x0, x1, x2) = x0, [a__U13](x0) = x0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = x0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U53(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U62(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 >= X1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 >= X1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 >= X1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 >= X1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 >= X1 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 >= X1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 >= X1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 >= X1 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = X1 + 1 >= X1 + 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 >= X1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = X1 >= X1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 >= X1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 >= X1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 >= X1 = U24(X1,X2,X3) a__U25(X1,X2) = X1 >= X1 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 >= X1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 + 1 >= X1 + 1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 1 >= 1 = U81(X1,X2) a__U82(X1,X2) = 1 >= 1 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U62(X1,X2)) -> mark#(X1) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = 0, [U25](x0, x1) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [isNeList](x0) = 0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = x0 + 1, [a__U61](x0, x1) = 1, [a__U56](x0) = x0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = x0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = x0, [a__U23](x0, x1, x2) = x0, [a__U22](x0, x1, x2) = x0, [a__U21](x0, x1, x2) = x0, [a__U13](x0) = x0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = x0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U53(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U62(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 1 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 >= X1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 >= X1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 >= X1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 >= X1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 >= X1 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 >= X1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 >= X1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 >= X1 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X1 + 1 >= X1 + 1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = X1 >= X1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 >= X1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 >= X1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 >= X1 = U24(X1,X2,X3) a__U25(X1,X2) = X1 >= X1 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 >= X1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X1,X2) = X1 + 1 >= X1 + 1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x0 + x1 + x2, [U52](x0, x1, x2) = x1 + x2, [U51](x0, x1, x2) = x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x0 + x1 + x2, [U41](x0, x1, x2) = x1 + x2, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2, [U22](x0, x1, x2) = x0 + x1 + x2, [U21](x0, x1, x2) = x0 + x1 + x2 + 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x0 + x1 + x2, [a__U52](x0, x1, x2) = x1 + x2, [a__U51](x0, x1, x2) = x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x0 + x1 + x2, [a__U41](x0, x1, x2) = x1 + x2, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2, [a__U22](x0, x1, x2) = x0 + x1 + x2, [a__U21](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 >= X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = x0 + 1, [U83](x0) = x0, [U82](x0, x1) = x1 + 1, [U81](x0, x1) = x1 + 1, [U74](x0) = 0, [isPal](x0) = x0 + 1, [U73](x0, x1) = x1, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2 + 1, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x0 + x1 + x2, [U52](x0, x1, x2) = x1 + x2, [U51](x0, x1, x2) = x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x0 + x1 + x2 + 1, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2, [U22](x0, x1, x2) = x0 + x1 + x2, [U21](x0, x1, x2) = x1 + x2, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = x0 + 1, [a__U82](x0, x1) = x1 + 1, [a__U81](x0, x1) = x1 + 1, [a__U74](x0) = 0, [a__U73](x0, x1) = x1, [a__isPal](x0) = x0 + 1, [a__U72](x0, x1) = x1, [a__U71](x0, x1, x2) = x2 + 1, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x0 + x1 + x2, [a__U52](x0, x1, x2) = x1 + x2, [a__U51](x0, x1, x2) = x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0 + x1, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2, [a__U22](x0, x1, x2) = x0 + x1 + x2, [a__U21](x0, x1, x2) = x1 + x2, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = P + 1 >= P = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = P >= P = a__U73(a__isPal(P),P) a__U73(tt(),P) = P >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = V + 1 >= V + 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = V + 1 >= V + 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= V = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V + 1 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 3 >= P + 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = V + 1 >= V + 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X2 >= X2 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X2 >= X2 = a__U73(mark(X1),X2) mark(isPal(X)) = X + 1 >= X + 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = X2 + 1 >= X2 + 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = X2 + 1 >= X2 + 1 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = X + 1 >= X + 1 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 >= X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 >= X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = X3 + 1 >= X3 + 1 = U71(X1,X2,X3) a__U72(X1,X2) = X2 >= X2 = U72(X1,X2) a__U73(X1,X2) = X2 >= X2 = U73(X1,X2) a__isPal(X) = X + 1 >= X + 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = X2 + 1 >= X2 + 1 = U81(X1,X2) a__U82(X1,X2) = X2 + 1 >= X2 + 1 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = X + 1 >= X + 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 1, [U82](x0, x1) = 1, [U81](x0, x1) = 1, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x0 + x1 + x2, [U52](x0, x1, x2) = x1 + x2 + 1, [U51](x0, x1, x2) = x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x1 + x2, [U41](x0, x1, x2) = x1 + x2, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2, [U22](x0, x1, x2) = x0 + x1 + x2 + 1, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 1, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 1, [a__U81](x0, x1) = 1, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x0 + x1 + x2, [a__U52](x0, x1, x2) = x1 + x2 + 1, [a__U51](x0, x1, x2) = x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x1 + x2, [a__U41](x0, x1, x2) = x1 + x2, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2, [a__U22](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 1 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 1 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 >= X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 1 >= 1 = U81(X1,X2) a__U82(X1,X2) = 1 >= 1 = U82(X1,X2) a__U83(X) = 1 >= 1 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U53(X1,X2,X3)) -> mark#(X1) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 1, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x0 + x1 + x2 + 1, [U52](x0, x1, x2) = x1 + x2 + 1, [U51](x0, x1, x2) = x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x1 + x2 + 1, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2, [U22](x0, x1, x2) = x1 + x2, [U21](x0, x1, x2) = x1 + x2, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U52](x0, x1, x2) = x1 + x2 + 1, [a__U51](x0, x1, x2) = x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x1 + x2 + 1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2, [a__U22](x0, x1, x2) = x1 + x2, [a__U21](x0, x1, x2) = x1 + x2, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X + 1 >= X + 1 = mark#(X) mark#(U11(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(U13(X)) = X + 1 >= X + 1 = mark#(X) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(U26(X)) = X + 1 >= X + 1 = mark#(X) mark#(U31(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U32(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U33(X)) = X + 1 >= X + 1 = mark#(X) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(U46(X)) = X + 1 >= X + 1 = mark#(X) mark#(U53(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(U56(X)) = X + 1 >= X + 1 = mark#(X) mark#(U91(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 >= X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X2 + X3 >= X2 + X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U23(X1,X2,X3)) -> mark#(X1) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = x0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x1 + x2, [U52](x0, x1, x2) = x1 + x2, [U51](x0, x1, x2) = x1 + x2, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x1 + x2, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2, [U23](x0, x1, x2) = x0 + x1 + x2 + 1, [U22](x0, x1, x2) = x1 + x2 + 1, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 1, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = x0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x1 + x2, [a__U52](x0, x1, x2) = x1 + x2, [a__U51](x0, x1, x2) = x1 + x2, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x1 + x2, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2, [a__U23](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U22](x0, x1, x2) = x1 + x2 + 1, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 2 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 >= X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 >= X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 >= X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X2 + X3 >= X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = X >= X = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U24(X1,X2,X3)) -> mark#(X1) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 1, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x1 + x2, [U52](x0, x1, x2) = x1 + x2, [U51](x0, x1, x2) = x1 + x2, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x1 + x2, [U41](x0, x1, x2) = x1 + x2, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1, [U24](x0, x1, x2) = x0 + x1 + x2 + 1, [U23](x0, x1, x2) = x1 + x2 + 1, [U22](x0, x1, x2) = x1 + x2 + 1, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 1, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x1 + x2, [a__U52](x0, x1, x2) = x1 + x2, [a__U51](x0, x1, x2) = x1 + x2, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x1 + x2, [a__U41](x0, x1, x2) = x1 + x2, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U23](x0, x1, x2) = x1 + x2 + 1, [a__U22](x0, x1, x2) = x1 + x2 + 1, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U25(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 >= X1 + X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 >= X1 + X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 >= X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 >= X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 >= X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X2 + X3 >= X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 1 >= 1 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U25(X1,X2)) -> mark#(X1) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x1 + x2 + 1, [U52](x0, x1, x2) = x1 + x2 + 1, [U51](x0, x1, x2) = x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2, [U42](x0, x1, x2) = x1 + x2, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x0 + x1 + 1, [U24](x0, x1, x2) = x1 + x2 + 1, [U23](x0, x1, x2) = x1 + x2 + 1, [U22](x0, x1, x2) = x1 + x2 + 1, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 1, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x1 + x2 + 1, [a__U52](x0, x1, x2) = x1 + x2 + 1, [a__U51](x0, x1, x2) = x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2, [a__U42](x0, x1, x2) = x1 + x2, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0 + x1 + 1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x1 + x2 + 1, [a__U23](x0, x1, x2) = x1 + x2 + 1, [a__U22](x0, x1, x2) = x1 + x2 + 1, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U25(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 + 1 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U24(X1,X2,X3) a__U25(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 >= X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x1 + x2, [U52](x0, x1, x2) = x1 + x2, [U51](x0, x1, x2) = x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x0 + x1 + x2 + 1, [U42](x0, x1, x2) = x1 + x2 + 1, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = x0, [U25](x0, x1) = x1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x1 + x2, [a__U52](x0, x1, x2) = x1 + x2, [a__U51](x0, x1, x2) = x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U42](x0, x1, x2) = x1 + x2 + 1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = x1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x2, [a__U23](x0, x1, x2) = x2, [a__U22](x0, x1, x2) = x2, [a__U21](x0, x1, x2) = x2, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U26(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V2 >= V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V2 >= V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V2 >= V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V2 >= V2 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 >= V2 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X3 >= X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X3 >= X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X3 >= X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X3 >= X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X2 >= X2 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X3 >= X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X3 >= X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X3 >= X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X3 >= X3 = U24(X1,X2,X3) a__U25(X1,X2) = X2 >= X2 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 >= X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X2 + X3 >= X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U26(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 1, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2, [U53](x0, x1, x2) = x1 + x2, [U52](x0, x1, x2) = x1 + x2, [U51](x0, x1, x2) = x1 + x2, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x1 + x2, [U42](x0, x1, x2) = x1 + x2, [U41](x0, x1, x2) = x1 + x2, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0 + 1, [isList](x0) = x0, [U25](x0, x1) = x1 + 1, [U24](x0, x1, x2) = x2 + 1, [U23](x0, x1, x2) = x2 + 1, [U22](x0, x1, x2) = x2 + 1, [U21](x0, x1, x2) = x2 + 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 1, [o] = 0, [i] = 1, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 1, [a__isPal](x0) = 0, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2, [a__U53](x0, x1, x2) = x1 + x2, [a__U52](x0, x1, x2) = x1 + x2, [a__U51](x0, x1, x2) = x1 + x2, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x1 + x2, [a__U42](x0, x1, x2) = x1 + x2, [a__U41](x0, x1, x2) = x1 + x2, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0 + 1, [a__U25](x0, x1) = x1 + 1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x2 + 1, [a__U23](x0, x1, x2) = x2 + 1, [a__U22](x0, x1, x2) = x2 + 1, [a__U21](x0, x1, x2) = x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U26(X)) = X + 1 >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 + 1 >= V2 + 1 = a__U26(a__isList(V2)) a__U26(tt()) = 1 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 1 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X2 + 1 >= X2 + 1 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = X + 1 >= X + 1 = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X3 + 1 >= X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X3 + 1 >= X3 + 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X3 + 1 >= X3 + 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X3 + 1 >= X3 + 1 = U24(X1,X2,X3) a__U25(X1,X2) = X2 + 1 >= X2 + 1 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = X + 1 >= X + 1 = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 >= X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X2 + X3 >= X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 >= X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 >= X2 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X2 + X3 >= X2 + X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = 1 >= 1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U54(X1,X2,X3)) -> mark#(X1) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1, [U54](x0, x1, x2) = x0 + x1 + x2 + 1, [U53](x0, x1, x2) = x1 + x2 + 1, [U52](x0, x1, x2) = x1 + x2 + 1, [U51](x0, x1, x2) = x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2, [U43](x0, x1, x2) = x1 + x2, [U42](x0, x1, x2) = x1 + x2, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = 0, [isList](x0) = x0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 1, [i] = 0, [e] = 1, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1, [a__U54](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U53](x0, x1, x2) = x1 + x2 + 1, [a__U52](x0, x1, x2) = x1 + x2 + 1, [a__U51](x0, x1, x2) = x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0, x1, x2) = x1 + x2, [a__U42](x0, x1, x2) = x1 + x2, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U55(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 >= X1 + X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 >= X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X2 + X3 >= X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 >= X1 + X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U55(X1,X2)) -> mark#(X1) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x0 + x1 + 1, [U54](x0, x1, x2) = x1 + x2 + 1, [U53](x0, x1, x2) = x1 + x2 + 1, [U52](x0, x1, x2) = x1 + x2 + 1, [U51](x0, x1, x2) = x1 + x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + x1, [U44](x0, x1, x2) = x0 + x1 + x2 + 1, [U43](x0, x1, x2) = x1 + x2 + 1, [U42](x0, x1, x2) = x1 + x2 + 1, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = 0, [isList](x0) = x0 + 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 1, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0 + x1 + 1, [a__U54](x0, x1, x2) = x1 + x2 + 1, [a__U53](x0, x1, x2) = x1 + x2 + 1, [a__U52](x0, x1, x2) = x1 + x2 + 1, [a__U51](x0, x1, x2) = x1 + x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1, [a__U44](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U43](x0, x1, x2) = x1 + x2 + 1, [a__U42](x0, x1, x2) = x1 + x2 + 1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0 + x1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 1, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U55(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 1 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 + 1 >= V2 + 1 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= V = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 >= X1 + X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 1 >= 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 >= X1 + X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x2, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x0 + x1 + 1, [U44](x0, x1, x2) = x1 + x2 + 1, [U43](x0, x1, x2) = x1 + x2 + 1, [U42](x0, x1, x2) = x1 + x2 + 1, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = 0, [isList](x0) = x0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 1, [U22](x0, x1, x2) = 1, [U21](x0, x1, x2) = 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0, [a__U55](x0, x1) = x1, [a__U54](x0, x1, x2) = x2, [a__U53](x0, x1, x2) = x2, [a__U52](x0, x1, x2) = x2, [a__U51](x0, x1, x2) = x2, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1 + 1, [a__U44](x0, x1, x2) = x1 + x2 + 1, [a__U43](x0, x1, x2) = x1 + x2 + 1, [a__U42](x0, x1, x2) = x1 + x2 + 1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 1, [a__U22](x0, x1, x2) = 1, [a__U21](x0, x1, x2) = 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U45(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U56(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 1 >= 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 1 >= 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 1 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 + 1 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V2 >= V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V2 >= V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V2 >= V2 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V2 >= V2 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 >= V2 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V2 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X3 >= X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X3 >= X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X3 >= X3 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X3 >= X3 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X2 >= X2 = a__U55(mark(X1),X2) mark(U56(X)) = X >= X = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = 1 >= 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 1 >= 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 1 >= 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X3 >= X3 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X3 >= X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X3 >= X3 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X3 >= X3 = U54(X1,X2,X3) a__U55(X1,X2) = X2 >= X2 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U56(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = x0 + 1, [U55](x0, x1) = x1 + 1, [U54](x0, x1, x2) = x2 + 1, [U53](x0, x1, x2) = x2 + 1, [U52](x0, x1, x2) = x2 + 1, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = 0, [isList](x0) = x0, [U25](x0, x1) = 1, [U24](x0, x1, x2) = 1, [U23](x0, x1, x2) = 1, [U22](x0, x1, x2) = 1, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = x0 + 1, [a__U55](x0, x1) = x1 + 1, [a__U54](x0, x1, x2) = x2 + 1, [a__U53](x0, x1, x2) = x2 + 1, [a__U52](x0, x1, x2) = x2 + 1, [a__U51](x0, x1, x2) = x2 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = x1, [a__U44](x0, x1, x2) = x2, [a__U43](x0, x1, x2) = x2, [a__U42](x0, x1, x2) = x2, [a__U41](x0, x1, x2) = x2, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0 + x1, [a__U26](x0) = 0, [a__U25](x0, x1) = 1, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = 1, [a__U23](x0, x1, x2) = 1, [a__U22](x0, x1, x2) = 1, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = mark#(X) mark#(U56(X)) = X + 1 >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 1 >= 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 1 >= 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 1 >= 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 1 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V2 >= V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V2 >= V2 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V2 >= V2 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V2 >= V2 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = V2 + 1 >= V2 + 1 = a__U56(a__isList(V2)) a__U56(tt()) = 1 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= V = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V2 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 1 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X3 >= X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X3 >= X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X3 >= X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X3 >= X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X2 >= X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X2 + 1 >= X2 + 1 = a__U55(mark(X1),X2) mark(U56(X)) = X + 1 >= X + 1 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 1 >= 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 1 >= 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 1 >= 1 = U24(X1,X2,X3) a__U25(X1,X2) = 1 >= 1 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X3 >= X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X3 >= X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X3 >= X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X3 >= X3 = U44(X1,X2,X3) a__U45(X1,X2) = X2 >= X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X3 + 1 >= X3 + 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X3 + 1 >= X3 + 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X3 + 1 >= X3 + 1 = U54(X1,X2,X3) a__U55(X1,X2) = X2 + 1 >= X2 + 1 = U55(X1,X2) a__U56(X) = X + 1 >= X + 1 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = x0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = x0, [U73](x0, x1) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 1, [U46](x0) = x0 + 1, [U45](x0, x1) = x1 + 1, [U44](x0, x1, x2) = x2 + 1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = x0, [U33](x0) = x0, [U32](x0, x1) = x0 + x1, [U31](x0, x1) = x0 + x1, [U26](x0) = 0, [isList](x0) = x0 + 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = x1 + x2, [isNeList](x0) = x0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = x0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = x0, [a__isPal](x0) = x0, [a__U72](x0, x1) = x1, [a__U71](x0, x1, x2) = x2, [a__U63](x0) = x0, [a__U62](x0, x1) = x1, [a__U61](x0, x1) = x1, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = x0 + 1, [a__U45](x0, x1) = x1 + 1, [a__U44](x0, x1, x2) = x2 + 1, [a__U43](x0, x1, x2) = x2 + 1, [a__U42](x0, x1, x2) = x2 + 1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = x0, [a__isQid](x0) = x0, [a__U32](x0, x1) = x0 + x1, [a__U31](x0, x1) = x0 + x1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = x1 + x2, [a__U13](x0) = x0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U46(X)) = X + 1 >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= V = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= V = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = V >= V = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = V2 + 1 >= V2 + 1 = a__U46(a__isNeList(V2)) a__U46(tt()) = 1 >= 0 = tt() a__U51(tt(),V1,V2) = 1 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = V >= V = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = V >= V = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = P >= P = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = P >= P = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 2 >= V1 + V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= V = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V >= V = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 2 >= P = a__U71(a__isQid(I),I,P) a__isPal(V) = V >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 + X2 >= X1 + X2 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X2 + 1 >= X2 + 1 = a__U45(mark(X1),X2) mark(U46(X)) = X + 1 >= X + 1 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = X2 >= X2 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X2 >= X2 = a__U62(mark(X1),X2) mark(U63(X)) = X >= X = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X3 >= X3 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = X2 >= X2 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = X >= X = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 >= X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = X1 + X2 >= X1 + X2 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = X >= X = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X3 + 1 >= X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X3 + 1 >= X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X3 + 1 >= X3 + 1 = U44(X1,X2,X3) a__U45(X1,X2) = X2 + 1 >= X2 + 1 = U45(X1,X2) a__U46(X) = X + 1 >= X + 1 = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = X2 >= X2 = U61(X1,X2) a__U62(X1,X2) = X2 >= X2 = U62(X1,X2) a__U63(X) = X >= X = U63(X) a__U71(X1,X2,X3) = X3 >= X3 = U71(X1,X2,X3) a__U72(X1,X2) = X2 >= X2 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = X >= X = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = X >= X = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U13(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = 0, [isList](x0) = x0 + 1, [U25](x0, x1) = 1, [U24](x0, x1, x2) = 1, [U23](x0, x1, x2) = 1, [U22](x0, x1, x2) = x1 + 1, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = 1, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [u] = 0, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0 + 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 1, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = 1, [a__U23](x0, x1, x2) = 1, [a__U22](x0, x1, x2) = x1 + 1, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = 1, [a__U12](x0, x1) = x0 + x1 + 1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0 + x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U13(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__U11(tt(),V) = V + 1 >= V + 1 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V + 1 >= 1 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V1 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + 1 >= 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 1 >= 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 1 >= 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 1 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= V + 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 1 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X1 + 1 >= X1 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = X1 >= X1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = 1 >= 1 = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X2 + 1 >= X2 + 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 1 >= 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 1 >= 1 = U24(X1,X2,X3) a__U25(X1,X2) = 1 >= 1 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X1 + 1 >= X1 + 1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U13(X)) -> mark#(X) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U91(X1,X2)) -> mark#(X1) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = x0 + x1 + 1, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 1, [isPal](x0) = 0, [U73](x0, x1) = 1, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 0, [U62](x0, x1) = 1, [U61](x0, x1) = 1, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = 1, [isList](x0) = x0 + 1, [U25](x0, x1) = 1, [U24](x0, x1, x2) = 1, [U23](x0, x1, x2) = 1, [U22](x0, x1, x2) = 1, [U21](x0, x1, x2) = 1, [isNeList](x0) = x0 + 1, [U13](x0) = x0, [isPalListKind](x0) = x0, [U12](x0, x1) = x1 + 1, [U11](x0, x1) = x1 + 1, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0 + x1 + 1, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 1, [a__U73](x0, x1) = 1, [a__isPal](x0) = 0, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 0, [a__U62](x0, x1) = 1, [a__U61](x0, x1) = 1, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x1, [a__U26](x0) = 1, [a__U25](x0, x1) = 1, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = 1, [a__U23](x0, x1, x2) = 1, [a__U22](x0, x1, x2) = 1, [a__U21](x0, x1, x2) = 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0 + 1, [a__U12](x0, x1) = x1 + 1, [a__isPalListKind](x0) = x0, [a__U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = mark#(X) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U91(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = V + 1 >= V + 1 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V + 1 >= V + 1 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 1 >= 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 1 >= 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 1 >= 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 1 >= 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 1 >= 1 = a__U26(a__isList(V2)) a__U26(tt()) = 1 >= 0 = tt() a__U31(tt(),V) = V >= V = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 1 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 1 >= 1 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 1 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = V2 + 1 >= V2 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= V + 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 2 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 2 >= 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V + 1 >= V = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 2 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 2 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 1 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 1 >= 0 = tt() a__isPalListKind(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X2 + 1 >= X2 + 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X2 + 1 >= X2 + 1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = X >= X = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X + 1 >= X + 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 1 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 1 >= 1 = a__U26(mark(X)) mark(U31(X1,X2)) = X2 >= X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 1 >= 1 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) a__U12(X1,X2) = X2 + 1 >= X2 + 1 = U12(X1,X2) a__isPalListKind(X) = X >= X = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U21(X1,X2,X3) = 1 >= 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 1 >= 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 1 >= 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 1 >= 1 = U24(X1,X2,X3) a__U25(X1,X2) = 1 >= 1 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 1 >= 1 = U26(X) a__U31(X1,X2) = X2 >= X2 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X1,X2) = 1 >= 1 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = 1 >= 1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 1 >= 1 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U13(X)) -> mark#(X) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = 0, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 1, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 1, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 1, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = 1, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0 + 1, [U31](x0, x1) = x1 + 1, [U26](x0) = 0, [isList](x0) = x0 + 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 1, [U23](x0, x1, x2) = 1, [U22](x0, x1, x2) = 1, [U21](x0, x1, x2) = x1 + 1, [isNeList](x0) = x0 + 1, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = x1 + 1, [U11](x0, x1) = x1 + 1, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 1, [a__isPal](x0) = 0, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 1, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 1, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0 + 1, [a__U31](x0, x1) = x1 + 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = 1, [a__U23](x0, x1, x2) = 1, [a__U22](x0, x1, x2) = 1, [a__U21](x0, x1, x2) = x1 + 1, [a__U13](x0) = x0, [a__isNeList](x0) = x0 + 1, [a__U12](x0, x1) = x1 + 1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = mark#(X) mark#(U32(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__U11(tt(),V) = V + 1 >= V + 1 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V + 1 >= V + 1 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + 1 >= 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 1 >= 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 1 >= 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 1 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V + 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 1 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= V + 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V + 1 >= V + 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X2 + 1 >= X2 + 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X2 + 1 >= X2 + 1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNeList(X)) = X + 1 >= X + 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X2 + 1 >= X2 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 + 1 >= X1 + 1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) a__U12(X1,X2) = X2 + 1 >= X2 + 1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U21(X1,X2,X3) = X2 + 1 >= X2 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 1 >= 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 1 >= 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 1 >= 1 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X2 + 1 >= X2 + 1 = U31(X1,X2) a__U32(X1,X2) = X1 + 1 >= X1 + 1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 1 >= 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = 1 >= 1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U13(X)) -> mark#(X) mark#(U33(X)) -> mark#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [U92](x0) = x0, [U91](x0, x1) = 1, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = x0, [isNeList](x0) = 0, [U13](x0) = x0 + 1, [isPalListKind](x0) = 1, [U12](x0, x1) = 1, [U11](x0, x1) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = 1, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 1, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = x0, [a__U13](x0) = x0 + 1, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 1, [a__isPalListKind](x0) = 1, [a__U11](x0, x1) = 1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: mark#(U92(X)) = X >= X = mark#(X) mark#(U13(X)) = X + 1 >= X = mark#(X) mark#(U33(X)) = X >= X = mark#(X) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = 1 >= 1 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 1 >= 1 = a__U13(a__isNeList(V)) a__U13(tt()) = 1 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 1 >= 1 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 1 >= 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = 1 >= 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 1 >= 0 = tt() a__isPalListKind(e()) = 1 >= 0 = tt() a__isPalListKind(i()) = 1 >= 0 = tt() a__isPalListKind(nil()) = 1 >= 0 = tt() a__isPalListKind(o()) = 1 >= 0 = tt() a__isPalListKind(u()) = 1 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 1 >= 1 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 1 = a__isPalListKind(X) mark(U13(X)) = X + 1 >= X + 1 = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 >= X1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = X >= X = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 1 >= 1 = U12(X1,X2) a__isPalListKind(X) = 1 >= 1 = isPalListKind(X) a__U13(X) = X + 1 >= X + 1 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = X1 >= X1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 1 >= 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = 1 >= 1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: mark#(U92(X)) -> mark#(X) mark#(U33(X)) -> mark#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 1, [U92](x0) = x0 + 1, [U91](x0, x1) = x0 + x1 + 1, [isNePal](x0) = 1, [U83](x0) = x0, [U82](x0, x1) = 1, [U81](x0, x1) = 1, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = 1, [U53](x0, x1, x2) = 1, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = 1, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = x0 + 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U26](x0) = 0, [isList](x0) = x0 + 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 1, [U13](x0) = 0, [isPalListKind](x0) = x0, [U12](x0, x1) = x0, [U11](x0, x1) = x1 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = x0 + 1, [a__U91](x0, x1) = x0 + x1 + 1, [a__U83](x0) = x0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 1, [a__U81](x0, x1) = 1, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = 1, [a__U53](x0, x1, x2) = 1, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0 + 1, [a__isQid](x0) = 0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 1, [a__U12](x0, x1) = x0, [a__isPalListKind](x0) = x0, [a__U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(U92(X)) = X + 2 >= X + 1 = mark#(X) mark#(U33(X)) = X + 2 >= X + 1 = mark#(X) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V + 1 >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isQid(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 1 >= 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = V2 + 1 >= V2 + 1 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 1 >= 0 = tt() a__isList(V) = V + 1 >= V + 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 2 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X2 + 1 >= X2 + 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = X >= X = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 0 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = X + 1 >= X + 1 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 >= X1 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U91(mark(X1),X2) mark(U92(X)) = X + 1 >= X + 1 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__isPalListKind(X) = X >= X = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 1 >= 1 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = X + 1 >= X + 1 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 1 >= 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 1 >= 1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 1 >= 1 = U81(X1,X2) a__U82(X1,X2) = 1 >= 1 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(X1,X2) a__U92(X) = X + 1 >= X + 1 = U92(X) problem: DPs: TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Qed DPs: a__U55#(tt(),V2) -> a__isList#(V2) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__isNeList#(__(V1,V2)) -> a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isPalListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isPalListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__isList#(V1) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__U21#(tt(),V1,V2) -> a__U22#(a__isPalListKind(V1),V1,V2) a__U22#(tt(),V1,V2) -> a__U23#(a__isPalListKind(V2),V1,V2) a__U23#(tt(),V1,V2) -> a__U24#(a__isPalListKind(V2),V1,V2) a__U24#(tt(),V1,V2) -> a__isList#(V1) a__U24#(tt(),V1,V2) -> a__U25#(a__isList(V1),V2) a__U25#(tt(),V2) -> a__isList#(V2) a__U44#(tt(),V1,V2) -> a__U45#(a__isList(V1),V2) a__U45#(tt(),V2) -> a__isNeList#(V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) -> a__isNeList#(V1) a__U54#(tt(),V1,V2) -> a__U55#(a__isNeList(V1),V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U55#](x0, x1) = x0 + x1, [a__U54#](x0, x1, x2) = x1 + x2 + 1, [a__U53#](x0, x1, x2) = x1 + x2 + 1, [a__U52#](x0, x1, x2) = x1 + x2 + 1, [a__U51#](x0, x1, x2) = x1 + x2 + 1, [a__U45#](x0, x1) = x1, [a__U44#](x0, x1, x2) = x1 + x2, [a__U43#](x0, x1, x2) = x1 + x2, [a__U42#](x0, x1, x2) = x1 + x2 + 1, [a__U41#](x0, x1, x2) = x1 + x2 + 1, [a__U25#](x0, x1) = x1, [a__isList#](x0) = x0, [a__U24#](x0, x1, x2) = x1 + x2, [a__U23#](x0, x1, x2) = x1 + x2, [a__U22#](x0, x1, x2) = x1 + x2, [a__U21#](x0, x1, x2) = x1 + x2 + 1, [a__isNeList#](x0) = x0, [a__U12#](x0, x1) = x1, [a__U11#](x0, x1) = x1, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 1, [U83](x0) = 1, [U82](x0, x1) = 1, [U81](x0, x1) = 1, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = x0, [U63](x0) = x0, [U62](x0, x1) = 1, [U61](x0, x1) = 1, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = 1, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 1, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U26](x0) = x0, [isList](x0) = x0 + 1, [U25](x0, x1) = x1 + 1, [U24](x0, x1, x2) = x2 + 1, [U23](x0, x1, x2) = x2 + 1, [U22](x0, x1, x2) = x2 + 1, [U21](x0, x1, x2) = x2 + 1, [isNeList](x0) = 1, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 1, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 1, [a__U81](x0, x1) = 1, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = x0, [a__U63](x0) = x0, [a__U62](x0, x1) = 1, [a__U61](x0, x1) = 1, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 1, [a__isQid](x0) = 1, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U26](x0) = x0, [a__U25](x0, x1) = x1 + 1, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = x2 + 1, [a__U23](x0, x1, x2) = x2 + 1, [a__U22](x0, x1, x2) = x2 + 1, [a__U21](x0, x1, x2) = x2 + 1, [a__U13](x0) = 0, [a__isNeList](x0) = 1, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: a__U55#(tt(),V2) = V2 >= V2 = a__isList#(V2) a__isList#(V) = V >= V = a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) = V >= V = a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) = V >= V = a__isNeList#(V) a__isNeList#(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U42#(a__isPalListKind(V1),V1,V2) a__U42#(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U43#(a__isPalListKind(V2),V1,V2) a__U43#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44#(a__isPalListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = V1 + V2 >= V1 = a__isList#(V1) a__isList#(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21#(a__isPalListKind(V1),V1,V2) a__U21#(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 = a__U22#(a__isPalListKind(V1),V1,V2) a__U22#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U23#(a__isPalListKind(V2),V1,V2) a__U23#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24#(a__isPalListKind(V2),V1,V2) a__U24#(tt(),V1,V2) = V1 + V2 >= V1 = a__isList#(V1) a__U24#(tt(),V1,V2) = V1 + V2 >= V2 = a__U25#(a__isList(V1),V2) a__U25#(tt(),V2) = V2 >= V2 = a__isList#(V2) a__U44#(tt(),V1,V2) = V1 + V2 >= V2 = a__U45#(a__isList(V1),V2) a__U45#(tt(),V2) = V2 >= V2 = a__isNeList#(V2) a__isNeList#(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) = V1 + V2 + 1 >= V1 = a__isNeList#(V1) a__U54#(tt(),V1,V2) = V1 + V2 + 1 >= V2 + 1 = a__U55#(a__isNeList(V1),V2) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = V2 + 1 >= V2 + 1 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isQid(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 1 >= 1 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 1 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 2 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 2 >= V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 1 >= 0 = tt() a__isQid(e()) = 1 >= 0 = tt() a__isQid(i()) = 1 >= 0 = tt() a__isQid(o()) = 1 >= 0 = tt() a__isQid(u()) = 1 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = X2 + 1 >= X2 + 1 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = X >= X = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 1 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = X >= X = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X1 >= X1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 1 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 1 >= 1 = isNeList(X) a__U21(X1,X2,X3) = X3 + 1 >= X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X3 + 1 >= X3 + 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X3 + 1 >= X3 + 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X3 + 1 >= X3 + 1 = U24(X1,X2,X3) a__U25(X1,X2) = X2 + 1 >= X2 + 1 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 1 >= 1 = U33(X) a__isQid(X) = 1 >= 1 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X1,X2) = 1 >= 1 = U62(X1,X2) a__U63(X) = X >= X = U63(X) a__U71(X1,X2,X3) = X1 >= X1 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 1 >= 1 = U81(X1,X2) a__U82(X1,X2) = 1 >= 1 = U82(X1,X2) a__U83(X) = 1 >= 1 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U55#(tt(),V2) -> a__isList#(V2) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__isNeList#(__(V1,V2)) -> a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isPalListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__isList#(V1) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__U22#(tt(),V1,V2) -> a__U23#(a__isPalListKind(V2),V1,V2) a__U23#(tt(),V1,V2) -> a__U24#(a__isPalListKind(V2),V1,V2) a__U24#(tt(),V1,V2) -> a__isList#(V1) a__U24#(tt(),V1,V2) -> a__U25#(a__isList(V1),V2) a__U25#(tt(),V2) -> a__isList#(V2) a__U44#(tt(),V1,V2) -> a__U45#(a__isList(V1),V2) a__U45#(tt(),V2) -> a__isNeList#(V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) -> a__U55#(a__isNeList(V1),V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U55#](x0, x1) = 0, [a__U54#](x0, x1, x2) = 0, [a__U53#](x0, x1, x2) = 0, [a__U52#](x0, x1, x2) = 0, [a__U51#](x0, x1, x2) = 0, [a__U45#](x0, x1) = 0, [a__U44#](x0, x1, x2) = 1, [a__U43#](x0, x1, x2) = 1, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U25#](x0, x1) = 0, [a__isList#](x0) = 0, [a__U24#](x0, x1, x2) = 0, [a__U23#](x0, x1, x2) = x1 + 1, [a__U22#](x0, x1, x2) = x1 + 1, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = 0, [a__U12#](x0, x1) = 0, [a__U11#](x0, x1) = 0, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [a____](x0, x1) = 0, [__](x0, x1) = 0 orientation: a__U55#(tt(),V2) = 0 >= 0 = a__isList#(V2) a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) = 0 >= 0 = a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) = 0 >= 0 = a__isNeList#(V) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) = 1 >= 1 = a__U44#(a__isPalListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = 1 >= 0 = a__isList#(V1) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__U22#(tt(),V1,V2) = V1 + 1 >= V1 + 1 = a__U23#(a__isPalListKind(V2),V1,V2) a__U23#(tt(),V1,V2) = V1 + 1 >= 0 = a__U24#(a__isPalListKind(V2),V1,V2) a__U24#(tt(),V1,V2) = 0 >= 0 = a__isList#(V1) a__U24#(tt(),V1,V2) = 0 >= 0 = a__U25#(a__isList(V1),V2) a__U25#(tt(),V2) = 0 >= 0 = a__isList#(V2) a__U44#(tt(),V1,V2) = 1 >= 0 = a__U45#(a__isList(V1),V2) a__U45#(tt(),V2) = 0 >= 0 = a__isNeList#(V2) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 0 >= 0 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = 0 >= 0 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = 0 >= 0 = a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) = 0 >= 0 = a__U55#(a__isNeList(V1),V2) a____(__(X,Y),Z) = 0 >= 0 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 0 >= 0 = mark(X) a____(nil(),X) = 0 >= 0 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 0 >= 0 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 0 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 0 >= 0 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U55#(tt(),V2) -> a__isList#(V2) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__isNeList#(__(V1,V2)) -> a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isPalListKind(V2),V1,V2) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__U22#(tt(),V1,V2) -> a__U23#(a__isPalListKind(V2),V1,V2) a__U24#(tt(),V1,V2) -> a__isList#(V1) a__U24#(tt(),V1,V2) -> a__U25#(a__isList(V1),V2) a__U25#(tt(),V2) -> a__isList#(V2) a__U45#(tt(),V2) -> a__isNeList#(V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) -> a__U55#(a__isNeList(V1),V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U55#](x0, x1) = 0, [a__U54#](x0, x1, x2) = 0, [a__U53#](x0, x1, x2) = 0, [a__U52#](x0, x1, x2) = 0, [a__U51#](x0, x1, x2) = 0, [a__U45#](x0, x1) = 0, [a__U44#](x0, x1, x2) = 0, [a__U43#](x0, x1, x2) = x1 + x2, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U25#](x0, x1) = 1, [a__isList#](x0) = 0, [a__U24#](x0, x1, x2) = 1, [a__U23#](x0, x1, x2) = 0, [a__U22#](x0, x1, x2) = x1 + x2 + 1, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = 0, [a__U12#](x0, x1) = 0, [a__U11#](x0, x1) = 0, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [a____](x0, x1) = 0, [__](x0, x1) = 0 orientation: a__U55#(tt(),V2) = 0 >= 0 = a__isList#(V2) a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) = 0 >= 0 = a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) = 0 >= 0 = a__isNeList#(V) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) = V1 + V2 >= 0 = a__U44#(a__isPalListKind(V2),V1,V2) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__U22#(tt(),V1,V2) = V1 + V2 + 1 >= 0 = a__U23#(a__isPalListKind(V2),V1,V2) a__U24#(tt(),V1,V2) = 1 >= 0 = a__isList#(V1) a__U24#(tt(),V1,V2) = 1 >= 1 = a__U25#(a__isList(V1),V2) a__U25#(tt(),V2) = 1 >= 0 = a__isList#(V2) a__U45#(tt(),V2) = 0 >= 0 = a__isNeList#(V2) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 0 >= 0 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = 0 >= 0 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = 0 >= 0 = a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) = 0 >= 0 = a__U55#(a__isNeList(V1),V2) a____(__(X,Y),Z) = 0 >= 0 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 0 >= 0 = mark(X) a____(nil(),X) = 0 >= 0 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 0 >= 0 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 0 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 0 >= 0 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U55#(tt(),V2) -> a__isList#(V2) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__isNeList#(__(V1,V2)) -> a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isPalListKind(V2),V1,V2) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__U24#(tt(),V1,V2) -> a__U25#(a__isList(V1),V2) a__U45#(tt(),V2) -> a__isNeList#(V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) -> a__U55#(a__isNeList(V1),V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U55#](x0, x1) = 0, [a__U54#](x0, x1, x2) = 0, [a__U53#](x0, x1, x2) = 0, [a__U52#](x0, x1, x2) = 0, [a__U51#](x0, x1, x2) = 0, [a__U45#](x0, x1) = x1 + 1, [a__U44#](x0, x1, x2) = 1, [a__U43#](x0, x1, x2) = x2 + 1, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U25#](x0, x1) = 0, [a__isList#](x0) = 0, [a__U24#](x0, x1, x2) = 0, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = 0, [a__U12#](x0, x1) = 0, [a__U11#](x0, x1) = 0, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 1, [U81](x0, x1) = 1, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = 0, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 1, [U62](x0, x1) = 1, [U61](x0, x1) = 1, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = x1, [U51](x0, x1, x2) = x1, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [isQid](x0) = x0, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = x1 + 1, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = x0 + 1, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 1, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 1, [a__U81](x0, x1) = 1, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 1, [a__U62](x0, x1) = 1, [a__U61](x0, x1) = 1, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = x1, [a__U51](x0, x1, x2) = x1, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = x2, [a__U41](x0, x1, x2) = x2, [a__U33](x0) = 0, [a__isQid](x0) = x0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = x1 + 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = x0 + 1, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: a__U55#(tt(),V2) = 0 >= 0 = a__isList#(V2) a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) = 0 >= 0 = a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) = 0 >= 0 = a__isNeList#(V) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) = V2 + 1 >= 1 = a__U44#(a__isPalListKind(V2),V1,V2) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__U24#(tt(),V1,V2) = 0 >= 0 = a__U25#(a__isList(V1),V2) a__U45#(tt(),V2) = V2 + 1 >= 0 = a__isNeList#(V2) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 0 >= 0 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = 0 >= 0 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = 0 >= 0 = a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) = 0 >= 0 = a__U55#(a__isNeList(V1),V2) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V + 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V2 >= V2 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V2 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 >= V1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V1 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 1 >= 1 = a__U63(a__isQid(V)) a__U63(tt()) = 1 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V + 1 >= V + 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V2 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 1 >= 0 = tt() a__isQid(u()) = 1 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = X + 1 >= X + 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 0 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X2 + 1 >= X2 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(U41(X1,X2,X3)) = X3 >= X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X3 >= X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 >= X2 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X2 >= X2 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X2 + 1 >= X2 + 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = X >= X = isQid(X) a__U41(X1,X2,X3) = X3 >= X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X3 >= X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = X2 >= X2 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X2 >= X2 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X1,X2) = 1 >= 1 = U62(X1,X2) a__U63(X) = 1 >= 1 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 1 >= 1 = U81(X1,X2) a__U82(X1,X2) = 1 >= 1 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U55#(tt(),V2) -> a__isList#(V2) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__isNeList#(__(V1,V2)) -> a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isPalListKind(V2),V1,V2) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__U24#(tt(),V1,V2) -> a__U25#(a__isList(V1),V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) -> a__U55#(a__isNeList(V1),V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U55#](x0, x1) = 0, [a__U54#](x0, x1, x2) = 0, [a__U53#](x0, x1, x2) = 0, [a__U52#](x0, x1, x2) = 0, [a__U51#](x0, x1, x2) = 0, [a__U44#](x0, x1, x2) = 1, [a__U43#](x0, x1, x2) = x2 + 1, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U25#](x0, x1) = 0, [a__isList#](x0) = 0, [a__U24#](x0, x1, x2) = 1, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = 0, [a__U12#](x0, x1) = 0, [a__U11#](x0, x1) = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 1, [U81](x0, x1) = 1, [U74](x0) = x0, [isPal](x0) = 1, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 1, [o] = 1, [i] = 0, [e] = 1, [a] = 0, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 1, [a__U81](x0, x1) = 1, [a__U74](x0) = x0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = x0, [a__U51](x0, x1, x2) = x0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 1, [mark](x0) = 1, [a____](x0, x1) = 1, [__](x0, x1) = 0 orientation: a__U55#(tt(),V2) = 0 >= 0 = a__isList#(V2) a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) = 0 >= 0 = a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) = 0 >= 0 = a__isNeList#(V) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) = V2 + 1 >= 1 = a__U44#(a__isPalListKind(V2),V1,V2) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__U24#(tt(),V1,V2) = 1 >= 0 = a__U25#(a__isList(V1),V2) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 0 >= 0 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = 0 >= 0 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = 0 >= 0 = a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) = 0 >= 0 = a__U55#(a__isNeList(V1),V2) a____(__(X,Y),Z) = 1 >= 1 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 1 >= 1 = mark(X) a____(nil(),X) = 1 >= 1 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 1 >= 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 0 = a__isPalListKind(X) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 0 = a__isList(X) mark(U26(X)) = 1 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 1 >= 1 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = 1 >= 1 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 1 >= 0 = tt() mark(a()) = 1 >= 0 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 1 >= 0 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = 1 >= 0 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X1 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = X1 >= X1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X1 >= X1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = 1 >= 1 = U81(X1,X2) a__U82(X1,X2) = 1 >= 1 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: a__U55#(tt(),V2) -> a__isList#(V2) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__isNeList#(__(V1,V2)) -> a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isPalListKind(V2),V1,V2) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) -> a__U55#(a__isNeList(V1),V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U55#](x0, x1) = x1, [a__U54#](x0, x1, x2) = x2, [a__U53#](x0, x1, x2) = x1 + x2, [a__U52#](x0, x1, x2) = x1 + x2, [a__U51#](x0, x1, x2) = x1 + x2, [a__U44#](x0, x1, x2) = 0, [a__U43#](x0, x1, x2) = x1 + x2 + 1, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = x1 + x2, [a__isList#](x0) = x0, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = x0, [a__U12#](x0, x1) = x1, [a__U11#](x0, x1) = x1, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = x0, [U63](x0) = x0, [U62](x0, x1) = 1, [U61](x0, x1) = 1, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 1, [U33](x0) = x0, [U32](x0, x1) = 1, [U31](x0, x1) = x1 + 1, [U26](x0) = 0, [isList](x0) = x0 + 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x2 + 1, [U22](x0, x1, x2) = x2 + 1, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0 + 1, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = x0, [a__U63](x0) = x0, [a__U62](x0, x1) = 1, [a__U61](x0, x1) = 1, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__isQid](x0) = 1, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = x1 + 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = x2, [a__U23](x0, x1, x2) = x2 + 1, [a__U22](x0, x1, x2) = x2 + 1, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = 0, [a__isNeList](x0) = x0 + 1, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: a__U55#(tt(),V2) = V2 >= V2 = a__isList#(V2) a__isList#(V) = V >= V = a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) = V >= V = a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) = V >= V = a__isNeList#(V) a__isNeList#(__(V1,V2)) = V1 + V2 >= V1 + V2 = a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) = V1 + V2 >= 0 = a__U42#(a__isPalListKind(V1),V1,V2) a__U43#(tt(),V1,V2) = V1 + V2 + 1 >= 0 = a__U44#(a__isPalListKind(V2),V1,V2) a__isList#(__(V1,V2)) = V1 + V2 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) = V1 + V2 >= V1 + V2 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = V1 + V2 >= V2 = a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) = V2 >= V2 = a__U55#(a__isNeList(V1),V2) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V2 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V2 + 1 >= V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V2 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V + 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 1 >= 1 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V + 1 >= V + 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 1 >= 0 = tt() a__isQid(e()) = 1 >= 0 = tt() a__isQid(i()) = 1 >= 0 = tt() a__isQid(o()) = 1 >= 0 = tt() a__isQid(u()) = 1 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = X + 1 >= X + 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X3 >= X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X2 + 1 >= X2 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(isQid(X)) = 1 >= 1 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = X >= X = a__U63(mark(X)) mark(U71(X1,X2,X3)) = X1 >= X1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X3 + 1 >= X3 + 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X3 + 1 >= X3 + 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X3 >= X3 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X2 + 1 >= X2 + 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 1 >= 1 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X1,X2) = 1 >= 1 = U62(X1,X2) a__U63(X) = X >= X = U63(X) a__U71(X1,X2,X3) = X1 >= X1 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U55#(tt(),V2) -> a__isList#(V2) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__isNeList#(__(V1,V2)) -> a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) -> a__U55#(a__isNeList(V1),V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U55#](x0, x1) = x1, [a__U54#](x0, x1, x2) = x2 + 1, [a__U53#](x0, x1, x2) = x2 + 1, [a__U52#](x0, x1, x2) = x2 + 1, [a__U51#](x0, x1, x2) = x2 + 1, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = x1, [a__isList#](x0) = x0, [a__U21#](x0, x1, x2) = x2 + 1, [a__isNeList#](x0) = x0, [a__U12#](x0, x1) = x1, [a__U11#](x0, x1) = x1, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = x0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = x0, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U26](x0) = 0, [isList](x0) = 1, [U25](x0, x1) = 1, [U24](x0, x1, x2) = 1, [U23](x0, x1, x2) = 1, [U22](x0, x1, x2) = 1, [U21](x0, x1, x2) = 1, [isNeList](x0) = 1, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 1, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = x0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 1, [a__isList](x0) = 1, [a__U24](x0, x1, x2) = 1, [a__U23](x0, x1, x2) = 1, [a__U22](x0, x1, x2) = 1, [a__U21](x0, x1, x2) = 1, [a__U13](x0) = 0, [a__isNeList](x0) = 1, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: a__U55#(tt(),V2) = V2 >= V2 = a__isList#(V2) a__isList#(V) = V >= V = a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) = V >= V = a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) = V >= V = a__isNeList#(V) a__isNeList#(__(V1,V2)) = V1 + V2 + 1 >= V1 = a__U41#(a__isPalListKind(V1),V1,V2) a__U41#(tt(),V1,V2) = V1 >= 0 = a__U42#(a__isPalListKind(V1),V1,V2) a__isList#(__(V1,V2)) = V1 + V2 + 1 >= V2 + 1 = a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) = V1 + V2 + 1 >= V2 + 1 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U54#(a__isPalListKind(V2),V1,V2) a__U54#(tt(),V1,V2) = V2 + 1 >= V2 = a__U55#(a__isNeList(V1),V2) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = 1 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 1 >= 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 1 >= 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 1 >= 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 1 >= 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 1 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 1 >= 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = 1 >= 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 2 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 1 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 1 >= 1 = isNeList(X) a__U21(X1,X2,X3) = 1 >= 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 1 >= 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 1 >= 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 1 >= 1 = U24(X1,X2,X3) a__U25(X1,X2) = 1 >= 1 = U25(X1,X2) a__isList(X) = 1 >= 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = X >= X = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U55#(tt(),V2) -> a__isList#(V2) a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__U41#(tt(),V1,V2) -> a__U42#(a__isPalListKind(V1),V1,V2) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U55#](x0, x1) = 1, [a__U54#](x0, x1, x2) = 0, [a__U53#](x0, x1, x2) = 0, [a__U52#](x0, x1, x2) = 0, [a__U51#](x0, x1, x2) = 0, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 1, [a__isList#](x0) = 0, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = 0, [a__U12#](x0, x1) = 0, [a__U11#](x0, x1) = 0, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [a____](x0, x1) = 0, [__](x0, x1) = 0 orientation: a__U55#(tt(),V2) = 1 >= 0 = a__isList#(V2) a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) = 0 >= 0 = a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) = 0 >= 0 = a__isNeList#(V) a__U41#(tt(),V1,V2) = 1 >= 0 = a__U42#(a__isPalListKind(V1),V1,V2) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 0 >= 0 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = 0 >= 0 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = 0 >= 0 = a__U54#(a__isPalListKind(V2),V1,V2) a____(__(X,Y),Z) = 0 >= 0 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 0 >= 0 = mark(X) a____(nil(),X) = 0 >= 0 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 0 >= 0 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 0 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 0 >= 0 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) -> a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U54#](x0, x1, x2) = 0, [a__U53#](x0, x1, x2) = 0, [a__U52#](x0, x1, x2) = 0, [a__U51#](x0, x1, x2) = 0, [a__isList#](x0) = x0 + 1, [a__U21#](x0, x1, x2) = 1, [a__isNeList#](x0) = 0, [a__U12#](x0, x1) = 0, [a__U11#](x0, x1) = 1, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = x0 + 1, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = x0, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 1, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = 1, [U55](x0, x1) = 1, [U54](x0, x1, x2) = 1, [U53](x0, x1, x2) = 1, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = x1 + 1, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = x1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x1, [isQid](x0) = 0, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = x1 + 1, [U26](x0) = 0, [isList](x0) = x0 + 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0 + 1, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = x1, [U11](x0, x1) = x1, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = x0 + 1, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 1, [a__U62](x0, x1) = x1 + 1, [a__U61](x0, x1) = x1 + 1, [a__U56](x0) = 1, [a__U55](x0, x1) = 1, [a__U54](x0, x1, x2) = 1, [a__U53](x0, x1, x2) = 1, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = x1 + 1, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = x1, [a__U42](x0, x1, x2) = x1, [a__U41](x0, x1, x2) = x1, [a__U33](x0) = 1, [a__isQid](x0) = 0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = x1 + 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = x2, [a__U22](x0, x1, x2) = x2, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = 0, [a__isNeList](x0) = x0 + 1, [a__U12](x0, x1) = x1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: a__isList#(V) = V + 1 >= 1 = a__U11#(a__isPalListKind(V),V) a__U11#(tt(),V) = 1 >= 0 = a__U12#(a__isPalListKind(V),V) a__U12#(tt(),V) = 0 >= 0 = a__isNeList#(V) a__isList#(__(V1,V2)) = V1 + V2 + 1 >= 1 = a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 0 >= 0 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = 0 >= 0 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = 0 >= 0 = a__U54#(a__isPalListKind(V2),V1,V2) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = V >= V = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = V >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V2 >= V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V2 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V + 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isQid(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = V1 >= V1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 >= V1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 1 >= 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 1 >= 1 = a__U56(a__isList(V2)) a__U56(tt()) = 1 >= 0 = tt() a__U61(tt(),V) = V + 1 >= V + 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = V + 1 >= 1 = a__U63(a__isQid(V)) a__U63(tt()) = 1 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= V = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 2 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V + 1 >= V + 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V + 1 >= V + 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = X2 >= X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X2 >= X2 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = X + 1 >= X + 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X3 >= X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X3 >= X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = X2 + 1 >= X2 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 >= X2 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 >= X2 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X2 >= X2 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 1 = a__U56(mark(X)) mark(U61(X1,X2)) = X2 + 1 >= X2 + 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = X2 + 1 >= X2 + 1 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = X + 1 >= X + 1 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = X2 >= X2 = U11(X1,X2) a__U12(X1,X2) = X2 >= X2 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X3 >= X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X3 >= X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X2 + 1 >= X2 + 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 1 >= 1 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 >= X2 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 >= X2 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X2 >= X2 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = X2 + 1 >= X2 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 1 >= 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 1 >= 1 = U54(X1,X2,X3) a__U55(X1,X2) = 1 >= 1 = U55(X1,X2) a__U56(X) = 1 >= 1 = U56(X) a__U61(X1,X2) = X2 + 1 >= X2 + 1 = U61(X1,X2) a__U62(X1,X2) = X2 + 1 >= X2 + 1 = U62(X1,X2) a__U63(X) = 1 >= 1 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = X + 1 >= X + 1 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__U12#(tt(),V) -> a__isNeList#(V) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U54#](x0, x1, x2) = 0, [a__U53#](x0, x1, x2) = 0, [a__U52#](x0, x1, x2) = 0, [a__U51#](x0, x1, x2) = 0, [a__isList#](x0) = 0, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = 0, [a__U12#](x0, x1) = x0 + 1, [a__U11#](x0, x1) = 0, [U92](x0) = 1, [U91](x0, x1) = 1, [isNePal](x0) = 1, [U83](x0) = 1, [U82](x0, x1) = 1, [U81](x0, x1) = 1, [U74](x0) = 1, [isPal](x0) = 1, [U73](x0, x1) = 1, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 1, [U62](x0, x1) = 1, [U61](x0, x1) = 1, [U56](x0) = 1, [U55](x0, x1) = 1, [U54](x0, x1, x2) = 1, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = 1, [U46](x0) = x0, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [isQid](x0) = 1, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U26](x0) = 1, [isList](x0) = 1, [U25](x0, x1) = 1, [U24](x0, x1, x2) = 1, [U23](x0, x1, x2) = 1, [U22](x0, x1, x2) = 1, [U21](x0, x1, x2) = 1, [isNeList](x0) = 1, [U13](x0) = 1, [isPalListKind](x0) = 1, [U12](x0, x1) = 1, [U11](x0, x1) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 1, [a__U91](x0, x1) = 1, [a__U83](x0) = 1, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 1, [a__U81](x0, x1) = 1, [a__U74](x0) = 1, [a__U73](x0, x1) = 1, [a__isPal](x0) = 1, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 1, [a__U62](x0, x1) = 1, [a__U61](x0, x1) = 1, [a__U56](x0) = 1, [a__U55](x0, x1) = 1, [a__U54](x0, x1, x2) = 1, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = x0, [a__U45](x0, x1) = 1, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = 1, [a__isQid](x0) = 1, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U26](x0) = 1, [a__U25](x0, x1) = 1, [a__isList](x0) = 1, [a__U24](x0, x1, x2) = 1, [a__U23](x0, x1, x2) = 1, [a__U22](x0, x1, x2) = 1, [a__U21](x0, x1, x2) = 1, [a__U13](x0) = 1, [a__isNeList](x0) = 1, [a__U12](x0, x1) = 1, [a__isPalListKind](x0) = 1, [a__U11](x0, x1) = 1, [tt] = 1, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__U12#(tt(),V) = 2 >= 0 = a__isNeList#(V) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) = 0 >= 0 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 0 >= 0 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = 0 >= 0 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = 0 >= 0 = a__U54#(a__isPalListKind(V2),V1,V2) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__U11(tt(),V) = 1 >= 1 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 1 >= 1 = a__U13(a__isNeList(V)) a__U13(tt()) = 1 >= 1 = tt() a__U21(tt(),V1,V2) = 1 >= 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 1 >= 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 1 >= 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 1 >= 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 1 >= 1 = a__U26(a__isList(V2)) a__U26(tt()) = 1 >= 1 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isQid(V)) a__U33(tt()) = 1 >= 1 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 1 >= 1 = a__U46(a__isNeList(V2)) a__U46(tt()) = 1 >= 1 = tt() a__U51(tt(),V1,V2) = 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 1 >= 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 1 >= 1 = a__U56(a__isList(V2)) a__U56(tt()) = 1 >= 1 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 1 >= 1 = a__U63(a__isQid(V)) a__U63(tt()) = 1 >= 1 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 1 >= 1 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 1 >= 1 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 1 >= 1 = tt() a__U91(tt(),V2) = 1 >= 1 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 1 >= 1 = tt() a__isList(V) = 1 >= 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 1 = tt() a__isList(__(V1,V2)) = 1 >= 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 1 = tt() a__isPalListKind(a()) = 1 >= 1 = tt() a__isPalListKind(e()) = 1 >= 1 = tt() a__isPalListKind(i()) = 1 >= 1 = tt() a__isPalListKind(nil()) = 1 >= 1 = tt() a__isPalListKind(o()) = 1 >= 1 = tt() a__isPalListKind(u()) = 1 >= 1 = tt() a__isPalListKind(__(V1,V2)) = 1 >= 1 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 1 >= 1 = tt() a__isQid(e()) = 1 >= 1 = tt() a__isQid(i()) = 1 >= 1 = tt() a__isQid(o()) = 1 >= 1 = tt() a__isQid(u()) = 1 >= 1 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 1 = a__isPalListKind(X) mark(U13(X)) = 1 >= 1 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 1 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 1 = a__isList(X) mark(U26(X)) = 1 >= 1 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 1 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 >= X1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 1 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 1 >= 1 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 1 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = 1 >= 1 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 1 >= 1 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 1 >= 1 = U12(X1,X2) a__isPalListKind(X) = 1 >= 1 = isPalListKind(X) a__U13(X) = 1 >= 1 = U13(X) a__isNeList(X) = 1 >= 1 = isNeList(X) a__U21(X1,X2,X3) = 1 >= 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 1 >= 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 1 >= 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 1 >= 1 = U24(X1,X2,X3) a__U25(X1,X2) = 1 >= 1 = U25(X1,X2) a__isList(X) = 1 >= 1 = isList(X) a__U26(X) = 1 >= 1 = U26(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 1 >= 1 = U33(X) a__isQid(X) = 1 >= 1 = isQid(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = 1 >= 1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 1 >= 1 = U54(X1,X2,X3) a__U55(X1,X2) = 1 >= 1 = U55(X1,X2) a__U56(X) = 1 >= 1 = U56(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X1,X2) = 1 >= 1 = U62(X1,X2) a__U63(X) = 1 >= 1 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = 1 >= 1 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 1 >= 1 = U74(X) a__U81(X1,X2) = 1 >= 1 = U81(X1,X2) a__U82(X1,X2) = 1 >= 1 = U82(X1,X2) a__U83(X) = 1 >= 1 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = 1 >= 1 = U91(X1,X2) a__U92(X) = 1 >= 1 = U92(X) problem: DPs: a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) -> a__U54#(a__isPalListKind(V2),V1,V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U54#](x0, x1, x2) = 0, [a__U53#](x0, x1, x2) = 1, [a__U52#](x0, x1, x2) = 1, [a__U51#](x0, x1, x2) = x0 + 1, [a__isList#](x0) = 0, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = x0 + 1, [a__U11#](x0, x1) = 0, [U92](x0) = x0, [U91](x0, x1) = 1, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = x0, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = x0, [U56](x0) = 1, [U55](x0, x1) = 1, [U54](x0, x1, x2) = 1, [U53](x0, x1, x2) = 1, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = 1, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = 1, [U26](x0) = x0, [isList](x0) = 1, [U25](x0, x1) = 1, [U24](x0, x1, x2) = 1, [U23](x0, x1, x2) = 1, [U22](x0, x1, x2) = 1, [U21](x0, x1, x2) = 1, [isNeList](x0) = 1, [U13](x0) = 0, [isPalListKind](x0) = 1, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 1, [o] = 0, [i] = 1, [e] = 0, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = 1, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = x0, [a__U56](x0) = 1, [a__U55](x0, x1) = 1, [a__U54](x0, x1, x2) = 1, [a__U53](x0, x1, x2) = 1, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = 1, [a__U26](x0) = x0, [a__U25](x0, x1) = 1, [a__isList](x0) = 1, [a__U24](x0, x1, x2) = 1, [a__U23](x0, x1, x2) = 1, [a__U22](x0, x1, x2) = 1, [a__U21](x0, x1, x2) = 1, [a__U13](x0) = 0, [a__isNeList](x0) = 1, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 1, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 1, [mark](x0) = 1, [a____](x0, x1) = 1, [__](x0, x1) = 1 orientation: a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) = 2 >= 2 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 1 >= 1 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = 1 >= 1 = a__U53#(a__isPalListKind(V2),V1,V2) a__U53#(tt(),V1,V2) = 1 >= 0 = a__U54#(a__isPalListKind(V2),V1,V2) a____(__(X,Y),Z) = 1 >= 1 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 1 >= 1 = mark(X) a____(nil(),X) = 1 >= 1 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 1 >= 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 1 >= 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 1 >= 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 1 >= 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 1 >= 1 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 1 >= 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 1 >= 1 = a__U56(a__isList(V2)) a__U56(tt()) = 1 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 1 >= 1 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 1 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = 1 >= 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 1 >= 0 = tt() a__isPalListKind(e()) = 1 >= 0 = tt() a__isPalListKind(i()) = 1 >= 0 = tt() a__isPalListKind(nil()) = 1 >= 0 = tt() a__isPalListKind(o()) = 1 >= 0 = tt() a__isPalListKind(u()) = 1 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 1 >= 1 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 1 >= 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 1 = a__isPalListKind(X) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 1 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 1 = a__isList(X) mark(U26(X)) = 1 >= 1 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 1 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 1 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = 1 >= 1 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 1 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 1 >= 0 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 1 >= 0 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = 1 >= 1 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 1 >= 1 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 1 >= 1 = isNeList(X) a__U21(X1,X2,X3) = 1 >= 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 1 >= 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 1 >= 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 1 >= 1 = U24(X1,X2,X3) a__U25(X1,X2) = 1 >= 1 = U25(X1,X2) a__isList(X) = 1 >= 1 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 1 >= 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 1 >= 1 = U54(X1,X2,X3) a__U55(X1,X2) = 1 >= 1 = U55(X1,X2) a__U56(X) = 1 >= 1 = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = 1 >= 1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) -> a__U53#(a__isPalListKind(V2),V1,V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U53#](x0, x1, x2) = 0, [a__U52#](x0, x1, x2) = 1, [a__U51#](x0, x1, x2) = 1, [a__isList#](x0) = 0, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = 1, [a__U11#](x0, x1) = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = 0, [U74](x0) = x0, [isPal](x0) = 0, [U73](x0, x1) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x0, [U63](x0) = x0, [U62](x0, x1) = 1, [U61](x0, x1) = 1, [U56](x0) = 1, [U55](x0, x1) = 1, [U54](x0, x1, x2) = 1, [U53](x0, x1, x2) = 1, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = 1, [U46](x0) = x0, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = x0, [isList](x0) = 0, [U25](x0, x1) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [isNeList](x0) = 1, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = x0, [a__U81](x0, x1) = 0, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 0, [a__U72](x0, x1) = x0, [a__U71](x0, x1, x2) = x0, [a__U63](x0) = x0, [a__U62](x0, x1) = 1, [a__U61](x0, x1) = 1, [a__U56](x0) = 1, [a__U55](x0, x1) = 1, [a__U54](x0, x1, x2) = 1, [a__U53](x0, x1, x2) = 1, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = x0, [a__U45](x0, x1) = 1, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = x0, [a__U25](x0, x1) = x0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = x0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = x0, [a__U21](x0, x1, x2) = x0, [a__U13](x0) = 0, [a__isNeList](x0) = 1, [a__U12](x0, x1) = x0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = 1, [a____](x0, x1) = 1, [__](x0, x1) = 1 orientation: a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) = 1 >= 1 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 1 >= 1 = a__U52#(a__isPalListKind(V1),V1,V2) a__U52#(tt(),V1,V2) = 1 >= 0 = a__U53#(a__isPalListKind(V2),V1,V2) a____(__(X,Y),Z) = 1 >= 1 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 1 >= 1 = mark(X) a____(nil(),X) = 1 >= 1 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 1 >= 1 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 1 >= 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 1 >= 1 = a__U56(a__isList(V2)) a__U56(tt()) = 1 >= 0 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 1 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 1 >= 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 0 = a__isPalListKind(X) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 1 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 0 = a__isList(X) mark(U26(X)) = 1 >= 1 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 1 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 1 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 0 = a__isPal(X) mark(U74(X)) = 1 >= 1 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = 1 >= 1 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 1 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = 1 >= 1 = __(X1,X2) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 1 >= 1 = isNeList(X) a__U21(X1,X2,X3) = X1 >= X1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 >= X1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X1 >= X1 = U24(X1,X2,X3) a__U25(X1,X2) = X1 >= X1 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = 1 >= 1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 1 >= 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 1 >= 1 = U54(X1,X2,X3) a__U55(X1,X2) = 1 >= 1 = U55(X1,X2) a__U56(X) = 1 >= 1 = U56(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X1,X2) = 1 >= 1 = U62(X1,X2) a__U63(X) = X >= X = U63(X) a__U71(X1,X2,X3) = X1 >= X1 = U71(X1,X2,X3) a__U72(X1,X2) = X1 >= X1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = X1 >= X1 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) -> a__U52#(a__isPalListKind(V1),V1,V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U52#](x0, x1, x2) = 0, [a__U51#](x0, x1, x2) = 1, [a__isList#](x0) = 0, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = 1, [a__U11#](x0, x1) = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 1, [U83](x0) = x0, [U82](x0, x1) = 1, [U81](x0, x1) = 0, [U74](x0) = x0, [isPal](x0) = 1, [U73](x0, x1) = x0, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = x0, [U62](x0, x1) = x0, [U61](x0, x1) = x0, [U56](x0) = x0, [U55](x0, x1) = 1, [U54](x0, x1, x2) = 1, [U53](x0, x1, x2) = 1, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = 1, [U46](x0) = x0, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [isList](x0) = 1, [U25](x0, x1) = 1, [U24](x0, x1, x2) = 1, [U23](x0, x1, x2) = 1, [U22](x0, x1, x2) = 1, [U21](x0, x1, x2) = 1, [isNeList](x0) = 1, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = 1, [U11](x0, x1) = 1, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 1, [a__U81](x0, x1) = 1, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = x0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0, [a__U56](x0) = x0, [a__U55](x0, x1) = 1, [a__U54](x0, x1, x2) = 1, [a__U53](x0, x1, x2) = 1, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = x0, [a__U45](x0, x1) = 1, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = x0, [a__U25](x0, x1) = 1, [a__isList](x0) = 1, [a__U24](x0, x1, x2) = 1, [a__U23](x0, x1, x2) = 1, [a__U22](x0, x1, x2) = 1, [a__U21](x0, x1, x2) = 1, [a__U13](x0) = x0, [a__isNeList](x0) = 1, [a__U12](x0, x1) = 1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 1, [tt] = 0, [nil] = 1, [mark](x0) = 1, [a____](x0, x1) = 1, [__](x0, x1) = 1 orientation: a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) = 1 >= 1 = a__U51#(a__isPalListKind(V1),V1,V2) a__U51#(tt(),V1,V2) = 1 >= 0 = a__U52#(a__isPalListKind(V1),V1,V2) a____(__(X,Y),Z) = 1 >= 1 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 1 >= 1 = mark(X) a____(nil(),X) = 1 >= 1 = mark(X) a__U11(tt(),V) = 1 >= 1 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 1 >= 1 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 1 >= 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 1 >= 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 1 >= 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 1 >= 1 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 1 >= 1 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 1 >= 1 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 1 >= 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 1 >= 1 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 1 >= 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = 1 >= 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 1 >= 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 0 = a__isPalListKind(X) mark(U13(X)) = 1 >= 1 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 1 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 1 = a__isList(X) mark(U26(X)) = 1 >= 1 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 1 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 1 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 1 >= 1 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 1 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = 1 >= 1 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 1 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = 1 >= 1 = __(X1,X2) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 1 >= 1 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = 1 >= 1 = isNeList(X) a__U21(X1,X2,X3) = 1 >= 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 1 >= 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 1 >= 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 1 >= 1 = U24(X1,X2,X3) a__U25(X1,X2) = 1 >= 1 = U25(X1,X2) a__isList(X) = 1 >= 1 = isList(X) a__U26(X) = X >= X = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = 1 >= 1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 1 >= 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 1 >= 1 = U54(X1,X2,X3) a__U55(X1,X2) = 1 >= 1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = X >= X = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = 1 >= 0 = U81(X1,X2) a__U82(X1,X2) = 1 >= 1 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) -> a__U51#(a__isPalListKind(V1),V1,V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U51#](x0, x1, x2) = 0, [a__isList#](x0) = 0, [a__U21#](x0, x1, x2) = 0, [a__isNeList#](x0) = 1, [a__U11#](x0, x1) = 0, [U92](x0) = 0, [U91](x0, x1) = x0, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = x0, [U74](x0) = x0, [isPal](x0) = 1, [U73](x0, x1) = 0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = 0, [U63](x0) = x0, [U62](x0, x1) = 1, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 1, [U54](x0, x1, x2) = 1, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 1, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 1, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U26](x0) = 0, [isList](x0) = 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = x0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 1, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [a__U92](x0) = 0, [a__U91](x0, x1) = x0, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = x0, [a__U74](x0) = x0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 1, [a__U72](x0, x1) = x0, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = x0, [a__U62](x0, x1) = 1, [a__U61](x0, x1) = 1, [a__U56](x0) = 0, [a__U55](x0, x1) = 1, [a__U54](x0, x1, x2) = 1, [a__U53](x0, x1, x2) = 1, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = 0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = x0, [a__isQid](x0) = 1, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 1, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = x0, [a__isNeList](x0) = 1, [a__U12](x0, x1) = 1, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 1, [tt] = 0, [nil] = 1, [mark](x0) = 1, [a____](x0, x1) = 1, [__](x0, x1) = 0 orientation: a__isList#(V) = 0 >= 0 = a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) = 0 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a__isNeList#(__(V1,V2)) = 1 >= 0 = a__U51#(a__isPalListKind(V1),V1,V2) a____(__(X,Y),Z) = 1 >= 1 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 1 >= 1 = mark(X) a____(nil(),X) = 1 >= 1 = mark(X) a__U11(tt(),V) = 1 >= 1 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 1 >= 1 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 1 >= 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 1 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 1 >= 1 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 1 >= 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = 1 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 1 >= 0 = tt() a__isQid(e()) = 1 >= 0 = tt() a__isQid(i()) = 1 >= 0 = tt() a__isQid(o()) = 1 >= 0 = tt() a__isQid(u()) = 1 >= 0 = tt() mark(__(X1,X2)) = 1 >= 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 0 = a__isPalListKind(X) mark(U13(X)) = 1 >= 1 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 1 = a__isList(X) mark(U26(X)) = 1 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 1 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 1 >= 1 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = 1 >= 0 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 1 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = 1 >= 0 = __(X1,X2) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 1 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = X >= X = U13(X) a__isNeList(X) = 1 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 1 >= 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = X >= 0 = U33(X) a__isQid(X) = 1 >= 1 = isQid(X) a__U41(X1,X2,X3) = 1 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 1 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 1 >= 1 = U54(X1,X2,X3) a__U55(X1,X2) = 1 >= 1 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 1 >= 0 = U61(X1,X2) a__U62(X1,X2) = 1 >= 1 = U62(X1,X2) a__U63(X) = X >= X = U63(X) a__U71(X1,X2,X3) = 1 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = X1 >= X1 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 >= X1 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__isList#(V) -> a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) -> a__U21#(a__isPalListKind(V1),V1,V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__isList#](x0) = 1, [a__U21#](x0, x1, x2) = 0, [a__U11#](x0, x1) = 1, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [a____](x0, x1) = 0, [__](x0, x1) = 0 orientation: a__isList#(V) = 1 >= 1 = a__U11#(a__isPalListKind(V),V) a__isList#(__(V1,V2)) = 1 >= 0 = a__U21#(a__isPalListKind(V1),V1,V2) a____(__(X,Y),Z) = 0 >= 0 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 0 >= 0 = mark(X) a____(nil(),X) = 0 >= 0 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 0 >= 0 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 0 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 0 >= 0 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__isList#(V) -> a__U11#(a__isPalListKind(V),V) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__isList#](x0) = 1, [a__U11#](x0, x1) = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = x0, [U82](x0, x1) = 0, [U81](x0, x1) = x0, [U74](x0) = x0, [isPal](x0) = 0, [U73](x0, x1) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x0, [U63](x0) = x0, [U62](x0, x1) = x0, [U61](x0, x1) = x0, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = x0, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 