MAYBE Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(U11(tt(),V)) -> isPalListKind#(V) active#(U11(tt(),V)) -> U12#(isPalListKind(V),V) active#(U12(tt(),V)) -> isNeList#(V) active#(U12(tt(),V)) -> U13#(isNeList(V)) active#(U21(tt(),V1,V2)) -> isPalListKind#(V1) active#(U21(tt(),V1,V2)) -> U22#(isPalListKind(V1),V1,V2) active#(U22(tt(),V1,V2)) -> isPalListKind#(V2) active#(U22(tt(),V1,V2)) -> U23#(isPalListKind(V2),V1,V2) active#(U23(tt(),V1,V2)) -> isPalListKind#(V2) active#(U23(tt(),V1,V2)) -> U24#(isPalListKind(V2),V1,V2) active#(U24(tt(),V1,V2)) -> isList#(V1) active#(U24(tt(),V1,V2)) -> U25#(isList(V1),V2) active#(U25(tt(),V2)) -> isList#(V2) active#(U25(tt(),V2)) -> U26#(isList(V2)) active#(U31(tt(),V)) -> isPalListKind#(V) active#(U31(tt(),V)) -> U32#(isPalListKind(V),V) active#(U32(tt(),V)) -> isQid#(V) active#(U32(tt(),V)) -> U33#(isQid(V)) active#(U41(tt(),V1,V2)) -> isPalListKind#(V1) active#(U41(tt(),V1,V2)) -> U42#(isPalListKind(V1),V1,V2) active#(U42(tt(),V1,V2)) -> isPalListKind#(V2) active#(U42(tt(),V1,V2)) -> U43#(isPalListKind(V2),V1,V2) active#(U43(tt(),V1,V2)) -> isPalListKind#(V2) active#(U43(tt(),V1,V2)) -> U44#(isPalListKind(V2),V1,V2) active#(U44(tt(),V1,V2)) -> isList#(V1) active#(U44(tt(),V1,V2)) -> U45#(isList(V1),V2) active#(U45(tt(),V2)) -> isNeList#(V2) active#(U45(tt(),V2)) -> U46#(isNeList(V2)) active#(U51(tt(),V1,V2)) -> isPalListKind#(V1) active#(U51(tt(),V1,V2)) -> U52#(isPalListKind(V1),V1,V2) active#(U52(tt(),V1,V2)) -> isPalListKind#(V2) active#(U52(tt(),V1,V2)) -> U53#(isPalListKind(V2),V1,V2) active#(U53(tt(),V1,V2)) -> isPalListKind#(V2) active#(U53(tt(),V1,V2)) -> U54#(isPalListKind(V2),V1,V2) active#(U54(tt(),V1,V2)) -> isNeList#(V1) active#(U54(tt(),V1,V2)) -> U55#(isNeList(V1),V2) active#(U55(tt(),V2)) -> isList#(V2) active#(U55(tt(),V2)) -> U56#(isList(V2)) active#(U61(tt(),V)) -> isPalListKind#(V) active#(U61(tt(),V)) -> U62#(isPalListKind(V),V) active#(U62(tt(),V)) -> isQid#(V) active#(U62(tt(),V)) -> U63#(isQid(V)) active#(U71(tt(),I,P)) -> isPalListKind#(I) active#(U71(tt(),I,P)) -> U72#(isPalListKind(I),P) active#(U72(tt(),P)) -> isPal#(P) active#(U72(tt(),P)) -> U73#(isPal(P),P) active#(U73(tt(),P)) -> isPalListKind#(P) active#(U73(tt(),P)) -> U74#(isPalListKind(P)) active#(U81(tt(),V)) -> isPalListKind#(V) active#(U81(tt(),V)) -> U82#(isPalListKind(V),V) active#(U82(tt(),V)) -> isNePal#(V) active#(U82(tt(),V)) -> U83#(isNePal(V)) active#(U91(tt(),V2)) -> isPalListKind#(V2) active#(U91(tt(),V2)) -> U92#(isPalListKind(V2)) active#(isList(V)) -> isPalListKind#(V) active#(isList(V)) -> U11#(isPalListKind(V),V) active#(isList(__(V1,V2))) -> isPalListKind#(V1) active#(isList(__(V1,V2))) -> U21#(isPalListKind(V1),V1,V2) active#(isNeList(V)) -> isPalListKind#(V) active#(isNeList(V)) -> U31#(isPalListKind(V),V) active#(isNeList(__(V1,V2))) -> isPalListKind#(V1) active#(isNeList(__(V1,V2))) -> U41#(isPalListKind(V1),V1,V2) active#(isNeList(__(V1,V2))) -> U51#(isPalListKind(V1),V1,V2) active#(isNePal(V)) -> isPalListKind#(V) active#(isNePal(V)) -> U61#(isPalListKind(V),V) active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(isNePal(__(I,__(P,I)))) -> U71#(isQid(I),I,P) active#(isPal(V)) -> isPalListKind#(V) active#(isPal(V)) -> U81#(isPalListKind(V),V) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V1) active#(isPalListKind(__(V1,V2))) -> U91#(isPalListKind(V1),V2) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U11(X1,X2)) -> active#(X1) active#(U11(X1,X2)) -> U11#(active(X1),X2) active#(U12(X1,X2)) -> active#(X1) active#(U12(X1,X2)) -> U12#(active(X1),X2) active#(U13(X)) -> active#(X) active#(U13(X)) -> U13#(active(X)) active#(U21(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(U23(X1,X2,X3)) -> active#(X1) active#(U23(X1,X2,X3)) -> U23#(active(X1),X2,X3) active#(U24(X1,X2,X3)) -> active#(X1) active#(U24(X1,X2,X3)) -> U24#(active(X1),X2,X3) active#(U25(X1,X2)) -> active#(X1) active#(U25(X1,X2)) -> U25#(active(X1),X2) active#(U26(X)) -> active#(X) active#(U26(X)) -> U26#(active(X)) active#(U31(X1,X2)) -> active#(X1) active#(U31(X1,X2)) -> U31#(active(X1),X2) active#(U32(X1,X2)) -> active#(X1) active#(U32(X1,X2)) -> U32#(active(X1),X2) active#(U33(X)) -> active#(X) active#(U33(X)) -> U33#(active(X)) active#(U41(X1,X2,X3)) -> active#(X1) active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3) active#(U42(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3) active#(U43(X1,X2,X3)) -> active#(X1) active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3) active#(U44(X1,X2,X3)) -> active#(X1) active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3) active#(U45(X1,X2)) -> active#(X1) active#(U45(X1,X2)) -> U45#(active(X1),X2) active#(U46(X)) -> active#(X) active#(U46(X)) -> U46#(active(X)) active#(U51(X1,X2,X3)) -> active#(X1) active#(U51(X1,X2,X3)) -> U51#(active(X1),X2,X3) active#(U52(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2,X3)) -> U52#(active(X1),X2,X3) active#(U53(X1,X2,X3)) -> active#(X1) active#(U53(X1,X2,X3)) -> U53#(active(X1),X2,X3) active#(U54(X1,X2,X3)) -> active#(X1) active#(U54(X1,X2,X3)) -> U54#(active(X1),X2,X3) active#(U55(X1,X2)) -> active#(X1) active#(U55(X1,X2)) -> U55#(active(X1),X2) active#(U56(X)) -> active#(X) active#(U56(X)) -> U56#(active(X)) active#(U61(X1,X2)) -> active#(X1) active#(U61(X1,X2)) -> U61#(active(X1),X2) active#(U62(X1,X2)) -> active#(X1) active#(U62(X1,X2)) -> U62#(active(X1),X2) active#(U63(X)) -> active#(X) active#(U63(X)) -> U63#(active(X)) active#(U71(X1,X2,X3)) -> active#(X1) active#(U71(X1,X2,X3)) -> U71#(active(X1),X2,X3) active#(U72(X1,X2)) -> active#(X1) active#(U72(X1,X2)) -> U72#(active(X1),X2) active#(U73(X1,X2)) -> active#(X1) active#(U73(X1,X2)) -> U73#(active(X1),X2) active#(U74(X)) -> active#(X) active#(U74(X)) -> U74#(active(X)) active#(U81(X1,X2)) -> active#(X1) active#(U81(X1,X2)) -> U81#(active(X1),X2) active#(U82(X1,X2)) -> active#(X1) active#(U82(X1,X2)) -> U82#(active(X1),X2) active#(U83(X)) -> active#(X) active#(U83(X)) -> U83#(active(X)) active#(U91(X1,X2)) -> active#(X1) active#(U91(X1,X2)) -> U91#(active(X1),X2) active#(U92(X)) -> active#(X) active#(U92(X)) -> U92#(active(X)) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U13#(mark(X)) -> U13#(X) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3) U25#(mark(X1),X2) -> U25#(X1,X2) U26#(mark(X)) -> U26#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U33#(mark(X)) -> U33#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U45#(mark(X1),X2) -> U45#(X1,X2) U46#(mark(X)) -> U46#(X) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U55#(mark(X1),X2) -> U55#(X1,X2) U56#(mark(X)) -> U56#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U62#(mark(X1),X2) -> U62#(X1,X2) U63#(mark(X)) -> U63#(X) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U72#(mark(X1),X2) -> U72#(X1,X2) U73#(mark(X1),X2) -> U73#(X1,X2) U74#(mark(X)) -> U74#(X) U81#(mark(X1),X2) -> U81#(X1,X2) U82#(mark(X1),X2) -> U82#(X1,X2) U83#(mark(X)) -> U83#(X) U91#(mark(X1),X2) -> U91#(X1,X2) U92#(mark(X)) -> U92#(X) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U11(X1,X2)) -> proper#(X2) proper#(U11(X1,X2)) -> proper#(X1) proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2)) proper#(U12(X1,X2)) -> proper#(X2) proper#(U12(X1,X2)) -> proper#(X1) proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2)) proper#(isPalListKind(X)) -> proper#(X) proper#(isPalListKind(X)) -> isPalListKind#(proper(X)) proper#(U13(X)) -> proper#(X) proper#(U13(X)) -> U13#(proper(X)) proper#(isNeList(X)) -> proper#(X) proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U23(X1,X2,X3)) -> proper#(X3) proper#(U23(X1,X2,X3)) -> proper#(X2) proper#(U23(X1,X2,X3)) -> proper#(X1) proper#(U23(X1,X2,X3)) -> U23#(proper(X1),proper(X2),proper(X3)) proper#(U24(X1,X2,X3)) -> proper#(X3) proper#(U24(X1,X2,X3)) -> proper#(X2) proper#(U24(X1,X2,X3)) -> proper#(X1) proper#(U24(X1,X2,X3)) -> U24#(proper(X1),proper(X2),proper(X3)) proper#(U25(X1,X2)) -> proper#(X2) proper#(U25(X1,X2)) -> proper#(X1) proper#(U25(X1,X2)) -> U25#(proper(X1),proper(X2)) proper#(isList(X)) -> proper#(X) proper#(isList(X)) -> isList#(proper(X)) proper#(U26(X)) -> proper#(X) proper#(U26(X)) -> U26#(proper(X)) proper#(U31(X1,X2)) -> proper#(X2) proper#(U31(X1,X2)) -> proper#(X1) proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2)) proper#(U32(X1,X2)) -> proper#(X2) proper#(U32(X1,X2)) -> proper#(X1) proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2)) proper#(U33(X)) -> proper#(X) proper#(U33(X)) -> U33#(proper(X)) proper#(isQid(X)) -> proper#(X) proper#(isQid(X)) -> isQid#(proper(X)) proper#(U41(X1,X2,X3)) -> proper#(X3) proper#(U41(X1,X2,X3)) -> proper#(X2) proper#(U41(X1,X2,X3)) -> proper#(X1) proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3)) proper#(U42(X1,X2,X3)) -> proper#(X3) proper#(U42(X1,X2,X3)) -> proper#(X2) proper#(U42(X1,X2,X3)) -> proper#(X1) proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3)) proper#(U43(X1,X2,X3)) -> proper#(X3) proper#(U43(X1,X2,X3)) -> proper#(X2) proper#(U43(X1,X2,X3)) -> proper#(X1) proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3)) proper#(U44(X1,X2,X3)) -> proper#(X3) proper#(U44(X1,X2,X3)) -> proper#(X2) proper#(U44(X1,X2,X3)) -> proper#(X1) proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3)) proper#(U45(X1,X2)) -> proper#(X2) proper#(U45(X1,X2)) -> proper#(X1) proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2)) proper#(U46(X)) -> proper#(X) proper#(U46(X)) -> U46#(proper(X)) proper#(U51(X1,X2,X3)) -> proper#(X3) proper#(U51(X1,X2,X3)) -> proper#(X2) proper#(U51(X1,X2,X3)) -> proper#(X1) proper#(U51(X1,X2,X3)) -> U51#(proper(X1),proper(X2),proper(X3)) proper#(U52(X1,X2,X3)) -> proper#(X3) proper#(U52(X1,X2,X3)) -> proper#(X2) proper#(U52(X1,X2,X3)) -> proper#(X1) proper#(U52(X1,X2,X3)) -> U52#(proper(X1),proper(X2),proper(X3)) proper#(U53(X1,X2,X3)) -> proper#(X3) proper#(U53(X1,X2,X3)) -> proper#(X2) proper#(U53(X1,X2,X3)) -> proper#(X1) proper#(U53(X1,X2,X3)) -> U53#(proper(X1),proper(X2),proper(X3)) proper#(U54(X1,X2,X3)) -> proper#(X3) proper#(U54(X1,X2,X3)) -> proper#(X2) proper#(U54(X1,X2,X3)) -> proper#(X1) proper#(U54(X1,X2,X3)) -> U54#(proper(X1),proper(X2),proper(X3)) proper#(U55(X1,X2)) -> proper#(X2) proper#(U55(X1,X2)) -> proper#(X1) proper#(U55(X1,X2)) -> U55#(proper(X1),proper(X2)) proper#(U56(X)) -> proper#(X) proper#(U56(X)) -> U56#(proper(X)) proper#(U61(X1,X2)) -> proper#(X2) proper#(U61(X1,X2)) -> proper#(X1) proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2)) proper#(U62(X1,X2)) -> proper#(X2) proper#(U62(X1,X2)) -> proper#(X1) proper#(U62(X1,X2)) -> U62#(proper(X1),proper(X2)) proper#(U63(X)) -> proper#(X) proper#(U63(X)) -> U63#(proper(X)) proper#(U71(X1,X2,X3)) -> proper#(X3) proper#(U71(X1,X2,X3)) -> proper#(X2) proper#(U71(X1,X2,X3)) -> proper#(X1) proper#(U71(X1,X2,X3)) -> U71#(proper(X1),proper(X2),proper(X3)) proper#(U72(X1,X2)) -> proper#(X2) proper#(U72(X1,X2)) -> proper#(X1) proper#(U72(X1,X2)) -> U72#(proper(X1),proper(X2)) proper#(U73(X1,X2)) -> proper#(X2) proper#(U73(X1,X2)) -> proper#(X1) proper#(U73(X1,X2)) -> U73#(proper(X1),proper(X2)) proper#(isPal(X)) -> proper#(X) proper#(isPal(X)) -> isPal#(proper(X)) proper#(U74(X)) -> proper#(X) proper#(U74(X)) -> U74#(proper(X)) proper#(U81(X1,X2)) -> proper#(X2) proper#(U81(X1,X2)) -> proper#(X1) proper#(U81(X1,X2)) -> U81#(proper(X1),proper(X2)) proper#(U82(X1,X2)) -> proper#(X2) proper#(U82(X1,X2)) -> proper#(X1) proper#(U82(X1,X2)) -> U82#(proper(X1),proper(X2)) proper#(U83(X)) -> proper#(X) proper#(U83(X)) -> U83#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(U91(X1,X2)) -> proper#(X2) proper#(U91(X1,X2)) -> proper#(X1) proper#(U91(X1,X2)) -> U91#(proper(X1),proper(X2)) proper#(U92(X)) -> proper#(X) proper#(U92(X)) -> U92#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) U11#(ok(X1),ok(X2)) -> U11#(X1,X2) U12#(ok(X1),ok(X2)) -> U12#(X1,X2) isPalListKind#(ok(X)) -> isPalListKind#(X) U13#(ok(X)) -> U13#(X) isNeList#(ok(X)) -> isNeList#(X) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) U23#(ok(X1),ok(X2),ok(X3)) -> U23#(X1,X2,X3) U24#(ok(X1),ok(X2),ok(X3)) -> U24#(X1,X2,X3) U25#(ok(X1),ok(X2)) -> U25#(X1,X2) isList#(ok(X)) -> isList#(X) U26#(ok(X)) -> U26#(X) U31#(ok(X1),ok(X2)) -> U31#(X1,X2) U32#(ok(X1),ok(X2)) -> U32#(X1,X2) U33#(ok(X)) -> U33#(X) isQid#(ok(X)) -> isQid#(X) U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3) U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3) U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3) U45#(ok(X1),ok(X2)) -> U45#(X1,X2) U46#(ok(X)) -> U46#(X) U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) U52#(ok(X1),ok(X2),ok(X3)) -> U52#(X1,X2,X3) U53#(ok(X1),ok(X2),ok(X3)) -> U53#(X1,X2,X3) U54#(ok(X1),ok(X2),ok(X3)) -> U54#(X1,X2,X3) U55#(ok(X1),ok(X2)) -> U55#(X1,X2) U56#(ok(X)) -> U56#(X) U61#(ok(X1),ok(X2)) -> U61#(X1,X2) U62#(ok(X1),ok(X2)) -> U62#(X1,X2) U63#(ok(X)) -> U63#(X) U71#(ok(X1),ok(X2),ok(X3)) -> U71#(X1,X2,X3) U72#(ok(X1),ok(X2)) -> U72#(X1,X2) U73#(ok(X1),ok(X2)) -> U73#(X1,X2) isPal#(ok(X)) -> isPal#(X) U74#(ok(X)) -> U74#(X) U81#(ok(X1),ok(X2)) -> U81#(X1,X2) U82#(ok(X1),ok(X2)) -> U82#(X1,X2) U83#(ok(X)) -> U83#(X) isNePal#(ok(X)) -> isNePal#(X) U91#(ok(X1),ok(X2)) -> U91#(X1,X2) U92#(ok(X)) -> U92#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(U11(tt(),V)) -> isPalListKind#(V) active#(U11(tt(),V)) -> U12#(isPalListKind(V),V) active#(U12(tt(),V)) -> isNeList#(V) active#(U12(tt(),V)) -> U13#(isNeList(V)) active#(U21(tt(),V1,V2)) -> isPalListKind#(V1) active#(U21(tt(),V1,V2)) -> U22#(isPalListKind(V1),V1,V2) active#(U22(tt(),V1,V2)) -> isPalListKind#(V2) active#(U22(tt(),V1,V2)) -> U23#(isPalListKind(V2),V1,V2) active#(U23(tt(),V1,V2)) -> isPalListKind#(V2) active#(U23(tt(),V1,V2)) -> U24#(isPalListKind(V2),V1,V2) active#(U24(tt(),V1,V2)) -> isList#(V1) active#(U24(tt(),V1,V2)) -> U25#(isList(V1),V2) active#(U25(tt(),V2)) -> isList#(V2) active#(U25(tt(),V2)) -> U26#(isList(V2)) active#(U31(tt(),V)) -> isPalListKind#(V) active#(U31(tt(),V)) -> U32#(isPalListKind(V),V) active#(U32(tt(),V)) -> isQid#(V) active#(U32(tt(),V)) -> U33#(isQid(V)) active#(U41(tt(),V1,V2)) -> isPalListKind#(V1) active#(U41(tt(),V1,V2)) -> U42#(isPalListKind(V1),V1,V2) active#(U42(tt(),V1,V2)) -> isPalListKind#(V2) active#(U42(tt(),V1,V2)) -> U43#(isPalListKind(V2),V1,V2) active#(U43(tt(),V1,V2)) -> isPalListKind#(V2) active#(U43(tt(),V1,V2)) -> U44#(isPalListKind(V2),V1,V2) active#(U44(tt(),V1,V2)) -> isList#(V1) active#(U44(tt(),V1,V2)) -> U45#(isList(V1),V2) active#(U45(tt(),V2)) -> isNeList#(V2) active#(U45(tt(),V2)) -> U46#(isNeList(V2)) active#(U51(tt(),V1,V2)) -> isPalListKind#(V1) active#(U51(tt(),V1,V2)) -> U52#(isPalListKind(V1),V1,V2) active#(U52(tt(),V1,V2)) -> isPalListKind#(V2) active#(U52(tt(),V1,V2)) -> U53#(isPalListKind(V2),V1,V2) active#(U53(tt(),V1,V2)) -> isPalListKind#(V2) active#(U53(tt(),V1,V2)) -> U54#(isPalListKind(V2),V1,V2) active#(U54(tt(),V1,V2)) -> isNeList#(V1) active#(U54(tt(),V1,V2)) -> U55#(isNeList(V1),V2) active#(U55(tt(),V2)) -> isList#(V2) active#(U55(tt(),V2)) -> U56#(isList(V2)) active#(U61(tt(),V)) -> isPalListKind#(V) active#(U61(tt(),V)) -> U62#(isPalListKind(V),V) active#(U62(tt(),V)) -> isQid#(V) active#(U62(tt(),V)) -> U63#(isQid(V)) active#(U71(tt(),I,P)) -> isPalListKind#(I) active#(U71(tt(),I,P)) -> U72#(isPalListKind(I),P) active#(U72(tt(),P)) -> isPal#(P) active#(U72(tt(),P)) -> U73#(isPal(P),P) active#(U73(tt(),P)) -> isPalListKind#(P) active#(U73(tt(),P)) -> U74#(isPalListKind(P)) active#(U81(tt(),V)) -> isPalListKind#(V) active#(U81(tt(),V)) -> U82#(isPalListKind(V),V) active#(U82(tt(),V)) -> isNePal#(V) active#(U82(tt(),V)) -> U83#(isNePal(V)) active#(U91(tt(),V2)) -> isPalListKind#(V2) active#(U91(tt(),V2)) -> U92#(isPalListKind(V2)) active#(isList(V)) -> isPalListKind#(V) active#(isList(V)) -> U11#(isPalListKind(V),V) active#(isList(__(V1,V2))) -> isPalListKind#(V1) active#(isList(__(V1,V2))) -> U21#(isPalListKind(V1),V1,V2) active#(isNeList(V)) -> isPalListKind#(V) active#(isNeList(V)) -> U31#(isPalListKind(V),V) active#(isNeList(__(V1,V2))) -> isPalListKind#(V1) active#(isNeList(__(V1,V2))) -> U41#(isPalListKind(V1),V1,V2) active#(isNeList(__(V1,V2))) -> U51#(isPalListKind(V1),V1,V2) active#(isNePal(V)) -> isPalListKind#(V) active#(isNePal(V)) -> U61#(isPalListKind(V),V) active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(isNePal(__(I,__(P,I)))) -> U71#(isQid(I),I,P) active#(isPal(V)) -> isPalListKind#(V) active#(isPal(V)) -> U81#(isPalListKind(V),V) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V1) active#(isPalListKind(__(V1,V2))) -> U91#(isPalListKind(V1),V2) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U11(X1,X2)) -> active#(X1) active#(U11(X1,X2)) -> U11#(active(X1),X2) active#(U12(X1,X2)) -> active#(X1) active#(U12(X1,X2)) -> U12#(active(X1),X2) active#(U13(X)) -> active#(X) active#(U13(X)) -> U13#(active(X)) active#(U21(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(U23(X1,X2,X3)) -> active#(X1) active#(U23(X1,X2,X3)) -> U23#(active(X1),X2,X3) active#(U24(X1,X2,X3)) -> active#(X1) active#(U24(X1,X2,X3)) -> U24#(active(X1),X2,X3) active#(U25(X1,X2)) -> active#(X1) active#(U25(X1,X2)) -> U25#(active(X1),X2) active#(U26(X)) -> active#(X) active#(U26(X)) -> U26#(active(X)) active#(U31(X1,X2)) -> active#(X1) active#(U31(X1,X2)) -> U31#(active(X1),X2) active#(U32(X1,X2)) -> active#(X1) active#(U32(X1,X2)) -> U32#(active(X1),X2) active#(U33(X)) -> active#(X) active#(U33(X)) -> U33#(active(X)) active#(U41(X1,X2,X3)) -> active#(X1) active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3) active#(U42(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3) active#(U43(X1,X2,X3)) -> active#(X1) active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3) active#(U44(X1,X2,X3)) -> active#(X1) active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3) active#(U45(X1,X2)) -> active#(X1) active#(U45(X1,X2)) -> U45#(active(X1),X2) active#(U46(X)) -> active#(X) active#(U46(X)) -> U46#(active(X)) active#(U51(X1,X2,X3)) -> active#(X1) active#(U51(X1,X2,X3)) -> U51#(active(X1),X2,X3) active#(U52(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2,X3)) -> U52#(active(X1),X2,X3) active#(U53(X1,X2,X3)) -> active#(X1) active#(U53(X1,X2,X3)) -> U53#(active(X1),X2,X3) active#(U54(X1,X2,X3)) -> active#(X1) active#(U54(X1,X2,X3)) -> U54#(active(X1),X2,X3) active#(U55(X1,X2)) -> active#(X1) active#(U55(X1,X2)) -> U55#(active(X1),X2) active#(U56(X)) -> active#(X) active#(U56(X)) -> U56#(active(X)) active#(U61(X1,X2)) -> active#(X1) active#(U61(X1,X2)) -> U61#(active(X1),X2) active#(U62(X1,X2)) -> active#(X1) active#(U62(X1,X2)) -> U62#(active(X1),X2) active#(U63(X)) -> active#(X) active#(U63(X)) -> U63#(active(X)) active#(U71(X1,X2,X3)) -> active#(X1) active#(U71(X1,X2,X3)) -> U71#(active(X1),X2,X3) active#(U72(X1,X2)) -> active#(X1) active#(U72(X1,X2)) -> U72#(active(X1),X2) active#(U73(X1,X2)) -> active#(X1) active#(U73(X1,X2)) -> U73#(active(X1),X2) active#(U74(X)) -> active#(X) active#(U74(X)) -> U74#(active(X)) active#(U81(X1,X2)) -> active#(X1) active#(U81(X1,X2)) -> U81#(active(X1),X2) active#(U82(X1,X2)) -> active#(X1) active#(U82(X1,X2)) -> U82#(active(X1),X2) active#(U83(X)) -> active#(X) active#(U83(X)) -> U83#(active(X)) active#(U91(X1,X2)) -> active#(X1) active#(U91(X1,X2)) -> U91#(active(X1),X2) active#(U92(X)) -> active#(X) active#(U92(X)) -> U92#(active(X)) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U13#(mark(X)) -> U13#(X) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3) U25#(mark(X1),X2) -> U25#(X1,X2) U26#(mark(X)) -> U26#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U33#(mark(X)) -> U33#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U45#(mark(X1),X2) -> U45#(X1,X2) U46#(mark(X)) -> U46#(X) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U55#(mark(X1),X2) -> U55#(X1,X2) U56#(mark(X)) -> U56#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U62#(mark(X1),X2) -> U62#(X1,X2) U63#(mark(X)) -> U63#(X) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U72#(mark(X1),X2) -> U72#(X1,X2) U73#(mark(X1),X2) -> U73#(X1,X2) U74#(mark(X)) -> U74#(X) U81#(mark(X1),X2) -> U81#(X1,X2) U82#(mark(X1),X2) -> U82#(X1,X2) U83#(mark(X)) -> U83#(X) U91#(mark(X1),X2) -> U91#(X1,X2) U92#(mark(X)) -> U92#(X) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U11(X1,X2)) -> proper#(X2) proper#(U11(X1,X2)) -> proper#(X1) proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2)) proper#(U12(X1,X2)) -> proper#(X2) proper#(U12(X1,X2)) -> proper#(X1) proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2)) proper#(isPalListKind(X)) -> proper#(X) proper#(isPalListKind(X)) -> isPalListKind#(proper(X)) proper#(U13(X)) -> proper#(X) proper#(U13(X)) -> U13#(proper(X)) proper#(isNeList(X)) -> proper#(X) proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U23(X1,X2,X3)) -> proper#(X3) proper#(U23(X1,X2,X3)) -> proper#(X2) proper#(U23(X1,X2,X3)) -> proper#(X1) proper#(U23(X1,X2,X3)) -> U23#(proper(X1),proper(X2),proper(X3)) proper#(U24(X1,X2,X3)) -> proper#(X3) proper#(U24(X1,X2,X3)) -> proper#(X2) proper#(U24(X1,X2,X3)) -> proper#(X1) proper#(U24(X1,X2,X3)) -> U24#(proper(X1),proper(X2),proper(X3)) proper#(U25(X1,X2)) -> proper#(X2) proper#(U25(X1,X2)) -> proper#(X1) proper#(U25(X1,X2)) -> U25#(proper(X1),proper(X2)) proper#(isList(X)) -> proper#(X) proper#(isList(X)) -> isList#(proper(X)) proper#(U26(X)) -> proper#(X) proper#(U26(X)) -> U26#(proper(X)) proper#(U31(X1,X2)) -> proper#(X2) proper#(U31(X1,X2)) -> proper#(X1) proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2)) proper#(U32(X1,X2)) -> proper#(X2) proper#(U32(X1,X2)) -> proper#(X1) proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2)) proper#(U33(X)) -> proper#(X) proper#(U33(X)) -> U33#(proper(X)) proper#(isQid(X)) -> proper#(X) proper#(isQid(X)) -> isQid#(proper(X)) proper#(U41(X1,X2,X3)) -> proper#(X3) proper#(U41(X1,X2,X3)) -> proper#(X2) proper#(U41(X1,X2,X3)) -> proper#(X1) proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3)) proper#(U42(X1,X2,X3)) -> proper#(X3) proper#(U42(X1,X2,X3)) -> proper#(X2) proper#(U42(X1,X2,X3)) -> proper#(X1) proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3)) proper#(U43(X1,X2,X3)) -> proper#(X3) proper#(U43(X1,X2,X3)) -> proper#(X2) proper#(U43(X1,X2,X3)) -> proper#(X1) proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3)) proper#(U44(X1,X2,X3)) -> proper#(X3) proper#(U44(X1,X2,X3)) -> proper#(X2) proper#(U44(X1,X2,X3)) -> proper#(X1) proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3)) proper#(U45(X1,X2)) -> proper#(X2) proper#(U45(X1,X2)) -> proper#(X1) proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2)) proper#(U46(X)) -> proper#(X) proper#(U46(X)) -> U46#(proper(X)) proper#(U51(X1,X2,X3)) -> proper#(X3) proper#(U51(X1,X2,X3)) -> proper#(X2) proper#(U51(X1,X2,X3)) -> proper#(X1) proper#(U51(X1,X2,X3)) -> U51#(proper(X1),proper(X2),proper(X3)) proper#(U52(X1,X2,X3)) -> proper#(X3) proper#(U52(X1,X2,X3)) -> proper#(X2) proper#(U52(X1,X2,X3)) -> proper#(X1) proper#(U52(X1,X2,X3)) -> U52#(proper(X1),proper(X2),proper(X3)) proper#(U53(X1,X2,X3)) -> proper#(X3) proper#(U53(X1,X2,X3)) -> proper#(X2) proper#(U53(X1,X2,X3)) -> proper#(X1) proper#(U53(X1,X2,X3)) -> U53#(proper(X1),proper(X2),proper(X3)) proper#(U54(X1,X2,X3)) -> proper#(X3) proper#(U54(X1,X2,X3)) -> proper#(X2) proper#(U54(X1,X2,X3)) -> proper#(X1) proper#(U54(X1,X2,X3)) -> U54#(proper(X1),proper(X2),proper(X3)) proper#(U55(X1,X2)) -> proper#(X2) proper#(U55(X1,X2)) -> proper#(X1) proper#(U55(X1,X2)) -> U55#(proper(X1),proper(X2)) proper#(U56(X)) -> proper#(X) proper#(U56(X)) -> U56#(proper(X)) proper#(U61(X1,X2)) -> proper#(X2) proper#(U61(X1,X2)) -> proper#(X1) proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2)) proper#(U62(X1,X2)) -> proper#(X2) proper#(U62(X1,X2)) -> proper#(X1) proper#(U62(X1,X2)) -> U62#(proper(X1),proper(X2)) proper#(U63(X)) -> proper#(X) proper#(U63(X)) -> U63#(proper(X)) proper#(U71(X1,X2,X3)) -> proper#(X3) proper#(U71(X1,X2,X3)) -> proper#(X2) proper#(U71(X1,X2,X3)) -> proper#(X1) proper#(U71(X1,X2,X3)) -> U71#(proper(X1),proper(X2),proper(X3)) proper#(U72(X1,X2)) -> proper#(X2) proper#(U72(X1,X2)) -> proper#(X1) proper#(U72(X1,X2)) -> U72#(proper(X1),proper(X2)) proper#(U73(X1,X2)) -> proper#(X2) proper#(U73(X1,X2)) -> proper#(X1) proper#(U73(X1,X2)) -> U73#(proper(X1),proper(X2)) proper#(isPal(X)) -> proper#(X) proper#(isPal(X)) -> isPal#(proper(X)) proper#(U74(X)) -> proper#(X) proper#(U74(X)) -> U74#(proper(X)) proper#(U81(X1,X2)) -> proper#(X2) proper#(U81(X1,X2)) -> proper#(X1) proper#(U81(X1,X2)) -> U81#(proper(X1),proper(X2)) proper#(U82(X1,X2)) -> proper#(X2) proper#(U82(X1,X2)) -> proper#(X1) proper#(U82(X1,X2)) -> U82#(proper(X1),proper(X2)) proper#(U83(X)) -> proper#(X) proper#(U83(X)) -> U83#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(U91(X1,X2)) -> proper#(X2) proper#(U91(X1,X2)) -> proper#(X1) proper#(U91(X1,X2)) -> U91#(proper(X1),proper(X2)) proper#(U92(X)) -> proper#(X) proper#(U92(X)) -> U92#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) U11#(ok(X1),ok(X2)) -> U11#(X1,X2) U12#(ok(X1),ok(X2)) -> U12#(X1,X2) isPalListKind#(ok(X)) -> isPalListKind#(X) U13#(ok(X)) -> U13#(X) isNeList#(ok(X)) -> isNeList#(X) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) U23#(ok(X1),ok(X2),ok(X3)) -> U23#(X1,X2,X3) U24#(ok(X1),ok(X2),ok(X3)) -> U24#(X1,X2,X3) U25#(ok(X1),ok(X2)) -> U25#(X1,X2) isList#(ok(X)) -> isList#(X) U26#(ok(X)) -> U26#(X) U31#(ok(X1),ok(X2)) -> U31#(X1,X2) U32#(ok(X1),ok(X2)) -> U32#(X1,X2) U33#(ok(X)) -> U33#(X) isQid#(ok(X)) -> isQid#(X) U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3) U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3) U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3) U45#(ok(X1),ok(X2)) -> U45#(X1,X2) U46#(ok(X)) -> U46#(X) U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) U52#(ok(X1),ok(X2),ok(X3)) -> U52#(X1,X2,X3) U53#(ok(X1),ok(X2),ok(X3)) -> U53#(X1,X2,X3) U54#(ok(X1),ok(X2),ok(X3)) -> U54#(X1,X2,X3) U55#(ok(X1),ok(X2)) -> U55#(X1,X2) U56#(ok(X)) -> U56#(X) U61#(ok(X1),ok(X2)) -> U61#(X1,X2) U62#(ok(X1),ok(X2)) -> U62#(X1,X2) U63#(ok(X)) -> U63#(X) U71#(ok(X1),ok(X2),ok(X3)) -> U71#(X1,X2,X3) U72#(ok(X1),ok(X2)) -> U72#(X1,X2) U73#(ok(X1),ok(X2)) -> U73#(X1,X2) isPal#(ok(X)) -> isPal#(X) U74#(ok(X)) -> U74#(X) U81#(ok(X1),ok(X2)) -> U81#(X1,X2) U82#(ok(X1),ok(X2)) -> U82#(X1,X2) U83#(ok(X)) -> U83#(X) isNePal#(ok(X)) -> isNePal#(X) U91#(ok(X1),ok(X2)) -> U91#(X1,X2) U92#(ok(X)) -> U92#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: ... SCC Processor: #sccs: 46 #rules: 205 #arcs: 17045/130321 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) active#(U11(X1,X2)) -> active#(X1) active#(U12(X1,X2)) -> active#(X1) active#(U13(X)) -> active#(X) active#(U21(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) active#(U23(X1,X2,X3)) -> active#(X1) active#(U24(X1,X2,X3)) -> active#(X1) active#(U25(X1,X2)) -> active#(X1) active#(U26(X)) -> active#(X) active#(U31(X1,X2)) -> active#(X1) active#(U32(X1,X2)) -> active#(X1) active#(U33(X)) -> active#(X) active#(U41(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2,X3)) -> active#(X1) active#(U43(X1,X2,X3)) -> active#(X1) active#(U44(X1,X2,X3)) -> active#(X1) active#(U45(X1,X2)) -> active#(X1) active#(U46(X)) -> active#(X) active#(U51(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2,X3)) -> active#(X1) active#(U53(X1,X2,X3)) -> active#(X1) active#(U54(X1,X2,X3)) -> active#(X1) active#(U55(X1,X2)) -> active#(X1) active#(U56(X)) -> active#(X) active#(U61(X1,X2)) -> active#(X1) active#(U62(X1,X2)) -> active#(X1) active#(U63(X)) -> active#(X) active#(U71(X1,X2,X3)) -> active#(X1) active#(U72(X1,X2)) -> active#(X1) active#(U73(X1,X2)) -> active#(X1) active#(U74(X)) -> active#(X) active#(U81(X1,X2)) -> active#(X1) active#(U82(X1,X2)) -> active#(X1) active#(U83(X)) -> active#(X) active#(U91(X1,X2)) -> active#(X1) active#(U92(X)) -> active#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0, [top](x0) = 0, [ok](x0) = 1, [proper](x0) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [U92](x0) = x0 + 1, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 1, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 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 + x1, [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, [U33](x0) = x0, [isQid](x0) = 1, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 1, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 1, [U12](x0, x1) = x0, [isPalListKind](x0) = 1, [U11](x0, x1) = x0, [tt] = 1, [nil] = 1, [mark](x0) = 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: active#(__(X1,X2)) = X1 + X2 >= X1 = active#(X1) active#(__(X1,X2)) = X1 + X2 >= X2 = active#(X2) active#(U11(X1,X2)) = X1 >= X1 = active#(X1) active#(U12(X1,X2)) = X1 >= X1 = active#(X1) active#(U13(X)) = X >= X = active#(X) active#(U21(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U22(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U23(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U24(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U25(X1,X2)) = X1 >= X1 = active#(X1) active#(U26(X)) = X >= X = active#(X) active#(U31(X1,X2)) = X1 >= X1 = active#(X1) active#(U32(X1,X2)) = X1 >= X1 = active#(X1) active#(U33(X)) = X >= X = active#(X) active#(U41(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U42(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U43(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U44(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U45(X1,X2)) = X1 >= X1 = active#(X1) active#(U46(X)) = X >= X = active#(X) active#(U51(X1,X2,X3)) = X1 + X2 >= X1 = active#(X1) active#(U52(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U53(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U54(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U55(X1,X2)) = X1 >= X1 = active#(X1) active#(U56(X)) = X >= X = active#(X) active#(U61(X1,X2)) = X1 >= X1 = active#(X1) active#(U62(X1,X2)) = X1 >= X1 = active#(X1) active#(U63(X)) = X >= X = active#(X) active#(U71(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U72(X1,X2)) = X1 >= X1 = active#(X1) active#(U73(X1,X2)) = X1 >= X1 = active#(X1) active#(U74(X)) = X >= X = active#(X) active#(U81(X1,X2)) = X1 >= X1 = active#(X1) active#(U82(X1,X2)) = X1 >= X1 = active#(X1) active#(U83(X)) = X >= X = active#(X) active#(U91(X1,X2)) = X1 >= X1 = active#(X1) active#(U92(X)) = X + 1 >= X = active#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= 1 = mark(X) active(__(nil(),X)) = X + 2 >= 1 = mark(X) active(U11(tt(),V)) = 2 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 2 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 