0, [a__U72](x0, x1) = x0, [a__U71](x0, x1, x2) = x0, [a__U63](x0) = x0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = x0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = x0, [a__U51](x0, x1, x2) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = 1, [a____](x0, x1) = 1, [__](x0, x1) = 1 orientation: a__isList#(V) = 1 >= 0 = a__U11#(a__isPalListKind(V),V) a____(__(X,Y),Z) = 1 >= 1 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 1 >= 1 = mark(X) a____(nil(),X) = 1 >= 1 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 1 >= 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 0 = a__isPalListKind(X) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 0 = a__isList(X) mark(U26(X)) = 1 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 1 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 1 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 0 = a__isPal(X) mark(U74(X)) = 1 >= 1 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 1 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = 1 >= 1 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 1 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = 1 >= 1 = __(X1,X2) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X1 >= X1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X1 >= X1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 >= X1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = X >= X = U63(X) a__U71(X1,X2,X3) = X1 >= X1 = U71(X1,X2,X3) a__U72(X1,X2) = X1 >= X1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 >= X1 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Qed DPs: a__isNePal#(__(I,__(P,I))) -> a__U71#(a__isQid(I),I,P) a__U71#(tt(),I,P) -> a__U72#(a__isPalListKind(I),P) a__U72#(tt(),P) -> a__isPal#(P) a__isPal#(V) -> a__U81#(a__isPalListKind(V),V) a__U81#(tt(),V) -> a__U82#(a__isPalListKind(V),V) a__U82#(tt(),V) -> a__isNePal#(V) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__isNePal#](x0) = x0, [a__U82#](x0, x1) = x1, [a__U81#](x0, x1) = x1, [a__isPal#](x0) = x0, [a__U72#](x0, x1) = x1, [a__U71#](x0, x1, x2) = x2 + 1, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 1, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 1, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 1, [U62](x0, x1) = 1, [U61](x0, x1) = 1, [U56](x0) = 0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = 1, [U53](x0, x1, x2) = 1, [U52](x0, x1, x2) = 1, [U51](x0, x1, x2) = 1, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 1, [isNeList](x0) = 1, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 1, [a__isPal](x0) = 0, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 1, [a__U62](x0, x1) = 1, [a__U61](x0, x1) = 1, [a__U56](x0) = 0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = 1, [a__U53](x0, x1, x2) = 1, [a__U52](x0, x1, x2) = 1, [a__U51](x0, x1, x2) = 1, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 1, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 1, [a__U13](x0) = 0, [a__isNeList](x0) = 1, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: a__isNePal#(__(I,__(P,I))) = 2I + P + 2 >= P + 1 = a__U71#(a__isQid(I),I,P) a__U71#(tt(),I,P) = P + 1 >= P = a__U72#(a__isPalListKind(I),P) a__U72#(tt(),P) = P >= P = a__isPal#(P) a__isPal#(V) = V >= V = a__U81#(a__isPalListKind(V),V) a__U81#(tt(),V) = V >= V = a__U82#(a__isPalListKind(V),V) a__U82#(tt(),V) = V >= V = a__isNePal#(V) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = 1 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 1 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 1 >= 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 1 >= 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 1 >= 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 1 >= 1 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 1 >= 1 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 1 >= 1 = a__U63(a__isQid(V)) a__U63(tt()) = 1 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 1 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 1 >= 1 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = 1 >= 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 1 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 1 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 1 >= 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 1 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = X1 >= X1 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 1 >= 1 = isNeList(X) a__U21(X1,X2,X3) = 1 >= 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 1 >= 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 1 >= 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 1 >= 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 1 >= 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 1 >= 1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X1,X2) = 1 >= 1 = U62(X1,X2) a__U63(X) = 1 >= 1 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = 1 >= 1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U72#(tt(),P) -> a__isPal#(P) a__isPal#(V) -> a__U81#(a__isPalListKind(V),V) a__U81#(tt(),V) -> a__U82#(a__isPalListKind(V),V) a__U82#(tt(),V) -> a__isNePal#(V) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__isNePal#](x0) = 0, [a__U82#](x0, x1) = 0, [a__U81#](x0, x1) = 1, [a__isPal#](x0) = 1, [a__U72#](x0, x1) = 1, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = x0, [a__U63](x0) = 0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [a____](x0, x1) = 0, [__](x0, x1) = 0 orientation: a__U72#(tt(),P) = 1 >= 1 = a__isPal#(P) a__isPal#(V) = 1 >= 1 = a__U81#(a__isPalListKind(V),V) a__U81#(tt(),V) = 1 >= 0 = a__U82#(a__isPalListKind(V),V) a__U82#(tt(),V) = 0 >= 0 = a__isNePal#(V) a____(__(X,Y),Z) = 0 >= 0 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 0 >= 0 = mark(X) a____(nil(),X) = 0 >= 0 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 0 >= 0 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 0 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 0 >= 0 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = X1 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = X1 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = X1 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U72#(tt(),P) -> a__isPal#(P) a__isPal#(V) -> a__U81#(a__isPalListKind(V),V) a__U82#(tt(),V) -> a__isNePal#(V) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__isNePal#](x0) = 0, [a__U82#](x0, x1) = 1, [a__U81#](x0, x1) = 0, [a__isPal#](x0) = 0, [a__U72#](x0, x1) = 0, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [a____](x0, x1) = x1, [__](x0, x1) = x1 orientation: a__U72#(tt(),P) = 0 >= 0 = a__isPal#(P) a__isPal#(V) = 0 >= 0 = a__U81#(a__isPalListKind(V),V) a__U82#(tt(),V) = 1 >= 0 = a__isNePal#(V) a____(__(X,Y),Z) = Z >= 0 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 0 >= 0 = mark(X) a____(nil(),X) = X >= 0 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 0 >= 0 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 0 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 0 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 0 >= 0 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X2 >= X2 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U72#(tt(),P) -> a__isPal#(P) a__isPal#(V) -> a__U81#(a__isPalListKind(V),V) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U81#](x0, x1) = 0, [a__isPal#](x0) = 0, [a__U72#](x0, x1) = x1 + 1, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 1, [U83](x0) = x0, [U82](x0, x1) = 1, [U81](x0, x1) = 1, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = 1, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = x2 + 1, [U53](x0, x1, x2) = x2 + 1, [U52](x0, x1, x2) = x2 + 1, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U26](x0) = 0, [isList](x0) = x0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 1, [U23](x0, x1, x2) = x2 + 1, [U22](x0, x1, x2) = x2 + 1, [U21](x0, x1, x2) = x1 + x2 + 1, [isNeList](x0) = x0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = x0, [a__isNePal](x0) = 1, [a__U82](x0, x1) = 1, [a__U81](x0, x1) = 1, [a__U74](x0) = 0, [a__U73](x0, x1) = 1, [a__isPal](x0) = 1, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = x2 + 1, [a__U53](x0, x1, x2) = x2 + 1, [a__U52](x0, x1, x2) = x2 + 1, [a__U51](x0, x1, x2) = x2 + 1, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = x1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = 0, [a__isQid](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = 1, [a__U23](x0, x1, x2) = x2 + 1, [a__U22](x0, x1, x2) = x2 + 1, [a__U21](x0, x1, x2) = x1 + x2 + 1, [a__U13](x0) = 0, [a__isNeList](x0) = x0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: a__U72#(tt(),P) = P + 1 >= 0 = a__isPal#(P) a__isPal#(V) = 0 >= 0 = a__U81#(a__isPalListKind(V),V) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 1 >= X = mark(X) a____(nil(),X) = X + 1 >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 + 1 >= V2 + 1 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V2 + 1 >= 1 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 1 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = V2 + 1 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 1 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 1 >= 1 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 1 >= 1 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V2 + 1 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 1 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 1 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 1 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 1 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(isQid(X)) = 0 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 >= X2 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 1 = a__U82(mark(X1),X2) mark(U83(X)) = X >= X = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 1 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = X >= X = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X3 + 1 >= X3 + 1 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X3 + 1 >= X3 + 1 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 1 >= 1 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 >= X2 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = X3 + 1 >= X3 + 1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X3 + 1 >= X3 + 1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X3 + 1 >= X3 + 1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X3 + 1 >= X3 + 1 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = 1 >= 1 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 1 >= 1 = U81(X1,X2) a__U82(X1,X2) = 1 >= 1 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 1 >= 1 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__isPal#(V) -> a__U81#(a__isPalListKind(V),V) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U81#](x0, x1) = 0, [a__isPal#](x0) = 1, [U92](x0) = x0, [U91](x0, x1) = x0, [isNePal](x0) = 0, [U83](x0) = x0, [U82](x0, x1) = 0, [U81](x0, x1) = x0, [U74](x0) = x0, [isPal](x0) = 0, [U73](x0, x1) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x0, [U63](x0) = x0, [U62](x0, x1) = x0, [U61](x0, x1) = x0, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [isQid](x0) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = 0, [isList](x0) = 0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = 0, [isNeList](x0) = 0, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [a__U92](x0) = x0, [a__U91](x0, x1) = x0, [a__U83](x0) = x0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = x0, [a__U74](x0) = x0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 0, [a__U72](x0, x1) = x0, [a__U71](x0, x1, x2) = x0, [a__U63](x0) = x0, [a__U62](x0, x1) = x0, [a__U61](x0, x1) = x0, [a__U56](x0) = x0, [a__U55](x0, x1) = x0, [a__U54](x0, x1, x2) = x0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = x0, [a__U51](x0, x1, x2) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__isQid](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = 0, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = 0, [a__U13](x0) = 0, [a__isNeList](x0) = 0, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = 1, [a____](x0, x1) = 1, [__](x0, x1) = 1 orientation: a__isPal#(V) = 1 >= 0 = a__U81#(a__isPalListKind(V),V) a____(__(X,Y),Z) = 1 >= 1 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 1 >= 1 = mark(X) a____(nil(),X) = 1 >= 1 = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = 0 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isQid(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = 0 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = 0 >= 0 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = 0 >= 0 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = 0 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 1 >= 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 1 >= 0 = a__isPalListKind(X) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = 1 >= 0 = a__isNeList(X) mark(U21(X1,X2,X3)) = 1 >= 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 1 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 1 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 1 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 1 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = 1 >= 0 = a__isList(X) mark(U26(X)) = 1 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 0 = a__isQid(X) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 1 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 1 >= 1 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 1 >= 1 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 1 >= 1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 1 >= 1 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 1 >= 1 = a__U55(mark(X1),X2) mark(U56(X)) = 1 >= 1 = a__U56(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 1 >= 1 = a__U62(mark(X1),X2) mark(U63(X)) = 1 >= 1 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 1 >= 1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 0 = a__isPal(X) mark(U74(X)) = 1 >= 1 = a__U74(mark(X)) mark(U81(X1,X2)) = 1 >= 1 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 1 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 1 >= 1 = a__U83(mark(X)) mark(isNePal(X)) = 1 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 1 >= 1 = a__U91(mark(X1),X2) mark(U92(X)) = 1 >= 1 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 1 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 1 >= 1 = i() mark(o()) = 1 >= 1 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = 1 >= 1 = __(X1,X2) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = 0 >= 0 = isNeList(X) a__U21(X1,X2,X3) = 0 >= 0 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = 0 >= 0 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__isQid(X) = 0 >= 0 = isQid(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2,X3) = X1 >= X1 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X1 >= X1 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = X1 >= X1 = U54(X1,X2,X3) a__U55(X1,X2) = X1 >= X1 = U55(X1,X2) a__U56(X) = X >= X = U56(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X1,X2) = X1 >= X1 = U62(X1,X2) a__U63(X) = X >= X = U63(X) a__U71(X1,X2,X3) = X1 >= X1 = U71(X1,X2,X3) a__U72(X1,X2) = X1 >= X1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = X >= X = U74(X) a__U81(X1,X2) = X1 >= X1 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = X >= X = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = X1 >= X1 = U91(X1,X2) a__U92(X) = X >= X = U92(X) problem: DPs: TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Qed DPs: a__U91#(tt(),V2) -> a__isPalListKind#(V2) a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) -> a__U91#(a__isPalListKind(V1),V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U91#](x0, x1) = x0 + x1 + 1, [a__isPalListKind#](x0) = x0 + 1, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = x0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 1, [U73](x0, x1) = x0, [U72](x0, x1) = 1, [U71](x0, x1, x2) = 1, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = x0, [U52](x0, x1, x2) = x0 + x2, [U51](x0, x1, x2) = x1 + x2, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = x1 + x2 + 1, [U41](x0, x1, x2) = x1 + x2 + 1, [isQid](x0) = 1, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U26](x0) = 0, [isList](x0) = x0 + 1, [U25](x0, x1) = 0, [U24](x0, x1, x2) = 0, [U23](x0, x1, x2) = 0, [U22](x0, x1, x2) = 0, [U21](x0, x1, x2) = x0 + x2, [isNeList](x0) = x0 + 1, [U13](x0) = 0, [isPalListKind](x0) = x0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = x0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = x0, [a__isPal](x0) = 1, [a__U72](x0, x1) = 1, [a__U71](x0, x1, x2) = 1, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = x0, [a__U52](x0, x1, x2) = x0 + x2, [a__U51](x0, x1, x2) = x1 + x2, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = x1 + x2 + 1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = 1, [a__isQid](x0) = 1, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0 + 1, [a__U24](x0, x1, x2) = 0, [a__U23](x0, x1, x2) = 0, [a__U22](x0, x1, x2) = 0, [a__U21](x0, x1, x2) = x0 + x2, [a__U13](x0) = 0, [a__isNeList](x0) = x0 + 1, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = x0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: a__U91#(tt(),V2) = V2 + 1 >= V2 + 1 = a__isPalListKind#(V2) a__isPalListKind#(__(V1,V2)) = V1 + V2 + 2 >= V1 + 1 = a__isPalListKind#(V1) a__isPalListKind#(__(V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = a__U91#(a__isPalListKind(V1),V2) a____(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 2 >= X = mark(X) a____(nil(),X) = X + 2 >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V2 >= 0 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = 0 >= 0 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = 0 >= 0 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = 0 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isQid(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 + 1 >= 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = V2 >= V2 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 1 >= 1 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 1 >= 1 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V + 1 >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 2 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 + 2 >= V1 + V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V + 1 >= 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 2 >= V1 + V2 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = V >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 2I + P + 2 >= 1 = a__U71(a__isQid(I),I,P) a__isPal(V) = 1 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 1 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 1 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = V1 + V2 + 1 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 1 >= 0 = tt() a__isQid(e()) = 1 >= 0 = tt() a__isQid(i()) = 1 >= 0 = tt() a__isQid(o()) = 1 >= 0 = tt() a__isQid(u()) = 1 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = X >= X = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = X + 1 >= X + 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = X1 + X3 >= X1 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = 0 >= 0 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = 0 >= 0 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = 0 >= 0 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X + 1 >= X + 1 = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = 1 >= 1 = a__isQid(X) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = X1 + X3 >= X1 + X3 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = X1 >= X1 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 1 >= 1 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 1 >= 1 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = X1 >= X1 = a__U73(mark(X1),X2) mark(isPal(X)) = 1 >= 1 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = X >= X = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U21(X1,X2,X3) = X1 + X3 >= X1 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = 0 >= 0 = U22(X1,X2,X3) a__U23(X1,X2,X3) = 0 >= 0 = U23(X1,X2,X3) a__U24(X1,X2,X3) = 0 >= 0 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X + 1 >= X + 1 = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 1 >= 1 = U33(X) a__isQid(X) = 1 >= 1 = isQid(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = X2 + X3 >= X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2,X3) = X1 + X3 >= X1 + X3 = U52(X1,X2,X3) a__U53(X1,X2,X3) = X1 >= X1 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 1 >= 1 = U71(X1,X2,X3) a__U72(X1,X2) = 1 >= 1 = U72(X1,X2) a__U73(X1,X2) = X1 >= X1 = U73(X1,X2) a__isPal(X) = 1 >= 1 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = X >= X = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: a__U91#(tt(),V2) -> a__isPalListKind#(V2) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U91#](x0, x1) = 1, [a__isPalListKind#](x0) = 0, [U92](x0) = 0, [U91](x0, x1) = 0, [isNePal](x0) = 0, [U83](x0) = 0, [U82](x0, x1) = 0, [U81](x0, x1) = 0, [U74](x0) = 0, [isPal](x0) = 0, [U73](x0, x1) = 0, [U72](x0, x1) = 0, [U71](x0, x1, x2) = 0, [U63](x0) = 0, [U62](x0, x1) = 0, [U61](x0, x1) = 0, [U56](x0) = 0, [U55](x0, x1) = 0, [U54](x0, x1, x2) = 0, [U53](x0, x1, x2) = 0, [U52](x0, x1, x2) = 0, [U51](x0, x1, x2) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2 + 1, [isQid](x0) = x0, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U26](x0) = 0, [isList](x0) = x0, [U25](x0, x1) = 0, [U24](x0, x1, x2) = x1 + x2, [U23](x0, x1, x2) = x1 + x2, [U22](x0, x1, x2) = x1 + x2, [U21](x0, x1, x2) = x1 + x2, [isNeList](x0) = x0 + 1, [U13](x0) = 0, [isPalListKind](x0) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 1, [a__U92](x0) = 0, [a__U91](x0, x1) = 0, [a__U83](x0) = 0, [a__isNePal](x0) = 0, [a__U82](x0, x1) = 0, [a__U81](x0, x1) = 0, [a__U74](x0) = 0, [a__U73](x0, x1) = 0, [a__isPal](x0) = 0, [a__U72](x0, x1) = 0, [a__U71](x0, x1, x2) = 0, [a__U63](x0) = 0, [a__U62](x0, x1) = 0, [a__U61](x0, x1) = 0, [a__U56](x0) = 0, [a__U55](x0, x1) = 0, [a__U54](x0, x1, x2) = 0, [a__U53](x0, x1, x2) = 0, [a__U52](x0, x1, x2) = 0, [a__U51](x0, x1, x2) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = x2 + 1, [a__U42](x0, x1, x2) = x2 + 1, [a__U41](x0, x1, x2) = x2 + 1, [a__U33](x0) = 1, [a__isQid](x0) = x0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U26](x0) = 0, [a__U25](x0, x1) = 0, [a__isList](x0) = x0, [a__U24](x0, x1, x2) = x1 + x2, [a__U23](x0, x1, x2) = x1 + x2, [a__U22](x0, x1, x2) = x1 + x2, [a__U21](x0, x1, x2) = x1 + x2, [a__U13](x0) = 0, [a__isNeList](x0) = x0 + 1, [a__U12](x0, x1) = 0, [a__isPalListKind](x0) = 0, [a__U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: a__U91#(tt(),V2) = 1 >= 0 = a__isPalListKind#(V2) a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X >= X = mark(X) a____(nil(),X) = X >= X = mark(X) a__U11(tt(),V) = 0 >= 0 = a__U12(a__isPalListKind(V),V) a__U12(tt(),V) = 0 >= 0 = a__U13(a__isNeList(V)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) = V1 + V2 >= 0 = a__U25(a__isList(V1),V2) a__U25(tt(),V2) = 0 >= 0 = a__U26(a__isList(V2)) a__U26(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isPalListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isQid(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V2 + 1 >= 1 = a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 0 = a__U45(a__isList(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNeList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) = 0 >= 0 = a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) = 0 >= 0 = a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) = 0 >= 0 = a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) = 0 >= 0 = a__U56(a__isList(V2)) a__U56(tt()) = 0 >= 0 = tt() a__U61(tt(),V) = 0 >= 0 = a__U62(a__isPalListKind(V),V) a__U62(tt(),V) = 0 >= 0 = a__U63(a__isQid(V)) a__U63(tt()) = 0 >= 0 = tt() a__U71(tt(),I,P) = 0 >= 0 = a__U72(a__isPalListKind(I),P) a__U72(tt(),P) = 0 >= 0 = a__U73(a__isPal(P),P) a__U73(tt(),P) = 0 >= 0 = a__U74(a__isPalListKind(P)) a__U74(tt()) = 0 >= 0 = tt() a__U81(tt(),V) = 0 >= 0 = a__U82(a__isPalListKind(V),V) a__U82(tt(),V) = 0 >= 0 = a__U83(a__isNePal(V)) a__U83(tt()) = 0 >= 0 = tt() a__U91(tt(),V2) = 0 >= 0 = a__U92(a__isPalListKind(V2)) a__U92(tt()) = 0 >= 0 = tt() a__isList(V) = V >= 0 = a__U11(a__isPalListKind(V),V) a__isList(nil()) = 0 >= 0 = tt() a__isList(__(V1,V2)) = V1 + V2 >= V1 + V2 = a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) = V + 1 >= 1 = a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= V2 + 1 = a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) = V1 + V2 + 1 >= 0 = a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) = 0 >= 0 = a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U71(a__isQid(I),I,P) a__isPal(V) = 0 >= 0 = a__U81(a__isPalListKind(V),V) a__isPal(nil()) = 0 >= 0 = tt() a__isPalListKind(a()) = 0 >= 0 = tt() a__isPalListKind(e()) = 0 >= 0 = tt() a__isPalListKind(i()) = 0 >= 0 = tt() a__isPalListKind(nil()) = 0 >= 0 = tt() a__isPalListKind(o()) = 0 >= 0 = tt() a__isPalListKind(u()) = 0 >= 0 = tt() a__isPalListKind(__(V1,V2)) = 0 >= 0 = a__U91(a__isPalListKind(V1),V2) a__isQid(a()) = 1 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 0 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 1 >= 0 = tt() mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(isPalListKind(X)) = 0 >= 0 = a__isPalListKind(X) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNeList(X)) = X + 1 >= X + 1 = a__isNeList(X) mark(U21(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) = 0 >= 0 = a__U25(mark(X1),X2) mark(isList(X)) = X >= X = a__isList(X) mark(U26(X)) = 0 >= 0 = a__U26(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2,X3)) = 0 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) = 0 >= 0 = a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) = 0 >= 0 = a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) = 0 >= 0 = a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) = 0 >= 0 = a__U55(mark(X1),X2) mark(U56(X)) = 0 >= 0 = a__U56(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X1,X2)) = 0 >= 0 = a__U62(mark(X1),X2) mark(U63(X)) = 0 >= 0 = a__U63(mark(X)) mark(U71(X1,X2,X3)) = 0 >= 0 = a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) = 0 >= 0 = a__U72(mark(X1),X2) mark(U73(X1,X2)) = 0 >= 0 = a__U73(mark(X1),X2) mark(isPal(X)) = 0 >= 0 = a__isPal(X) mark(U74(X)) = 0 >= 0 = a__U74(mark(X)) mark(U81(X1,X2)) = 0 >= 0 = a__U81(mark(X1),X2) mark(U82(X1,X2)) = 0 >= 0 = a__U82(mark(X1),X2) mark(U83(X)) = 0 >= 0 = a__U83(mark(X)) mark(isNePal(X)) = 0 >= 0 = a__isNePal(X) mark(U91(X1,X2)) = 0 >= 0 = a__U91(mark(X1),X2) mark(U92(X)) = 0 >= 0 = a__U92(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 1 >= 1 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__isPalListKind(X) = 0 >= 0 = isPalListKind(X) a__U13(X) = 0 >= 0 = U13(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U21(X1,X2,X3) = X2 + X3 >= X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X2 + X3 >= X2 + X3 = U22(X1,X2,X3) a__U23(X1,X2,X3) = X2 + X3 >= X2 + X3 = U23(X1,X2,X3) a__U24(X1,X2,X3) = X2 + X3 >= X2 + X3 = U24(X1,X2,X3) a__U25(X1,X2) = 0 >= 0 = U25(X1,X2) a__isList(X) = X >= X = isList(X) a__U26(X) = 0 >= 0 = U26(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 1 >= 1 = U33(X) a__isQid(X) = X >= X = isQid(X) a__U41(X1,X2,X3) = X3 + 1 >= X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X3 + 1 >= X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X3 + 1 >= X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2,X3) = 0 >= 0 = U52(X1,X2,X3) a__U53(X1,X2,X3) = 0 >= 0 = U53(X1,X2,X3) a__U54(X1,X2,X3) = 0 >= 0 = U54(X1,X2,X3) a__U55(X1,X2) = 0 >= 0 = U55(X1,X2) a__U56(X) = 0 >= 0 = U56(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X1,X2) = 0 >= 0 = U62(X1,X2) a__U63(X) = 0 >= 0 = U63(X) a__U71(X1,X2,X3) = 0 >= 0 = U71(X1,X2,X3) a__U72(X1,X2) = 0 >= 0 = U72(X1,X2) a__U73(X1,X2) = 0 >= 0 = U73(X1,X2) a__isPal(X) = 0 >= 0 = isPal(X) a__U74(X) = 0 >= 0 = U74(X) a__U81(X1,X2) = 0 >= 0 = U81(X1,X2) a__U82(X1,X2) = 0 >= 0 = U82(X1,X2) a__U83(X) = 0 >= 0 = U83(X) a__isNePal(X) = 0 >= 0 = isNePal(X) a__U91(X1,X2) = 0 >= 0 = U91(X1,X2) a__U92(X) = 0 >= 0 = U92(X) problem: DPs: TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt(),V) -> a__U12(a__isPalListKind(V),V) a__U12(tt(),V) -> a__U13(a__isNeList(V)) a__U13(tt()) -> tt() a__U21(tt(),V1,V2) -> a__U22(a__isPalListKind(V1),V1,V2) a__U22(tt(),V1,V2) -> a__U23(a__isPalListKind(V2),V1,V2) a__U23(tt(),V1,V2) -> a__U24(a__isPalListKind(V2),V1,V2) a__U24(tt(),V1,V2) -> a__U25(a__isList(V1),V2) a__U25(tt(),V2) -> a__U26(a__isList(V2)) a__U26(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isPalListKind(V),V) a__U32(tt(),V) -> a__U33(a__isQid(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isPalListKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isPalListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isPalListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isList(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNeList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isPalListKind(V1),V1,V2) a__U52(tt(),V1,V2) -> a__U53(a__isPalListKind(V2),V1,V2) a__U53(tt(),V1,V2) -> a__U54(a__isPalListKind(V2),V1,V2) a__U54(tt(),V1,V2) -> a__U55(a__isNeList(V1),V2) a__U55(tt(),V2) -> a__U56(a__isList(V2)) a__U56(tt()) -> tt() a__U61(tt(),V) -> a__U62(a__isPalListKind(V),V) a__U62(tt(),V) -> a__U63(a__isQid(V)) a__U63(tt()) -> tt() a__U71(tt(),I,P) -> a__U72(a__isPalListKind(I),P) a__U72(tt(),P) -> a__U73(a__isPal(P),P) a__U73(tt(),P) -> a__U74(a__isPalListKind(P)) a__U74(tt()) -> tt() a__U81(tt(),V) -> a__U82(a__isPalListKind(V),V) a__U82(tt(),V) -> a__U83(a__isNePal(V)) a__U83(tt()) -> tt() a__U91(tt(),V2) -> a__U92(a__isPalListKind(V2)) a__U92(tt()) -> tt() a__isList(V) -> a__U11(a__isPalListKind(V),V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isPalListKind(V1),V1,V2) a__isNeList(V) -> a__U31(a__isPalListKind(V),V) a__isNeList(__(V1,V2)) -> a__U41(a__isPalListKind(V1),V1,V2) a__isNeList(__(V1,V2)) -> a__U51(a__isPalListKind(V1),V1,V2) a__isNePal(V) -> a__U61(a__isPalListKind(V),V) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),I,P) a__isPal(V) -> a__U81(a__isPalListKind(V),V) a__isPal(nil()) -> tt() a__isPalListKind(a()) -> tt() a__isPalListKind(e()) -> tt() a__isPalListKind(i()) -> tt() a__isPalListKind(nil()) -> tt() a__isPalListKind(o()) -> tt() a__isPalListKind(u()) -> tt() a__isPalListKind(__(V1,V2)) -> a__U91(a__isPalListKind(V1),V2) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(U23(X1,X2,X3)) -> a__U23(mark(X1),X2,X3) mark(U24(X1,X2,X3)) -> a__U24(mark(X1),X2,X3) mark(U25(X1,X2)) -> a__U25(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U53(X1,X2,X3)) -> a__U53(mark(X1),X2,X3) mark(U54(X1,X2,X3)) -> a__U54(mark(X1),X2,X3) mark(U55(X1,X2)) -> a__U55(mark(X1),X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X1,X2)) -> a__U62(mark(X1),X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2)) -> a__U72(mark(X1),X2) mark(U73(X1,X2)) -> a__U73(mark(X1),X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1,X2)) -> a__U81(mark(X1),X2) mark(U82(X1,X2)) -> a__U82(mark(X1),X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1,X2)) -> a__U91(mark(X1),X2) mark(U92(X)) -> a__U92(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isPalListKind(X) -> isPalListKind(X) a__U13(X) -> U13(X) a__isNeList(X) -> isNeList(X) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__U23(X1,X2,X3) -> U23(X1,X2,X3) a__U24(X1,X2,X3) -> U24(X1,X2,X3) a__U25(X1,X2) -> U25(X1,X2) a__isList(X) -> isList(X) a__U26(X) -> U26(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__isQid(X) -> isQid(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U53(X1,X2,X3) -> U53(X1,X2,X3) a__U54(X1,X2,X3) -> U54(X1,X2,X3) a__U55(X1,X2) -> U55(X1,X2) a__U56(X) -> U56(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X1,X2) -> U62(X1,X2) a__U63(X) -> U63(X) a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U72(X1,X2) -> U72(X1,X2) a__U73(X1,X2) -> U73(X1,X2) a__isPal(X) -> isPal(X) a__U74(X) -> U74(X) a__U81(X1,X2) -> U81(X1,X2) a__U82(X1,X2) -> U82(X1,X2) a__U83(X) -> U83(X) a__isNePal(X) -> isNePal(X) a__U91(X1,X2) -> U91(X1,X2) a__U92(X) -> U92(X) Qed