2 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 2 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 2 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 2 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 2 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 2 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 2 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + 2 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 2 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 2 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 2 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 2 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 2 >= 1 = mark(tt()) active(U61(tt(),V)) = 2 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 2 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 2 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 2 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 2 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 2 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 2 >= 1 = mark(tt()) active(U81(tt(),V)) = 2 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 2 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 2 >= 1 = mark(tt()) active(U91(tt(),V2)) = 2 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 3 >= 1 = mark(tt()) active(isList(V)) = 2 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 2 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 2 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 2 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 2 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 2 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 2 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 2 >= 1 = mark(tt()) active(isPalListKind(a())) = 2 >= 1 = mark(tt()) active(isPalListKind(e())) = 2 >= 1 = mark(tt()) active(isPalListKind(i())) = 2 >= 1 = mark(tt()) active(isPalListKind(nil())) = 2 >= 1 = mark(tt()) active(isPalListKind(o())) = 2 >= 1 = mark(tt()) active(isPalListKind(u())) = 2 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 2 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 2 >= 1 = mark(tt()) active(isQid(e())) = 2 >= 1 = mark(tt()) active(isQid(i())) = 2 >= 1 = mark(tt()) active(isQid(o())) = 2 >= 1 = mark(tt()) active(isQid(u())) = 2 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 2 >= X + 2 = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + 1 >= 1 = mark(__(X1,X2)) U11(mark(X1),X2) = 1 >= 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = 1 >= 1 = mark(U12(X1,X2)) U13(mark(X)) = 1 >= 1 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 1 >= 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 1 >= 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 1 >= 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 1 >= 1 = mark(U25(X1,X2)) U26(mark(X)) = 1 >= 1 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = 1 >= 1 = mark(U32(X1,X2)) U33(mark(X)) = 1 >= 1 = mark(U33(X)) U41(mark(X1),X2,X3) = 1 >= 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 1 >= 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 1 >= 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = 1 >= 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = 1 >= 1 = mark(U45(X1,X2)) U46(mark(X)) = 1 >= 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X2 + 1 >= 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 1 >= 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = 1 >= 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 1 >= 1 = mark(U55(X1,X2)) U56(mark(X)) = 1 >= 1 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 1 = mark(U62(X1,X2)) U63(mark(X)) = 1 >= 1 = mark(U63(X)) U71(mark(X1),X2,X3) = 1 >= 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 1 >= 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = 1 >= 1 = mark(U73(X1,X2)) U74(mark(X)) = 1 >= 1 = mark(U74(X)) U81(mark(X1),X2) = 1 >= 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = 1 >= 1 = mark(U82(X1,X2)) U83(mark(X)) = 1 >= 1 = mark(U83(X)) U91(mark(X1),X2) = 1 >= 1 = mark(U91(X1,X2)) U92(mark(X)) = 2 >= 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 >= X1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 1 >= 1 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 >= X1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 >= X1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 >= X1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 >= X1 = U25(proper(X1),proper(X2)) proper(isList(X)) = 1 >= 1 = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 1 >= 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 >= X1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 >= X1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 >= X1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 >= X1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 >= X1 + X2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 >= X1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 >= X1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 >= X1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 >= X1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X >= X = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = 2 >= 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 1 >= 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 1 >= 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 1 >= 1 = ok(isPalListKind(X)) U13(ok(X)) = 1 >= 1 = ok(U13(X)) isNeList(ok(X)) = 1 >= 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 1 >= 1 = ok(U25(X1,X2)) isList(ok(X)) = 1 >= 1 = ok(isList(X)) U26(ok(X)) = 1 >= 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = 1 >= 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 1 >= 1 = ok(U32(X1,X2)) U33(ok(X)) = 1 >= 1 = ok(U33(X)) isQid(ok(X)) = 1 >= 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 1 >= 1 = ok(U45(X1,X2)) U46(ok(X)) = 1 >= 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 2 >= 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 1 >= 1 = ok(U55(X1,X2)) U56(ok(X)) = 1 >= 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = 1 >= 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 1 >= 1 = ok(U62(X1,X2)) U63(ok(X)) = 1 >= 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 1 >= 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 1 >= 1 = ok(U73(X1,X2)) isPal(ok(X)) = 1 >= 1 = ok(isPal(X)) U74(ok(X)) = 1 >= 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = 1 >= 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 1 >= 1 = ok(U82(X1,X2)) U83(ok(X)) = 1 >= 1 = ok(U83(X)) isNePal(ok(X)) = 1 >= 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 1 >= 1 = ok(U91(X1,X2)) U92(ok(X)) = 2 >= 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) active#(U11(X1,X2)) -> active#(X1) active#(U12(X1,X2)) -> active#(X1) active#(U13(X)) -> active#(X) active#(U21(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) active#(U23(X1,X2,X3)) -> active#(X1) active#(U24(X1,X2,X3)) -> active#(X1) active#(U25(X1,X2)) -> active#(X1) active#(U26(X)) -> active#(X) active#(U31(X1,X2)) -> active#(X1) active#(U32(X1,X2)) -> active#(X1) active#(U33(X)) -> active#(X) active#(U41(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2,X3)) -> active#(X1) active#(U43(X1,X2,X3)) -> active#(X1) active#(U44(X1,X2,X3)) -> active#(X1) active#(U45(X1,X2)) -> active#(X1) active#(U46(X)) -> active#(X) active#(U51(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2,X3)) -> active#(X1) active#(U53(X1,X2,X3)) -> active#(X1) active#(U54(X1,X2,X3)) -> active#(X1) active#(U55(X1,X2)) -> active#(X1) active#(U56(X)) -> active#(X) active#(U61(X1,X2)) -> active#(X1) active#(U62(X1,X2)) -> active#(X1) active#(U63(X)) -> active#(X) active#(U71(X1,X2,X3)) -> active#(X1) active#(U72(X1,X2)) -> active#(X1) active#(U73(X1,X2)) -> active#(X1) active#(U74(X)) -> active#(X) active#(U81(X1,X2)) -> active#(X1) active#(U82(X1,X2)) -> active#(X1) active#(U83(X)) -> active#(X) active#(U91(X1,X2)) -> active#(X1) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = 0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 1, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = 1, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(X1,X2)) = X1 + X2 + 1 >= X1 = active#(X1) active#(__(X1,X2)) = X1 + X2 + 1 >= X2 = active#(X2) active#(U11(X1,X2)) = X1 >= X1 = active#(X1) active#(U12(X1,X2)) = X1 >= X1 = active#(X1) active#(U13(X)) = X >= X = active#(X) active#(U21(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U22(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U23(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U24(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U25(X1,X2)) = X1 >= X1 = active#(X1) active#(U26(X)) = X >= X = active#(X) active#(U31(X1,X2)) = X1 >= X1 = active#(X1) active#(U32(X1,X2)) = X1 >= X1 = active#(X1) active#(U33(X)) = X >= X = active#(X) active#(U41(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U42(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U43(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U44(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U45(X1,X2)) = X1 >= X1 = active#(X1) active#(U46(X)) = X >= X = active#(X) active#(U51(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U52(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U53(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U54(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U55(X1,X2)) = X1 >= X1 = active#(X1) active#(U56(X)) = X >= X = active#(X) active#(U61(X1,X2)) = X1 >= X1 = active#(X1) active#(U62(X1,X2)) = X1 >= X1 = active#(X1) active#(U63(X)) = X >= X = active#(X) active#(U71(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U72(X1,X2)) = X1 >= X1 = active#(X1) active#(U73(X1,X2)) = X1 >= X1 = active#(X1) active#(U74(X)) = X >= X = active#(X) active#(U81(X1,X2)) = X1 >= X1 = active#(X1) active#(U82(X1,X2)) = X1 >= X1 = active#(X1) active#(U83(X)) = X >= X = active#(X) active#(U91(X1,X2)) = X1 >= X1 = active#(X1) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= 0 = mark(X) active(__(nil(),X)) = X + 2 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 0 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 0 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 0 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = 0 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 0 >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 0 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 1 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 >= X1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 >= X1 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X1 >= X1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 >= X1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 >= X1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 >= X1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X1 >= X1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 >= X1 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = 0 >= 0 = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = 0 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = 0 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = 0 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 0 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = 0 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 0 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = 0 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = 0 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 >= X1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 1 >= 1 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 >= X1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 >= X1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 >= X1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 >= X1 = U25(proper(X1),proper(X2)) proper(isList(X)) = 1 >= 1 = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 >= X1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 >= X1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 >= X1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 >= X1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 >= X1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 >= X1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 >= X1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 >= X1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 1 >= 1 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 1 >= 1 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(U11(X1,X2)) -> active#(X1) active#(U12(X1,X2)) -> active#(X1) active#(U13(X)) -> active#(X) active#(U21(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) active#(U23(X1,X2,X3)) -> active#(X1) active#(U24(X1,X2,X3)) -> active#(X1) active#(U25(X1,X2)) -> active#(X1) active#(U26(X)) -> active#(X) active#(U31(X1,X2)) -> active#(X1) active#(U32(X1,X2)) -> active#(X1) active#(U33(X)) -> active#(X) active#(U41(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2,X3)) -> active#(X1) active#(U43(X1,X2,X3)) -> active#(X1) active#(U44(X1,X2,X3)) -> active#(X1) active#(U45(X1,X2)) -> active#(X1) active#(U46(X)) -> active#(X) active#(U51(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2,X3)) -> active#(X1) active#(U53(X1,X2,X3)) -> active#(X1) active#(U54(X1,X2,X3)) -> active#(X1) active#(U55(X1,X2)) -> active#(X1) active#(U56(X)) -> active#(X) active#(U61(X1,X2)) -> active#(X1) active#(U62(X1,X2)) -> active#(X1) active#(U63(X)) -> active#(X) active#(U71(X1,X2,X3)) -> active#(X1) active#(U72(X1,X2)) -> active#(X1) active#(U73(X1,X2)) -> active#(X1) active#(U74(X)) -> active#(X) active#(U81(X1,X2)) -> active#(X1) active#(U82(X1,X2)) -> active#(X1) active#(U83(X)) -> active#(X) active#(U91(X1,X2)) -> active#(X1) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [U92](x0) = 0, [U91](x0, x1) = x0, [U83](x0) = x0 + 1, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [U72](x0, x1) = x0 + x1, [U71](x0, x1, x2) = x0, [U63](x0) = x0, [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 + x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x0 + x1, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0 + x1, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = 0, [U24](x0, x1, x2) = x0 + x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + x1, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 1, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = 0 orientation: active#(U11(X1,X2)) = X1 + X2 >= X1 = active#(X1) active#(U12(X1,X2)) = X1 >= X1 = active#(X1) active#(U13(X)) = X >= X = active#(X) active#(U21(X1,X2,X3)) = X1 + X2 >= X1 = active#(X1) active#(U22(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U23(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U24(X1,X2,X3)) = X1 + X3 >= X1 = active#(X1) active#(U25(X1,X2)) = X1 + X2 >= X1 = active#(X1) active#(U26(X)) = X >= X = active#(X) active#(U31(X1,X2)) = X1 >= X1 = active#(X1) active#(U32(X1,X2)) = X1 >= X1 = active#(X1) active#(U33(X)) = X >= X = active#(X) active#(U41(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U42(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U43(X1,X2,X3)) = X1 + X2 >= X1 = active#(X1) active#(U44(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U45(X1,X2)) = X1 >= X1 = active#(X1) active#(U46(X)) = X >= X = active#(X) active#(U51(X1,X2,X3)) = X1 + X2 >= X1 = active#(X1) active#(U52(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U53(X1,X2,X3)) = X1 + X3 >= X1 = active#(X1) active#(U54(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U55(X1,X2)) = X1 >= X1 = active#(X1) active#(U56(X)) = X >= X = active#(X) active#(U61(X1,X2)) = X1 + X2 >= X1 = active#(X1) active#(U62(X1,X2)) = X1 >= X1 = active#(X1) active#(U63(X)) = X >= X = active#(X) active#(U71(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U72(X1,X2)) = X1 + X2 >= X1 = active#(X1) active#(U73(X1,X2)) = X1 >= X1 = active#(X1) active#(U74(X)) = X >= X = active#(X) active#(U81(X1,X2)) = X1 >= X1 = active#(X1) active#(U82(X1,X2)) = X1 >= X1 = active#(X1) active#(U83(X)) = X + 1 >= X = active#(X) active#(U91(X1,X2)) = X1 >= X1 = active#(X1) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 0 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P + 1 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 0 = mark(tt()) active(U81(tt(),V)) = 1 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 2 >= 0 = mark(tt()) active(U91(tt(),V2)) = 1 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 0 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = 0 >= 0 = __(active(X1),X2) active(__(X1,X2)) = 0 >= 0 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 >= X1 + X2 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X3 >= X1 + X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 >= X1 + X2 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 >= X1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 >= X1 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 >= X1 + X2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X3 >= X1 + X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 >= X1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + X2 >= X1 + X2 = U61(active(X1),X2) active(U62(X1,X2)) = X1 >= X1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X1 >= X1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + X2 >= X1 + X2 = U72(active(X1),X2) active(U73(X1,X2)) = X1 >= X1 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = 0 >= 0 = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X2 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X2 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = 0 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = 0 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X2 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = 0 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 0 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = 0 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = 0 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 1 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 >= X1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 >= X1 + X2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 >= X1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 >= X1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X3 >= X1 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 >= X1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 >= X1 + X2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 >= X1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 >= X1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 >= X1 + X2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 >= X1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X3 >= X1 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 >= X1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 >= X1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 + X2 >= X1 + X2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + X2 >= X1 + X2 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 1 >= 0 = ok(a()) proper(e()) = 1 >= 0 = ok(e()) proper(i()) = 1 >= 0 = ok(i()) proper(o()) = 1 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 0 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 1 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(U11(X1,X2)) -> active#(X1) active#(U12(X1,X2)) -> active#(X1) active#(U13(X)) -> active#(X) active#(U21(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) active#(U23(X1,X2,X3)) -> active#(X1) active#(U24(X1,X2,X3)) -> active#(X1) active#(U25(X1,X2)) -> active#(X1) active#(U26(X)) -> active#(X) active#(U31(X1,X2)) -> active#(X1) active#(U32(X1,X2)) -> active#(X1) active#(U33(X)) -> active#(X) active#(U41(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2,X3)) -> active#(X1) active#(U43(X1,X2,X3)) -> active#(X1) active#(U44(X1,X2,X3)) -> active#(X1) active#(U45(X1,X2)) -> active#(X1) active#(U46(X)) -> active#(X) active#(U51(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2,X3)) -> active#(X1) active#(U53(X1,X2,X3)) -> active#(X1) active#(U54(X1,X2,X3)) -> active#(X1) active#(U55(X1,X2)) -> active#(X1) active#(U56(X)) -> active#(X) active#(U61(X1,X2)) -> active#(X1) active#(U62(X1,X2)) -> active#(X1) active#(U63(X)) -> active#(X) active#(U71(X1,X2,X3)) -> active#(X1) active#(U72(X1,X2)) -> active#(X1) active#(U73(X1,X2)) -> active#(X1) active#(U74(X)) -> active#(X) active#(U81(X1,X2)) -> active#(X1) active#(U82(X1,X2)) -> active#(X1) active#(U91(X1,X2)) -> active#(X1) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = 1, [U91](x0, x1) = x0 + 1, [U83](x0) = 1, [isNePal](x0) = 1, [U82](x0, x1) = x0 + 1, [U81](x0, x1) = x0 + 1, [U74](x0) = x0 + 1, [U73](x0, x1) = x0 + 1, [isPal](x0) = 1, [U72](x0, x1) = x0 + 1, [U71](x0, x1, x2) = x0 + 1, [U63](x0) = x0 + 1, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0 + 1, [U55](x0, x1) = x0 + 1, [U54](x0, x1, x2) = x0 + 1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x0 + 1, [U51](x0, x1, x2) = x0 + 1, [U46](x0) = x0 + 1, [U45](x0, x1) = x0 + 1, [U44](x0, x1, x2) = x0 + 1, [U43](x0, x1, x2) = x0 + 1, [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + 1, [U33](x0) = x0 + 1, [isQid](x0) = 1, [U32](x0, x1) = x0 + 1, [U31](x0, x1) = x0 + 1, [U26](x0) = x0 + 1, [U25](x0, x1) = x0 + 1, [isList](x0) = 1, [U24](x0, x1, x2) = x0 + 1, [U23](x0, x1, x2) = x0 + 1, [U22](x0, x1, x2) = x0 + 1, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0 + 1, [isNeList](x0) = 1, [U12](x0, x1) = x0 + 1, [isPalListKind](x0) = 1, [U11](x0, x1) = x0 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = 1 orientation: active#(U11(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U12(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U13(X)) = X + 2 >= X + 1 = active#(X) active#(U21(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U22(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U23(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U24(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U25(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U26(X)) = X + 2 >= X + 1 = active#(X) active#(U31(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U32(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U33(X)) = X + 2 >= X + 1 = active#(X) active#(U41(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U42(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U43(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U44(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U45(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U46(X)) = X + 2 >= X + 1 = active#(X) active#(U51(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U52(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U53(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U54(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U55(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U56(X)) = X + 2 >= X + 1 = active#(X) active#(U61(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U62(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U63(X)) = X + 2 >= X + 1 = active#(X) active#(U71(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U72(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U73(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U74(X)) = X + 2 >= X + 1 = active#(X) active#(U81(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U82(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U91(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = 1 >= 1 = __(active(X1),X2) active(__(X1,X2)) = 1 >= 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = 1 >= 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = 1 >= 1 = U92(active(X)) __(mark(X1),X2) = 1 >= 1 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 1 = mark(__(X1,X2)) U11(mark(X1),X2) = 2 >= 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = 2 >= 1 = mark(U12(X1,X2)) U13(mark(X)) = 2 >= 1 = mark(U13(X)) U21(mark(X1),X2,X3) = 2 >= 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 2 >= 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 2 >= 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 2 >= 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 2 >= 1 = mark(U25(X1,X2)) U26(mark(X)) = 2 >= 1 = mark(U26(X)) U31(mark(X1),X2) = 2 >= 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = 2 >= 1 = mark(U32(X1,X2)) U33(mark(X)) = 2 >= 1 = mark(U33(X)) U41(mark(X1),X2,X3) = 2 >= 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 2 >= 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 2 >= 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = 2 >= 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = 2 >= 1 = mark(U45(X1,X2)) U46(mark(X)) = 2 >= 1 = mark(U46(X)) U51(mark(X1),X2,X3) = 2 >= 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 2 >= 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 2 >= 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = 2 >= 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 2 >= 1 = mark(U55(X1,X2)) U56(mark(X)) = 2 >= 1 = mark(U56(X)) U61(mark(X1),X2) = 2 >= 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = 2 >= 1 = mark(U62(X1,X2)) U63(mark(X)) = 2 >= 1 = mark(U63(X)) U71(mark(X1),X2,X3) = 2 >= 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 2 >= 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = 2 >= 1 = mark(U73(X1,X2)) U74(mark(X)) = 2 >= 1 = mark(U74(X)) U81(mark(X1),X2) = 2 >= 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = 2 >= 1 = mark(U82(X1,X2)) U83(mark(X)) = 1 >= 1 = mark(U83(X)) U91(mark(X1),X2) = 2 >= 1 = mark(U91(X1,X2)) U92(mark(X)) = 1 >= 1 = mark(U92(X)) proper(__(X1,X2)) = 1 >= 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 1 >= 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = 1 >= 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = 1 >= 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 1 >= 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = 1 >= 1 = U83(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = 1 >= 1 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 1 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 1 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 1 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 1 >= 0 = ok(U13(X)) isNeList(ok(X)) = 1 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 1 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 1 >= 0 = ok(isList(X)) U26(ok(X)) = 1 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 1 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 1 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 1 >= 0 = ok(U33(X)) isQid(ok(X)) = 1 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 1 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 1 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 1 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 1 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 1 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 1 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 1 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 1 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 1 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 1 >= 0 = ok(isPal(X)) U74(ok(X)) = 1 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 1 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 1 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 1 >= 0 = ok(U83(X)) isNePal(ok(X)) = 1 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 1 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 1 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(U11(X1,X2)) -> proper#(X2) proper#(U11(X1,X2)) -> proper#(X1) proper#(U12(X1,X2)) -> proper#(X2) proper#(U12(X1,X2)) -> proper#(X1) proper#(isPalListKind(X)) -> proper#(X) proper#(U13(X)) -> proper#(X) proper#(isNeList(X)) -> proper#(X) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U23(X1,X2,X3)) -> proper#(X3) proper#(U23(X1,X2,X3)) -> proper#(X2) proper#(U23(X1,X2,X3)) -> proper#(X1) proper#(U24(X1,X2,X3)) -> proper#(X3) proper#(U24(X1,X2,X3)) -> proper#(X2) proper#(U24(X1,X2,X3)) -> proper#(X1) proper#(U25(X1,X2)) -> proper#(X2) proper#(U25(X1,X2)) -> proper#(X1) proper#(isList(X)) -> proper#(X) proper#(U26(X)) -> proper#(X) proper#(U31(X1,X2)) -> proper#(X2) proper#(U31(X1,X2)) -> proper#(X1) proper#(U32(X1,X2)) -> proper#(X2) proper#(U32(X1,X2)) -> proper#(X1) proper#(U33(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) proper#(U41(X1,X2,X3)) -> proper#(X3) proper#(U41(X1,X2,X3)) -> proper#(X2) proper#(U41(X1,X2,X3)) -> proper#(X1) proper#(U42(X1,X2,X3)) -> proper#(X3) proper#(U42(X1,X2,X3)) -> proper#(X2) proper#(U42(X1,X2,X3)) -> proper#(X1) proper#(U43(X1,X2,X3)) -> proper#(X3) proper#(U43(X1,X2,X3)) -> proper#(X2) proper#(U43(X1,X2,X3)) -> proper#(X1) proper#(U44(X1,X2,X3)) -> proper#(X3) proper#(U44(X1,X2,X3)) -> proper#(X2) proper#(U44(X1,X2,X3)) -> proper#(X1) proper#(U45(X1,X2)) -> proper#(X2) proper#(U45(X1,X2)) -> proper#(X1) proper#(U46(X)) -> proper#(X) proper#(U51(X1,X2,X3)) -> proper#(X3) proper#(U51(X1,X2,X3)) -> proper#(X2) proper#(U51(X1,X2,X3)) -> proper#(X1) proper#(U52(X1,X2,X3)) -> proper#(X3) proper#(U52(X1,X2,X3)) -> proper#(X2) proper#(U52(X1,X2,X3)) -> proper#(X1) proper#(U53(X1,X2,X3)) -> proper#(X3) proper#(U53(X1,X2,X3)) -> proper#(X2) proper#(U53(X1,X2,X3)) -> proper#(X1) proper#(U54(X1,X2,X3)) -> proper#(X3) proper#(U54(X1,X2,X3)) -> proper#(X2) proper#(U54(X1,X2,X3)) -> proper#(X1) proper#(U55(X1,X2)) -> proper#(X2) proper#(U55(X1,X2)) -> proper#(X1) proper#(U56(X)) -> proper#(X) proper#(U61(X1,X2)) -> proper#(X2) proper#(U61(X1,X2)) -> proper#(X1) proper#(U62(X1,X2)) -> proper#(X2) proper#(U62(X1,X2)) -> proper#(X1) proper#(U63(X)) -> proper#(X) proper#(U71(X1,X2,X3)) -> proper#(X3) proper#(U71(X1,X2,X3)) -> proper#(X2) proper#(U71(X1,X2,X3)) -> proper#(X1) proper#(U72(X1,X2)) -> proper#(X2) proper#(U72(X1,X2)) -> proper#(X1) proper#(U73(X1,X2)) -> proper#(X2) proper#(U73(X1,X2)) -> proper#(X1) proper#(isPal(X)) -> proper#(X) proper#(U74(X)) -> proper#(X) proper#(U81(X1,X2)) -> proper#(X2) proper#(U81(X1,X2)) -> proper#(X1) proper#(U82(X1,X2)) -> proper#(X2) proper#(U82(X1,X2)) -> proper#(X1) proper#(U83(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) proper#(U91(X1,X2)) -> proper#(X2) proper#(U91(X1,X2)) -> proper#(X1) proper#(U92(X)) -> proper#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0 + 1, [U91](x0, x1) = x0 + x1 + 1, [U83](x0) = x0 + 1, [isNePal](x0) = x0 + 1, [U82](x0, x1) = x0 + x1 + 1, [U81](x0, x1) = x0 + x1 + 1, [U74](x0) = x0 + 1, [U73](x0, x1) = x0 + x1 + 1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0 + x1 + 1, [U71](x0, x1, x2) = x0 + x1 + x2 + 1, [U63](x0) = x0 + 1, [U62](x0, x1) = x0 + x1 + 1, [U61](x0, x1) = x0 + x1 + 1, [U56](x0) = x0 + 1, [U55](x0, x1) = x0 + x1 + 1, [U54](x0, x1, x2) = x0 + x1 + x2 + 1, [U53](x0, x1, x2) = x0 + x1 + x2 + 1, [U52](x0, x1, x2) = x0 + x1 + x2 + 1, [U51](x0, x1, x2) = x0 + x1 + x2 + 1, [U46](x0) = x0 + 1, [U45](x0, x1) = x0 + x1 + 1, [U44](x0, x1, x2) = x0 + x1 + x2 + 1, [U43](x0, x1, x2) = x0 + x1 + x2 + 1, [U42](x0, x1, x2) = x0 + x1 + x2 + 1, [U41](x0, x1, x2) = x0 + x1 + x2 + 1, [U33](x0) = x0 + 1, [isQid](x0) = x0 + 1, [U32](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + x1 + 1, [U26](x0) = x0 + 1, [U25](x0, x1) = x0 + x1 + 1, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x0 + x1 + x2 + 1, [U23](x0, x1, x2) = x0 + x1 + x2 + 1, [U22](x0, x1, x2) = x0 + x1 + x2 + 1, [U21](x0, x1, x2) = x0 + x1 + x2 + 1, [U13](x0) = x0 + 1, [isNeList](x0) = x0 + 1, [U12](x0, x1) = x0 + x1 + 1, [isPalListKind](x0) = x0 + 1, [U11](x0, x1) = x0 + x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: proper#(__(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(__(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U11(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U11(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U12(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U12(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(isPalListKind(X)) = X + 2 >= X + 1 = proper#(X) proper#(U13(X)) = X + 2 >= X + 1 = proper#(X) proper#(isNeList(X)) = X + 2 >= X + 1 = proper#(X) proper#(U21(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U21(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U21(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U22(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U22(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U22(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U23(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U23(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U23(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U24(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U24(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U24(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U25(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U25(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(isList(X)) = X + 2 >= X + 1 = proper#(X) proper#(U26(X)) = X + 2 >= X + 1 = proper#(X) proper#(U31(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U31(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U32(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U32(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U33(X)) = X + 2 >= X + 1 = proper#(X) proper#(isQid(X)) = X + 2 >= X + 1 = proper#(X) proper#(U41(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U41(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U41(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U42(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U42(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U42(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U43(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U43(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U43(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U44(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U44(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U44(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U45(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U45(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U46(X)) = X + 2 >= X + 1 = proper#(X) proper#(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U52(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U52(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U52(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U53(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U53(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U53(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U54(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U54(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U54(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U55(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U55(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U56(X)) = X + 2 >= X + 1 = proper#(X) proper#(U61(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U61(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U62(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U62(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U63(X)) = X + 2 >= X + 1 = proper#(X) proper#(U71(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U71(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U71(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U72(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U72(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U73(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U73(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(isPal(X)) = X + 2 >= X + 1 = proper#(X) proper#(U74(X)) = X + 2 >= X + 1 = proper#(X) proper#(U81(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U81(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U82(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U82(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U83(X)) = X + 2 >= X + 1 = proper#(X) proper#(isNePal(X)) = X + 2 >= X + 1 = proper#(X) proper#(U91(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U91(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U92(X)) = X + 2 >= X + 1 = proper#(X) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= 1 = mark(X) active(__(nil(),X)) = X + 1 >= 1 = mark(X) active(U11(tt(),V)) = V + 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V + 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = I + P + 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P + 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P + 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = V + 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V + 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = V2 + 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V + 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 3 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 + 2 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X2 + 2 >= 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + 2 >= 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 2 >= 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 2 >= 1 = mark(U12(X1,X2)) U13(mark(X)) = 2 >= 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 + 2 >= 1 = mark(U25(X1,X2)) U26(mark(X)) = 2 >= 1 = mark(U26(X)) U31(mark(X1),X2) = X2 + 2 >= 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 + 2 >= 1 = mark(U32(X1,X2)) U33(mark(X)) = 2 >= 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 + 2 >= 1 = mark(U45(X1,X2)) U46(mark(X)) = 2 >= 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 + 2 >= 1 = mark(U55(X1,X2)) U56(mark(X)) = 2 >= 1 = mark(U56(X)) U61(mark(X1),X2) = X2 + 2 >= 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 2 >= 1 = mark(U62(X1,X2)) U63(mark(X)) = 2 >= 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + X3 + 2 >= 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 + 2 >= 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 + 2 >= 1 = mark(U73(X1,X2)) U74(mark(X)) = 2 >= 1 = mark(U74(X)) U81(mark(X1),X2) = X2 + 2 >= 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 + 2 >= 1 = mark(U82(X1,X2)) U83(mark(X)) = 2 >= 1 = mark(U83(X)) U91(mark(X1),X2) = X2 + 2 >= 1 = mark(U91(X1,X2)) U92(mark(X)) = 2 >= 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 1 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 1 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 1 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 1 >= 0 = ok(U13(X)) isNeList(ok(X)) = 1 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 1 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 1 >= 0 = ok(isList(X)) U26(ok(X)) = 1 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 1 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 1 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 1 >= 0 = ok(U33(X)) isQid(ok(X)) = 1 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 1 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 1 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 1 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 1 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 1 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 1 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 1 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 1 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 1 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 1 >= 0 = ok(isPal(X)) U74(ok(X)) = 1 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 1 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 1 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 1 >= 0 = ok(U83(X)) isNePal(ok(X)) = 1 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 1 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 1 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U92#(mark(X)) -> U92#(X) U92#(ok(X)) -> U92#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U92#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U92#(mark(X)) = X + 1 >= X = U92#(X) U92#(ok(X)) = X >= X = U92#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U92#(ok(X)) -> U92#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U92#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U92#(ok(X)) = X + 1 >= X = U92#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U91#(mark(X1),X2) -> U91#(X1,X2) U91#(ok(X1),ok(X2)) -> U91#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U91#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U91#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U91#(X1,X2) U91#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U91#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U91#(mark(X1),X2) -> U91#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U91#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U91#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U91#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isNePal#(ok(X)) -> isNePal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isNePal#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isNePal#(ok(X)) = X + 1 >= X = isNePal#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U83#(mark(X)) -> U83#(X) U83#(ok(X)) -> U83#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U83#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U83#(mark(X)) = X + 1 >= X = U83#(X) U83#(ok(X)) = X >= X = U83#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U83#(ok(X)) -> U83#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U83#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U83#(ok(X)) = X + 1 >= X = U83#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U82#(mark(X1),X2) -> U82#(X1,X2) U82#(ok(X1),ok(X2)) -> U82#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U82#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U82#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U82#(X1,X2) U82#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U82#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U82#(mark(X1),X2) -> U82#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U82#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U82#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U82#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U81#(mark(X1),X2) -> U81#(X1,X2) U81#(ok(X1),ok(X2)) -> U81#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U81#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U81#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U81#(X1,X2) U81#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U81#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U81#(mark(X1),X2) -> U81#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U81#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U81#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U81#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U74#(mark(X)) -> U74#(X) U74#(ok(X)) -> U74#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U74#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U74#(mark(X)) = X + 1 >= X = U74#(X) U74#(ok(X)) = X >= X = U74#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U74#(ok(X)) -> U74#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U74#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U74#(ok(X)) = X + 1 >= X = U74#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isPal#(ok(X)) -> isPal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isPal#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isPal#(ok(X)) = X + 1 >= X = isPal#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U73#(mark(X1),X2) -> U73#(X1,X2) U73#(ok(X1),ok(X2)) -> U73#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U73#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U73#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U73#(X1,X2) U73#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U73#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U73#(mark(X1),X2) -> U73#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U73#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U73#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U73#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U72#(mark(X1),X2) -> U72#(X1,X2) U72#(ok(X1),ok(X2)) -> U72#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U72#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U72#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U72#(X1,X2) U72#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U72#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U72#(mark(X1),X2) -> U72#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U72#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U72#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U72#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(ok(X1),ok(X2),ok(X3)) -> U71#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U71#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U71#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U71#(X1,X2,X3) U71#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U71#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U71#(ok(X1),ok(X2),ok(X3)) -> U71#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U71#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U71#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U71#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U63#(mark(X)) -> U63#(X) U63#(ok(X)) -> U63#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U63#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U63#(mark(X)) = X + 1 >= X = U63#(X) U63#(ok(X)) = X >= X = U63#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U63#(ok(X)) -> U63#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U63#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U63#(ok(X)) = X + 1 >= X = U63#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U62#(mark(X1),X2) -> U62#(X1,X2) U62#(ok(X1),ok(X2)) -> U62#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U62#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U62#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U62#(X1,X2) U62#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U62#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U62#(mark(X1),X2) -> U62#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U62#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U62#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U62#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U61#(mark(X1),X2) -> U61#(X1,X2) U61#(ok(X1),ok(X2)) -> U61#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U61#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U61#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U61#(X1,X2) U61#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U61#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U61#(mark(X1),X2) -> U61#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U61#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U61#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U61#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U56#(mark(X)) -> U56#(X) U56#(ok(X)) -> U56#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U56#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U56#(mark(X)) = X + 1 >= X = U56#(X) U56#(ok(X)) = X >= X = U56#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U56#(ok(X)) -> U56#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U56#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U56#(ok(X)) = X + 1 >= X = U56#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U55#(mark(X1),X2) -> U55#(X1,X2) U55#(ok(X1),ok(X2)) -> U55#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U55#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U55#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U55#(X1,X2) U55#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U55#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U55#(mark(X1),X2) -> U55#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U55#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U55#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U55#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U54#(ok(X1),ok(X2),ok(X3)) -> U54#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U54#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U54#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U54#(X1,X2,X3) U54#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U54#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U54#(ok(X1),ok(X2),ok(X3)) -> U54#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U54#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U54#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U54#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U53#(ok(X1),ok(X2),ok(X3)) -> U53#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U53#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U53#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U53#(X1,X2,X3) U53#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U53#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U53#(ok(X1),ok(X2),ok(X3)) -> U53#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U53#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U53#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U53#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U52#(ok(X1),ok(X2),ok(X3)) -> U52#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U52#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U52#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U52#(X1,X2,X3) U52#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U52#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U52#(ok(X1),ok(X2),ok(X3)) -> U52#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U52#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U52#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U52#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U51#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U51#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U51#(X1,X2,X3) U51#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U51#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U51#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U51#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U51#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U46#(mark(X)) -> U46#(X) U46#(ok(X)) -> U46#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U46#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U46#(mark(X)) = X + 1 >= X = U46#(X) U46#(ok(X)) = X >= X = U46#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U46#(ok(X)) -> U46#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U46#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U46#(ok(X)) = X + 1 >= X = U46#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U45#(mark(X1),X2) -> U45#(X1,X2) U45#(ok(X1),ok(X2)) -> U45#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U45#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U45#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U45#(X1,X2) U45#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U45#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U45#(mark(X1),X2) -> U45#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U45#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U45#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U45#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U44#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U44#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U44#(X1,X2,X3) U44#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U44#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U44#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U44#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U44#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U43#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U43#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U43#(X1,X2,X3) U43#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U43#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U43#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U43#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U43#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U42#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U42#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U42#(X1,X2,X3) U42#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U42#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U42#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U42#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U42#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U41#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U41#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U41#(X1,X2,X3) U41#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U41#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U41#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U41#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U41#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isQid#(ok(X)) -> isQid#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isQid#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isQid#(ok(X)) = X + 1 >= X = isQid#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U33#(mark(X)) -> U33#(X) U33#(ok(X)) -> U33#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U33#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U33#(mark(X)) = X + 1 >= X = U33#(X) U33#(ok(X)) = X >= X = U33#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U33#(ok(X)) -> U33#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U33#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U33#(ok(X)) = X + 1 >= X = U33#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U32#(mark(X1),X2) -> U32#(X1,X2) U32#(ok(X1),ok(X2)) -> U32#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U32#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U32#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U32#(X1,X2) U32#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U32#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U32#(mark(X1),X2) -> U32#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U32#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U32#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U32#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U31#(mark(X1),X2) -> U31#(X1,X2) U31#(ok(X1),ok(X2)) -> U31#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U31#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U31#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U31#(X1,X2) U31#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U31#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U31#(mark(X1),X2) -> U31#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U31#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U31#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U31#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U26#(mark(X)) -> U26#(X) U26#(ok(X)) -> U26#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U26#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U26#(mark(X)) = X + 1 >= X = U26#(X) U26#(ok(X)) = X >= X = U26#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U26#(ok(X)) -> U26#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U26#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U26#(ok(X)) = X + 1 >= X = U26#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isList#(ok(X)) -> isList#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isList#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isList#(ok(X)) = X + 1 >= X = isList#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U25#(mark(X1),X2) -> U25#(X1,X2) U25#(ok(X1),ok(X2)) -> U25#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U25#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U25#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U25#(X1,X2) U25#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U25#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U25#(mark(X1),X2) -> U25#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U25#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U25#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U25#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3) U24#(ok(X1),ok(X2),ok(X3)) -> U24#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U24#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U24#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U24#(X1,X2,X3) U24#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U24#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U24#(ok(X1),ok(X2),ok(X3)) -> U24#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U24#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U24#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U24#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U23#(ok(X1),ok(X2),ok(X3)) -> U23#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U23#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U23#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U23#(X1,X2,X3) U23#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U23#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U23#(ok(X1),ok(X2),ok(X3)) -> U23#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U23#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U23#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U23#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U22#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U22#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U22#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U22#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U22#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U22#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U22#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U21#](x0, x1, x2) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U21#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U21#(X1,X2,X3) U21#(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = U21#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U21#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1 + 1, [U63](x0) = x0, [U62](x0, x1) = x1 + 1, [U61](x0, x1) = x1 + 1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x0 + 1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x1, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = x0 + 1, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0, [isPalListKind](x0) = x0, [U11](x0, x1) = x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U21#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = U21#(X1,X2,X3) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V + 1 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 0 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 0 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 0 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I + 1 >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 0 >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 2 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 >= X1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 >= X1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 >= X1 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X2 >= X2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X3 >= X3 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X1 >= X1 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = 0 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = 0 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = 0 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X2 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X3 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = 1 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 + 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = 0 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 2 >= X2 + 2 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 2 >= X2 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 2 >= X2 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isNeList#(ok(X)) -> isNeList#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isNeList#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isNeList#(ok(X)) = X + 1 >= X = isNeList#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U13#(mark(X)) -> U13#(X) U13#(ok(X)) -> U13#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U13#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0, [isList](x0) = 0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x0, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0, [U13](x0) = x0, [isNeList](x0) = 0, [U12](x0, x1) = x0, [isPalListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U13#(mark(X)) = X + 1 >= X = U13#(X) U13#(ok(X)) = X >= X = U13#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = 1 >= 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 1 >= 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = 1 >= 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 1 >= 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = 1 >= 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 1 >= 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = 1 >= 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = 1 >= 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 1 >= 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + 1 >= X1 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + 1 >= X1 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + 1 >= X1 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = 0 >= 0 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = 0 >= 0 = U13(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = 0 >= 0 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = 0 >= 0 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = 0 >= 0 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = 0 >= 0 = U25(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U26(X)) = 0 >= 0 = U26(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = 0 >= 0 = U32(proper(X1),proper(X2)) proper(U33(X)) = 0 >= 0 = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = 0 >= 0 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = 0 >= 0 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = 0 >= 0 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = 0 >= 0 = U45(proper(X1),proper(X2)) proper(U46(X)) = 0 >= 0 = U46(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = 0 >= 0 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = 0 >= 0 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = 0 >= 0 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = 0 >= 0 = U55(proper(X1),proper(X2)) proper(U56(X)) = 0 >= 0 = U56(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = 0 >= 0 = U62(proper(X1),proper(X2)) proper(U63(X)) = 0 >= 0 = U63(proper(X)) proper(U71(X1,X2,X3)) = 0 >= 0 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = 0 >= 0 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = 0 >= 0 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = 0 >= 0 = U74(proper(X)) proper(U81(X1,X2)) = 0 >= 0 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = 0 >= 0 = U82(proper(X1),proper(X2)) proper(U83(X)) = 0 >= 0 = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = 0 >= 0 = U91(proper(X1),proper(X2)) proper(U92(X)) = 0 >= 0 = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 >= X1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 >= X1 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 >= X1 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 >= X1 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 >= X1 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 >= X1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 >= X1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 >= X1 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U13#(ok(X)) -> U13#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U13#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U13#(ok(X)) = X + 1 >= X = U13#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isPalListKind#(ok(X)) -> isPalListKind#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isPalListKind#](x0) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0 + 1, [U72](x0, x1) = x0, [U71](x0, x1, x2) = x1, [U63](x0) = x0, [U62](x0, x1) = x0 + 1, [U61](x0, x1) = x0 + 1, [U56](x0) = x0, [U55](x0, x1) = x0, [U54](x0, x1, x2) = x1 + 1, [U53](x0, x1, x2) = x2, [U52](x0, x1, x2) = x0, [U51](x0, x1, x2) = x2, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + 1, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x0, [U23](x0, x1, x2) = x2, [U22](x0, x1, x2) = x0, [U21](x0, x1, x2) = x0 + 1, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1 + 1, [isPalListKind](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isPalListKind#(ok(X)) = X + 1 >= X = isPalListKind#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = 0 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V2 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = 0 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = 0 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V2 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + 1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = 0 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 1 >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = I >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 0 >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = 0 >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = 0 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 1 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 >= X1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X3 >= X3 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 >= X1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 >= X1 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 >= X1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 >= X1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 >= X1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X3 >= X3 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 >= X1 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X2 >= X2 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 >= X1 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X1 >= X1 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X1 >= X1 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 + 1 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = 0 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X3 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = 0 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = 0 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = 0 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = 0 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = 0 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X3 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 + 1 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = 0 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = 1 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X2 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = 0 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = 0 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = 0 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 2 >= X2 + 2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 2 >= X1 + 2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 2 >= X2 + 2 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + 1 >= X1 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + 2 >= X1 + 2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 2 >= X2 + 2 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U12#(mark(X1),X2) -> U12#(X1,X2) U12#(ok(X1),ok(X2)) -> U12#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U12#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U12#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U12#(X1,X2) U12#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U12#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U12#(mark(X1),X2) -> U12#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U12#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U12#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U12#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U11#(mark(X1),X2) -> U11#(X1,X2) U11#(ok(X1),ok(X2)) -> U11#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U11#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: U11#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U11#(X1,X2) U11#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U11#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U11#(mark(X1),X2) -> U11#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U11#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U11#(mark(X1),X2) = X1 + 2 >= X1 + 1 = U11#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x0 + x1, [U81](x0, x1) = x0 + x1, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 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 + 1, [U42](x0, x1, x2) = x0 + x1 + x2 + 1, [U41](x0, x1, x2) = x0 + x1 + x2 + 1, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: __#(mark(X1),X2) = X2 >= X2 = __#(X1,X2) __#(X1,mark(X2)) = X2 + 1 >= X2 = __#(X1,X2) __#(ok(X1),ok(X2)) = X2 >= X2 = __#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = V + 1 >= V + 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V + 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = P + 1 >= P + 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P + 1 >= P + 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = V + 1 >= V + 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V + 1 >= V + 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V + 1 >= V + 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 3 >= P + 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V + 1 >= V + 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + X3 + 1 >= X1 + X3 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + X3 + 1 >= X1 + X3 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 + X2 >= X1 + X2 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 + X2 >= X1 + X2 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 + X3 >= X1 + X3 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 + X2 >= X1 + X2 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X >= X = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 + X2 >= X1 + X2 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 + X2 >= X1 + X2 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = X >= X = ok(U13(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U25(X1,X2)) isList(ok(X)) = X >= X = ok(isList(X)) U26(ok(X)) = X >= X = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X1 >= X1 = ok(U32(X1,X2)) U33(ok(X)) = X >= X = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U45(X1,X2)) U46(ok(X)) = X >= X = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U55(X1,X2)) U56(ok(X)) = X >= X = ok(U56(X)) U61(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U62(X1,X2)) U63(ok(X)) = X >= X = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X1 + X3 >= X1 + X3 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X1 >= X1 = ok(U73(X1,X2)) isPal(ok(X)) = X >= X = ok(isPal(X)) U74(ok(X)) = X >= X = ok(U74(X)) U81(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U82(X1,X2)) U83(ok(X)) = X >= X = ok(U83(X)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X1 >= X1 = ok(U91(X1,X2)) U92(ok(X)) = X >= X = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x1, [U83](x0) = x0, [isNePal](x0) = x0, [U82](x0, x1) = x1, [U81](x0, x1) = x1, [U74](x0) = x0, [U73](x0, x1) = x1, [isPal](x0) = x0, [U72](x0, x1) = x1, [U71](x0, x1, x2) = x2, [U63](x0) = x0, [U62](x0, x1) = x1, [U61](x0, x1) = x1, [U56](x0) = x0, [U55](x0, x1) = x1, [U54](x0, x1, x2) = x1, [U53](x0, x1, x2) = x1, [U52](x0, x1, x2) = x2, [U51](x0, x1, x2) = x2 + 1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [isQid](x0) = x0, [U32](x0, x1) = x1, [U31](x0, x1) = x0, [U26](x0) = x0, [U25](x0, x1) = x1, [isList](x0) = x0, [U24](x0, x1, x2) = x2, [U23](x0, x1, x2) = x1, [U22](x0, x1, x2) = x2, [U21](x0, x1, x2) = x2, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x1, [isPalListKind](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: __#(mark(X1),X2) = X2 + 1 >= X2 + 1 = __#(X1,X2) __#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = __#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V >= 0 = mark(U13(isNeList(V))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V2 >= 0 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 >= 0 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V2 >= 0 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 >= 0 = mark(U26(isList(V2))) active(U26(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = V >= 0 = mark(U33(isQid(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 >= 0 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 >= 0 = mark(U46(isNeList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V2 >= 0 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 >= 0 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 >= 0 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 >= 0 = mark(U56(isList(V2))) active(U56(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = V >= 0 = mark(U63(isQid(V))) active(U63(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),I,P)) = P >= 0 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = P >= 0 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = P >= 0 = mark(U74(isPalListKind(P))) active(U74(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V)) = V >= 0 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = V >= 0 = mark(U83(isNePal(V))) active(U83(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),V2)) = V2 >= 0 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V2 + 1 >= 0 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 2 >= 0 = mark(U71(isQid(I),I,P)) active(isPal(V)) = V >= 0 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X1,X2)) = X2 >= X2 = U12(active(X1),X2) active(U13(X)) = X >= X = U13(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X3 >= X3 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X2 >= X2 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X3 >= X3 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X2 >= X2 = U25(active(X1),X2) active(U26(X)) = X >= X = U26(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X1,X2)) = X2 >= X2 = U32(active(X1),X2) active(U33(X)) = X >= X = U33(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X2 >= X2 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X2 >= X2 = U45(active(X1),X2) active(U46(X)) = X >= X = U46(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X3 >= X3 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X2 >= X2 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X2 >= X2 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X2 >= X2 = U55(active(X1),X2) active(U56(X)) = X >= X = U56(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X1,X2)) = X2 >= X2 = U62(active(X1),X2) active(U63(X)) = X >= X = U63(active(X)) active(U71(X1,X2,X3)) = X3 >= X3 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X2 >= X2 = U72(active(X1),X2) active(U73(X1,X2)) = X2 >= X2 = U73(active(X1),X2) active(U74(X)) = X >= X = U74(active(X)) active(U81(X1,X2)) = X2 >= X2 = U81(active(X1),X2) active(U82(X1,X2)) = X2 >= X2 = U82(active(X1),X2) active(U83(X)) = X >= X = U83(active(X)) active(U91(X1,X2)) = X2 >= X2 = U91(active(X1),X2) active(U92(X)) = X >= X = U92(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X1),X2) = X2 >= 0 = mark(U12(X1,X2)) U13(mark(X)) = 0 >= 0 = mark(U13(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X3 >= 0 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X2 >= 0 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X3 >= 0 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X2 >= 0 = mark(U25(X1,X2)) U26(mark(X)) = 0 >= 0 = mark(U26(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X1),X2) = X2 >= 0 = mark(U32(X1,X2)) U33(mark(X)) = 0 >= 0 = mark(U33(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X2 >= 0 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X2 >= 0 = mark(U45(X1,X2)) U46(mark(X)) = 0 >= 0 = mark(U46(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X3 >= 0 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X2 >= 0 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X2 >= 0 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X2 >= 0 = mark(U55(X1,X2)) U56(mark(X)) = 0 >= 0 = mark(U56(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X1),X2) = X2 >= 0 = mark(U62(X1,X2)) U63(mark(X)) = 0 >= 0 = mark(U63(X)) U71(mark(X1),X2,X3) = X3 >= 0 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X2 >= 0 = mark(U72(X1,X2)) U73(mark(X1),X2) = X2 >= 0 = mark(U73(X1,X2)) U74(mark(X)) = 0 >= 0 = mark(U74(X)) U81(mark(X1),X2) = X2 >= 0 = mark(U81(X1,X2)) U82(mark(X1),X2) = X2 >= 0 = mark(U82(X1,X2)) U83(mark(X)) = 0 >= 0 = mark(U83(X)) U91(mark(X1),X2) = X2 >= 0 = mark(U91(X1,X2)) U92(mark(X)) = 0 >= 0 = mark(U92(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X1,X2)) = X2 + 1 >= X2 + 1 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(U13(X)) = X + 1 >= X + 1 = U13(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X2 + 1 >= X2 + 1 = U25(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U26(X)) = X + 1 >= X + 1 = U26(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X2 + 1 >= X2 + 1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X + 1 >= X + 1 = U33(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X2 + 1 >= X2 + 1 = U45(proper(X1),proper(X2)) proper(U46(X)) = X + 1 >= X + 1 = U46(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X2 + 1 >= X2 + 1 = U55(proper(X1),proper(X2)) proper(U56(X)) = X + 1 >= X + 1 = U56(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X2 + 1 >= X2 + 1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X + 1 >= X + 1 = U63(proper(X)) proper(U71(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X2 + 1 >= X2 + 1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X2 + 1 >= X2 + 1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(U74(X)) = X + 1 >= X + 1 = U74(proper(X)) proper(U81(X1,X2)) = X2 + 1 >= X2 + 1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X2 + 1 >= X2 + 1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X + 1 >= X + 1 = U83(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(U91(X1,X2)) = X2 + 1 >= X2 + 1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X + 1 >= X + 1 = U92(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U12(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) U13(ok(X)) = X + 1 >= X + 1 = ok(U13(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U25(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U26(ok(X)) = X + 1 >= X + 1 = ok(U26(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U32(X1,X2)) U33(ok(X)) = X + 1 >= X + 1 = ok(U33(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U45(X1,X2)) U46(ok(X)) = X + 1 >= X + 1 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U55(X1,X2)) U56(ok(X)) = X + 1 >= X + 1 = ok(U56(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U62(X1,X2)) U63(ok(X)) = X + 1 >= X + 1 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U73(X1,X2)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) U74(ok(X)) = X + 1 >= X + 1 = ok(U74(X)) U81(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U82(X1,X2)) U83(ok(X)) = X + 1 >= X + 1 = ok(U83(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U91(X1,X2)) U92(ok(X)) = X + 1 >= X + 1 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: __#(mark(X1),X2) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [U92](x0) = x0, [U91](x0, x1) = x0, [U83](x0) = x0, [isNePal](x0) = 0, [U82](x0, x1) = x0, [U81](x0, x1) = x0, [U74](x0) = x0, [U73](x0, x1) = x0, [isPal](x0) = 0, [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 + 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 + 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) = x0 + x1 + x2, [U33](x0) = x0, [isQid](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0 + x1, [U26](x0) = x0, [U25](x0, x1) = x0 + x1, [isList](x0) = x0, [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, [U13](x0) = x0, [isNeList](x0) = x0, [U12](x0, x1) = x0 + x1, [isPalListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: __#(mark(X1),X2) = X1 + 2 >= X1 + 1 = __#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(U11(tt(),V)) = V + 1 >= V + 1 = mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) = V + 1 >= V + 1 = mark(U13(isNeList(V))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U25(isList(V1),V2)) active(U25(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U26(isList(V2))) active(U26(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isQid(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U45(isList(V1),V2)) active(U45(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U46(isNeList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U56(isList(V2))) active(U56(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) = 1 >= 1 = mark(U63(isQid(V))) active(U63(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),I,P)) = 1 >= 1 = mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) = 1 >= 1 = mark(U73(isPal(P),P)) active(U73(tt(),P)) = 1 >= 1 = mark(U74(isPalListKind(P))) active(U74(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V)) = 1 >= 1 = mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) = 1 >= 1 = mark(U83(isNePal(V))) active(U83(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),V2)) = 1 >= 1 = mark(U92(isPalListKind(V2))) active(U92(tt())) = 1 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) = V + 1 >= V + 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 1 = mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(U71(isQid(I),I,P)) active(isPal(V)) = 1 >= 1 = mark(U81(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(U91(isPalListKind(V1),V2)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(active(X1),X2) active(U13(X)) = X + 1 >= X + 1 = U13(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U22(active(X1),X2,X3) active(U23(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U23(active(X1),X2,X3) active(U24(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U24(active(X1),X2,X3) active(U25(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U25(active(X1),X2) active(U26(X)) = X + 1 >= X + 1 = U26(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X1,X2)) = X1 + 1 >= X1 + 1 = U32(active(X1),X2) active(U33(X)) = X + 1 >= X + 1 = U33(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(active(X1),X2,X3) active(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(active(X1),X2,X3) active(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(active(X1),X2,X3) active(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(active(X1),X2) active(U46(X)) = X + 1 >= X + 1 = U46(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = U51(active(X1),X2,X3) active(U52(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U52(active(X1),X2,X3) active(U53(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U53(active(X1),X2,X3) active(U54(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U54(active(X1),X2,X3) active(U55(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U55(active(X1),X2) active(U56(X)) = X + 1 >= X + 1 = U56(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X1,X2)) = X1 + 1 >= X1 + 1 = U62(active(X1),X2) active(U63(X)) = X + 1 >= X + 1 = U63(active(X)) active(U71(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2,X3) active(U72(X1,X2)) = X1 + 1 >= X1 + 1 = U72(active(X1),X2) active(U73(X1,X2)) = X1 + 1 >= X1 + 1 = U73(active(X1),X2) active(U74(X)) = X + 1 >= X + 1 = U74(active(X)) active(U81(X1,X2)) = X1 + 1 >= X1 + 1 = U81(active(X1),X2) active(U82(X1,X2)) = X1 + 1 >= X1 + 1 = U82(active(X1),X2) active(U83(X)) = X + 1 >= X + 1 = U83(active(X)) active(U91(X1,X2)) = X1 + 1 >= X1 + 1 = U91(active(X1),X2) active(U92(X)) = X + 1 >= X + 1 = U92(active(X)) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U11(X1,X2)) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U12(X1,X2)) U13(mark(X)) = X + 1 >= X + 1 = mark(U13(X)) U21(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U24(X1,X2,X3)) U25(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U25(X1,X2)) U26(mark(X)) = X + 1 >= X + 1 = mark(U26(X)) U31(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U31(X1,X2)) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U32(X1,X2)) U33(mark(X)) = X + 1 >= X + 1 = mark(U33(X)) U41(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U44(X1,X2,X3)) U45(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U45(X1,X2)) U46(mark(X)) = X + 1 >= X + 1 = mark(U46(X)) U51(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 2 = mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(U54(X1,X2,X3)) U55(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U55(X1,X2)) U56(mark(X)) = X + 1 >= X + 1 = mark(U56(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U62(X1,X2)) U63(mark(X)) = X + 1 >= X + 1 = mark(U63(X)) U71(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2,X3)) U72(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U72(X1,X2)) U73(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U73(X1,X2)) U74(mark(X)) = X + 1 >= X + 1 = mark(U74(X)) U81(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U81(X1,X2)) U82(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U82(X1,X2)) U83(mark(X)) = X + 1 >= X + 1 = mark(U83(X)) U91(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U91(X1,X2)) U92(mark(X)) = X + 1 >= X + 1 = mark(U92(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 >= X1 + X2 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X1,X2)) = X1 + X2 >= X1 + X2 = U12(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(U13(X)) = X >= X = U13(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) = X1 + X2 >= X1 + X2 = U25(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U26(X)) = X >= X = U26(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X1,X2)) = X1 >= X1 = U32(proper(X1),proper(X2)) proper(U33(X)) = X >= X = U33(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) = X1 + X2 >= X1 + X2 = U45(proper(X1),proper(X2)) proper(U46(X)) = X >= X = U46(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) = X1 + X2 >= X1 + X2 = U55(proper(X1),proper(X2)) proper(U56(X)) = X >= X = U56(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X1,X2)) = X1 >= X1 = U62(proper(X1),proper(X2)) proper(U63(X)) = X >= X = U63(proper(X)) proper(U71(X1,X2,X3)) = X1 >= X1 = U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) = X1 >= X1 = U72(proper(X1),proper(X2)) proper(U73(X1,X2)) = X1 >= X1 = U73(proper(X1),proper(X2)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(U74(X)) = X >= X = U74(proper(X)) proper(U81(X1,X2)) = X1 >= X1 = U81(proper(X1),proper(X2)) proper(U82(X1,X2)) = X1 >= X1 = U82(proper(X1),proper(X2)) proper(U83(X)) = X >= X = U83(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(U91(X1,X2)) = X1 >= X1 = U91(proper(X1),proper(X2)) proper(U92(X)) = X >= X = U92(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X1),ok(X2)) = 0 >= 0 = ok(U12(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) U13(ok(X)) = 0 >= 0 = ok(U13(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) = 0 >= 0 = ok(U25(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U26(ok(X)) = 0 >= 0 = ok(U26(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X1),ok(X2)) = 0 >= 0 = ok(U32(X1,X2)) U33(ok(X)) = 0 >= 0 = ok(U33(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) = 0 >= 0 = ok(U45(X1,X2)) U46(ok(X)) = 0 >= 0 = ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) = 0 >= 0 = ok(U55(X1,X2)) U56(ok(X)) = 0 >= 0 = ok(U56(X)) U61(ok(X1),ok(X2)) = 0 >= 0 = ok(U61(X1,X2)) U62(ok(X1),ok(X2)) = 0 >= 0 = ok(U62(X1,X2)) U63(ok(X)) = 0 >= 0 = ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) = 0 >= 0 = ok(U72(X1,X2)) U73(ok(X1),ok(X2)) = 0 >= 0 = ok(U73(X1,X2)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) U74(ok(X)) = 0 >= 0 = ok(U74(X)) U81(ok(X1),ok(X2)) = 0 >= 0 = ok(U81(X1,X2)) U82(ok(X1),ok(X2)) = 0 >= 0 = ok(U82(X1,X2)) U83(ok(X)) = 0 >= 0 = ok(U83(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) U91(ok(X1),ok(X2)) = 0 >= 0 = ok(U91(X1,X2)) U92(ok(X)) = 0 >= 0 = ok(U92(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V)) active(U12(tt(),V)) -> mark(U13(isNeList(V))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2)) active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2)) active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2)) active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2)) active(U25(tt(),V2)) -> mark(U26(isList(V2))) active(U26(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isQid(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNeList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isList(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V)) active(U62(tt(),V)) -> mark(U63(isQid(V))) active(U63(tt())) -> mark(tt()) active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P)) active(U72(tt(),P)) -> mark(U73(isPal(P),P)) active(U73(tt(),P)) -> mark(U74(isPalListKind(P))) active(U74(tt())) -> mark(tt()) active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V)) active(U82(tt(),V)) -> mark(U83(isNePal(V))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2))) active(U92(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P)) active(isPal(V)) -> mark(U81(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2)) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X1,X2)) -> U12(active(X1),X2) active(U13(X)) -> U13(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3) active(U25(X1,X2)) -> U25(active(X1),X2) active(U26(X)) -> U26(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X1,X2)) -> U32(active(X1),X2) active(U33(X)) -> U33(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X1,X2)) -> U73(active(X1),X2) active(U74(X)) -> U74(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X)) -> U92(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U13(mark(X)) -> mark(U13(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3)) U25(mark(X1),X2) -> mark(U25(X1,X2)) U26(mark(X)) -> mark(U26(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X1),X2) -> mark(U32(X1,X2)) U33(mark(X)) -> mark(U33(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X1),X2) -> mark(U73(X1,X2)) U74(mark(X)) -> mark(U74(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X)) -> mark(U92(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(U13(X)) -> U13(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3)) proper(U25(X1,X2)) -> U25(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U26(X)) -> U26(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) proper(U33(X)) -> U33(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(U63(X)) -> U63(proper(X)) proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X1,X2)) -> U73(proper(X1),proper(X2)) proper(isPal(X)) -> isPal(proper(X)) proper(U74(X)) -> U74(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X)) -> U92(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U13(ok(X)) -> ok(U13(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3)) U25(ok(X1),ok(X2)) -> ok(U25(X1,X2)) isList(ok(X)) -> ok(isList(X)) U26(ok(X)) -> ok(U26(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) U33(ok(X)) -> ok(U33(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) U63(ok(X)) -> ok(U63(X)) U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X1),ok(X2)) -> ok(U73(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U74(ok(X)) -> ok(U74(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) isNePal(ok(X)) -> ok(isNePal(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X)) -> ok(U92(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed