WORST_CASE(?,O(n^2)) * Step 1: Sum WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0 ,u/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,U13,U21,U22,U23,U24,U25,U26,U31,U32,U33,U41,U42 ,U43,U44,U45,U46,U51,U52,U53,U54,U55,U56,U61,U62,U63,U71,U72,U73,U74,U81,U82,U83,U91,U92,__,a,activate,e,i ,isList,isNeList,isNePal,isPal,isPalListKind,isQid,nil,o,u} and constructors {n____,n__a,n__e,n__i,n__nil ,n__o,n__u,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DependencyPairs WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0 ,u/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,U13,U21,U22,U23,U24,U25,U26,U31,U32,U33,U41,U42 ,U43,U44,U45,U46,U51,U52,U53,U54,U55,U56,U61,U62,U63,U71,U72,U73,U74,U81,U82,U83,U91,U92,__,a,activate,e,i ,isList,isNeList,isNePal,isPal,isPalListKind,isQid,nil,o,u} and constructors {n____,n__a,n__e,n__i,n__nil ,n__o,n__u,tt} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) U13#(tt()) -> c_3() U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U26#(tt()) -> c_9() U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U33#(tt()) -> c_12() U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) U46#(tt()) -> c_18() U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U56#(tt()) -> c_24() U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U63#(tt()) -> c_27() U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P)) U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) U74#(tt()) -> c_31() U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) U83#(tt()) -> c_34() U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) U92#(tt()) -> c_36() __#(X,nil()) -> c_37() __#(X1,X2) -> c_38() __#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) __#(nil(),X) -> c_40() a#() -> c_41() activate#(X) -> c_42() activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) activate#(n__a()) -> c_44(a#()) activate#(n__e()) -> c_45(e#()) activate#(n__i()) -> c_46(i#()) activate#(n__nil()) -> c_47(nil#()) activate#(n__o()) -> c_48(o#()) activate#(n__u()) -> c_49(u#()) e#() -> c_50() i#() -> c_51() isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isList#(n__nil()) -> c_54() isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPal#(n__nil()) -> c_61() isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) isPalListKind#(n__a()) -> c_63() isPalListKind#(n__e()) -> c_64() isPalListKind#(n__i()) -> c_65() isPalListKind#(n__nil()) -> c_66() isPalListKind#(n__o()) -> c_67() isPalListKind#(n__u()) -> c_68() isQid#(n__a()) -> c_69() isQid#(n__e()) -> c_70() isQid#(n__i()) -> c_71() isQid#(n__o()) -> c_72() isQid#(n__u()) -> c_73() nil#() -> c_74() o#() -> c_75() u#() -> c_76() Weak DPs and mark the set of starting terms. * Step 3: PredecessorEstimation WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) U13#(tt()) -> c_3() U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U26#(tt()) -> c_9() U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U33#(tt()) -> c_12() U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) U46#(tt()) -> c_18() U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U56#(tt()) -> c_24() U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U63#(tt()) -> c_27() U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P)) U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) U74#(tt()) -> c_31() U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) U83#(tt()) -> c_34() U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) U92#(tt()) -> c_36() __#(X,nil()) -> c_37() __#(X1,X2) -> c_38() __#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) __#(nil(),X) -> c_40() a#() -> c_41() activate#(X) -> c_42() activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) activate#(n__a()) -> c_44(a#()) activate#(n__e()) -> c_45(e#()) activate#(n__i()) -> c_46(i#()) activate#(n__nil()) -> c_47(nil#()) activate#(n__o()) -> c_48(o#()) activate#(n__u()) -> c_49(u#()) e#() -> c_50() i#() -> c_51() isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isList#(n__nil()) -> c_54() isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPal#(n__nil()) -> c_61() isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) isPalListKind#(n__a()) -> c_63() isPalListKind#(n__e()) -> c_64() isPalListKind#(n__i()) -> c_65() isPalListKind#(n__nil()) -> c_66() isPalListKind#(n__o()) -> c_67() isPalListKind#(n__u()) -> c_68() isQid#(n__a()) -> c_69() isQid#(n__e()) -> c_70() isQid#(n__i()) -> c_71() isQid#(n__o()) -> c_72() isQid#(n__u()) -> c_73() nil#() -> c_74() o#() -> c_75() u#() -> c_76() - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/4,c_2/3,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/3,c_9/0,c_10/4,c_11/3,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4 ,c_17/3,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/3,c_24/0,c_25/4,c_26/3,c_27/0,c_28/4,c_29/4,c_30/3,c_31/0 ,c_32/4,c_33/3,c_34/0,c_35/3,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/4,c_53/5,c_54/0,c_55/4,c_56/5,c_57/5,c_58/4,c_59/5,c_60/4,c_61/0 ,c_62/4,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {3,9,12,18,24,27,31,34,36,37,38,39,40,41,42,50,51,54,59,61,63,64,65,66,67,68,69,70,71,72,73,74,75,76} by application of Pre({3,9,12,18,24,27,31,34,36,37,38,39,40,41,42,50,51,54,59,61,63,64,65,66,67,68,69,70,71,72,73,74,75 ,76}) = {1,2,4,5,6,7,8,10,11,13,14,15,16,17,19,20,21,22,23,25,26,28,29,30,32,33,35,43,44,45,46,47,48,49,52 ,53,55,56,57,58,60,62}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 2: U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) 3: U13#(tt()) -> c_3() 4: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 5: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 6: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 7: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) 8: U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) 9: U26#(tt()) -> c_9() 10: U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 11: U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) 12: U33#(tt()) -> c_12() 13: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 14: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 15: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 16: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) 17: U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) 18: U46#(tt()) -> c_18() 19: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 20: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 21: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 22: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) 23: U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) 24: U56#(tt()) -> c_24() 25: U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 26: U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) 27: U63#(tt()) -> c_27() 28: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) 29: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P)) 30: U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) 31: U74#(tt()) -> c_31() 32: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 33: U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) 34: U83#(tt()) -> c_34() 35: U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) 36: U92#(tt()) -> c_36() 37: __#(X,nil()) -> c_37() 38: __#(X1,X2) -> c_38() 39: __#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) 40: __#(nil(),X) -> c_40() 41: a#() -> c_41() 42: activate#(X) -> c_42() 43: activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) 44: activate#(n__a()) -> c_44(a#()) 45: activate#(n__e()) -> c_45(e#()) 46: activate#(n__i()) -> c_46(i#()) 47: activate#(n__nil()) -> c_47(nil#()) 48: activate#(n__o()) -> c_48(o#()) 49: activate#(n__u()) -> c_49(u#()) 50: e#() -> c_50() 51: i#() -> c_51() 52: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 53: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 54: isList#(n__nil()) -> c_54() 55: isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 56: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 57: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 58: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 59: isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) 60: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 61: isPal#(n__nil()) -> c_61() 62: isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) 63: isPalListKind#(n__a()) -> c_63() 64: isPalListKind#(n__e()) -> c_64() 65: isPalListKind#(n__i()) -> c_65() 66: isPalListKind#(n__nil()) -> c_66() 67: isPalListKind#(n__o()) -> c_67() 68: isPalListKind#(n__u()) -> c_68() 69: isQid#(n__a()) -> c_69() 70: isQid#(n__e()) -> c_70() 71: isQid#(n__i()) -> c_71() 72: isQid#(n__o()) -> c_72() 73: isQid#(n__u()) -> c_73() 74: nil#() -> c_74() 75: o#() -> c_75() 76: u#() -> c_76() * Step 4: PredecessorEstimation WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P)) U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) activate#(n__a()) -> c_44(a#()) activate#(n__e()) -> c_45(e#()) activate#(n__i()) -> c_46(i#()) activate#(n__nil()) -> c_47(nil#()) activate#(n__o()) -> c_48(o#()) activate#(n__u()) -> c_49(u#()) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) - Weak DPs: U13#(tt()) -> c_3() U26#(tt()) -> c_9() U33#(tt()) -> c_12() U46#(tt()) -> c_18() U56#(tt()) -> c_24() U63#(tt()) -> c_27() U74#(tt()) -> c_31() U83#(tt()) -> c_34() U92#(tt()) -> c_36() __#(X,nil()) -> c_37() __#(X1,X2) -> c_38() __#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) __#(nil(),X) -> c_40() a#() -> c_41() activate#(X) -> c_42() e#() -> c_50() i#() -> c_51() isList#(n__nil()) -> c_54() isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) isPal#(n__nil()) -> c_61() isPalListKind#(n__a()) -> c_63() isPalListKind#(n__e()) -> c_64() isPalListKind#(n__i()) -> c_65() isPalListKind#(n__nil()) -> c_66() isPalListKind#(n__o()) -> c_67() isPalListKind#(n__u()) -> c_68() isQid#(n__a()) -> c_69() isQid#(n__e()) -> c_70() isQid#(n__i()) -> c_71() isQid#(n__o()) -> c_72() isQid#(n__u()) -> c_73() nil#() -> c_74() o#() -> c_75() u#() -> c_76() - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/4,c_2/3,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/3,c_9/0,c_10/4,c_11/3,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4 ,c_17/3,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/3,c_24/0,c_25/4,c_26/3,c_27/0,c_28/4,c_29/4,c_30/3,c_31/0 ,c_32/4,c_33/3,c_34/0,c_35/3,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/4,c_53/5,c_54/0,c_55/4,c_56/5,c_57/5,c_58/4,c_59/5,c_60/4,c_61/0 ,c_62/4,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {28,29,30,31,32,33,34} by application of Pre({28,29,30,31,32,33,34}) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,35 ,36,37,38,39,40,41,42}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 2: U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) 3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) 7: U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) 8: U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 9: U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) 10: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 11: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 12: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 13: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) 14: U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) 15: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 16: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 17: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 18: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) 19: U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) 20: U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 21: U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) 22: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) 23: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P)) 24: U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) 25: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 26: U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) 27: U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) 28: activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) 29: activate#(n__a()) -> c_44(a#()) 30: activate#(n__e()) -> c_45(e#()) 31: activate#(n__i()) -> c_46(i#()) 32: activate#(n__nil()) -> c_47(nil#()) 33: activate#(n__o()) -> c_48(o#()) 34: activate#(n__u()) -> c_49(u#()) 35: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 36: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 37: isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 38: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 39: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 40: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 41: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 42: isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) 43: U13#(tt()) -> c_3() 44: U26#(tt()) -> c_9() 45: U33#(tt()) -> c_12() 46: U46#(tt()) -> c_18() 47: U56#(tt()) -> c_24() 48: U63#(tt()) -> c_27() 49: U74#(tt()) -> c_31() 50: U83#(tt()) -> c_34() 51: U92#(tt()) -> c_36() 52: __#(X,nil()) -> c_37() 53: __#(X1,X2) -> c_38() 54: __#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) 55: __#(nil(),X) -> c_40() 56: a#() -> c_41() 57: activate#(X) -> c_42() 58: e#() -> c_50() 59: i#() -> c_51() 60: isList#(n__nil()) -> c_54() 61: isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) 62: isPal#(n__nil()) -> c_61() 63: isPalListKind#(n__a()) -> c_63() 64: isPalListKind#(n__e()) -> c_64() 65: isPalListKind#(n__i()) -> c_65() 66: isPalListKind#(n__nil()) -> c_66() 67: isPalListKind#(n__o()) -> c_67() 68: isPalListKind#(n__u()) -> c_68() 69: isQid#(n__a()) -> c_69() 70: isQid#(n__e()) -> c_70() 71: isQid#(n__i()) -> c_71() 72: isQid#(n__o()) -> c_72() 73: isQid#(n__u()) -> c_73() 74: nil#() -> c_74() 75: o#() -> c_75() 76: u#() -> c_76() * Step 5: PredecessorEstimation WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P)) U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) - Weak DPs: U13#(tt()) -> c_3() U26#(tt()) -> c_9() U33#(tt()) -> c_12() U46#(tt()) -> c_18() U56#(tt()) -> c_24() U63#(tt()) -> c_27() U74#(tt()) -> c_31() U83#(tt()) -> c_34() U92#(tt()) -> c_36() __#(X,nil()) -> c_37() __#(X1,X2) -> c_38() __#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) __#(nil(),X) -> c_40() a#() -> c_41() activate#(X) -> c_42() activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) activate#(n__a()) -> c_44(a#()) activate#(n__e()) -> c_45(e#()) activate#(n__i()) -> c_46(i#()) activate#(n__nil()) -> c_47(nil#()) activate#(n__o()) -> c_48(o#()) activate#(n__u()) -> c_49(u#()) e#() -> c_50() i#() -> c_51() isList#(n__nil()) -> c_54() isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) isPal#(n__nil()) -> c_61() isPalListKind#(n__a()) -> c_63() isPalListKind#(n__e()) -> c_64() isPalListKind#(n__i()) -> c_65() isPalListKind#(n__nil()) -> c_66() isPalListKind#(n__o()) -> c_67() isPalListKind#(n__u()) -> c_68() isQid#(n__a()) -> c_69() isQid#(n__e()) -> c_70() isQid#(n__i()) -> c_71() isQid#(n__o()) -> c_72() isQid#(n__u()) -> c_73() nil#() -> c_74() o#() -> c_75() u#() -> c_76() - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/4,c_2/3,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/3,c_9/0,c_10/4,c_11/3,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4 ,c_17/3,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/3,c_24/0,c_25/4,c_26/3,c_27/0,c_28/4,c_29/4,c_30/3,c_31/0 ,c_32/4,c_33/3,c_34/0,c_35/3,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/4,c_53/5,c_54/0,c_55/4,c_56/5,c_57/5,c_58/4,c_59/5,c_60/4,c_61/0 ,c_62/4,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {9,21} by application of Pre({9,21}) = {8,20}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 2: U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) 3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) 7: U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) 8: U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 9: U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) 10: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 11: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 12: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 13: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) 14: U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) 15: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 16: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 17: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) 18: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) 19: U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) 20: U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 21: U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) 22: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) 23: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P)) 24: U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) 25: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 26: U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) 27: U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) 28: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 29: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 30: isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 31: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 32: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) 33: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 34: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) 35: isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) 36: U13#(tt()) -> c_3() 37: U26#(tt()) -> c_9() 38: U33#(tt()) -> c_12() 39: U46#(tt()) -> c_18() 40: U56#(tt()) -> c_24() 41: U63#(tt()) -> c_27() 42: U74#(tt()) -> c_31() 43: U83#(tt()) -> c_34() 44: U92#(tt()) -> c_36() 45: __#(X,nil()) -> c_37() 46: __#(X1,X2) -> c_38() 47: __#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) 48: __#(nil(),X) -> c_40() 49: a#() -> c_41() 50: activate#(X) -> c_42() 51: activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) 52: activate#(n__a()) -> c_44(a#()) 53: activate#(n__e()) -> c_45(e#()) 54: activate#(n__i()) -> c_46(i#()) 55: activate#(n__nil()) -> c_47(nil#()) 56: activate#(n__o()) -> c_48(o#()) 57: activate#(n__u()) -> c_49(u#()) 58: e#() -> c_50() 59: i#() -> c_51() 60: isList#(n__nil()) -> c_54() 61: isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) 62: isPal#(n__nil()) -> c_61() 63: isPalListKind#(n__a()) -> c_63() 64: isPalListKind#(n__e()) -> c_64() 65: isPalListKind#(n__i()) -> c_65() 66: isPalListKind#(n__nil()) -> c_66() 67: isPalListKind#(n__o()) -> c_67() 68: isPalListKind#(n__u()) -> c_68() 69: isQid#(n__a()) -> c_69() 70: isQid#(n__e()) -> c_70() 71: isQid#(n__i()) -> c_71() 72: isQid#(n__o()) -> c_72() 73: isQid#(n__u()) -> c_73() 74: nil#() -> c_74() 75: o#() -> c_75() 76: u#() -> c_76() * Step 6: RemoveWeakSuffixes WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P)) U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) - Weak DPs: U13#(tt()) -> c_3() U26#(tt()) -> c_9() U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U33#(tt()) -> c_12() U46#(tt()) -> c_18() U56#(tt()) -> c_24() U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) U63#(tt()) -> c_27() U74#(tt()) -> c_31() U83#(tt()) -> c_34() U92#(tt()) -> c_36() __#(X,nil()) -> c_37() __#(X1,X2) -> c_38() __#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) __#(nil(),X) -> c_40() a#() -> c_41() activate#(X) -> c_42() activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) activate#(n__a()) -> c_44(a#()) activate#(n__e()) -> c_45(e#()) activate#(n__i()) -> c_46(i#()) activate#(n__nil()) -> c_47(nil#()) activate#(n__o()) -> c_48(o#()) activate#(n__u()) -> c_49(u#()) e#() -> c_50() i#() -> c_51() isList#(n__nil()) -> c_54() isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) isPal#(n__nil()) -> c_61() isPalListKind#(n__a()) -> c_63() isPalListKind#(n__e()) -> c_64() isPalListKind#(n__i()) -> c_65() isPalListKind#(n__nil()) -> c_66() isPalListKind#(n__o()) -> c_67() isPalListKind#(n__u()) -> c_68() isQid#(n__a()) -> c_69() isQid#(n__e()) -> c_70() isQid#(n__i()) -> c_71() isQid#(n__o()) -> c_72() isQid#(n__u()) -> c_73() nil#() -> c_74() o#() -> c_75() u#() -> c_76() - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/4,c_2/3,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/3,c_9/0,c_10/4,c_11/3,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4 ,c_17/3,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/3,c_24/0,c_25/4,c_26/3,c_27/0,c_28/4,c_29/4,c_30/3,c_31/0 ,c_32/4,c_33/3,c_34/0,c_35/3,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/4,c_53/5,c_54/0,c_55/4,c_56/5,c_57/5,c_58/4,c_59/5,c_60/4,c_61/0 ,c_62/4,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: RemoveWeakSuffixes + Details: Consider the dependency graph 1:S:U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)):2 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 2:S:U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) -->_3 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):30 -->_2 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):29 -->_2 isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):28 -->_3 activate#(X) -> c_42():50 -->_1 U13#(tt()) -> c_3():34 3:S:U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):4 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 4:S:U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):5 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 5:S:U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)):6 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 6:S:U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):27 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):26 -->_1 U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)):7 -->_2 isList#(n__nil()) -> c_54():60 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 7:S:U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) -->_3 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):27 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):26 -->_2 isList#(n__nil()) -> c_54():60 -->_3 activate#(X) -> c_42():50 -->_1 U26#(tt()) -> c_9():35 8:S:U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_1 U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)):36 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 9:S:U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):10 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 10:S:U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):11 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 11:S:U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)):12 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 12:S:U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):27 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):26 -->_1 U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)):13 -->_2 isList#(n__nil()) -> c_54():60 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 13:S:U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) -->_3 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):30 -->_2 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):29 -->_2 isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):28 -->_3 activate#(X) -> c_42():50 -->_1 U46#(tt()) -> c_18():38 14:S:U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):15 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 15:S:U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):16 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 16:S:U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)):17 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 17:S:U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):30 -->_2 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):29 -->_2 isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):28 -->_1 U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)):18 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 18:S:U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) -->_3 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):27 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):26 -->_2 isList#(n__nil()) -> c_54():60 -->_3 activate#(X) -> c_42():50 -->_1 U56#(tt()) -> c_24():39 19:S:U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_1 U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)):40 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 20:S:U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)) ,isPal#(activate(P)) ,activate#(P) ,activate#(P)):21 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 21:S:U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)) ,isPal#(activate(P)) ,activate#(P) ,activate#(P)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):32 -->_1 U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)):22 -->_2 isPal#(n__nil()) -> c_61():62 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 22:S:U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) -->_3 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_3 activate#(X) -> c_42():50 -->_1 U74#(tt()) -> c_31():42 23:S:U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)):24 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 24:S:U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) -->_3 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):31 -->_3 activate#(X) -> c_42():50 -->_1 U83#(tt()) -> c_34():43 25:S:U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) -->_3 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_3 activate#(X) -> c_42():50 -->_1 U92#(tt()) -> c_36():44 26:S:isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 -->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):1 27:S:isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 -->_1 U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):3 28:S:isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 -->_1 U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):8 29:S:isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 -->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):9 30:S:isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_5 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_5 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_5 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_5 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_5 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_5 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_5 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_5 activate#(X) -> c_42():50 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 -->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):14 31:S:isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 -->_1 U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):19 32:S:isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 -->_1 U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):23 33:S:isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) -->_4 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__u()) -> c_49(u#()):57 -->_4 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_4 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_4 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_4 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_4 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_4 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isPalListKind#(n__u()) -> c_68():68 -->_2 isPalListKind#(n__o()) -> c_67():67 -->_2 isPalListKind#(n__nil()) -> c_66():66 -->_2 isPalListKind#(n__i()) -> c_65():65 -->_2 isPalListKind#(n__e()) -> c_64():64 -->_2 isPalListKind#(n__a()) -> c_63():63 -->_4 activate#(X) -> c_42():50 -->_3 activate#(X) -> c_42():50 -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))) ,isPalListKind#(activate(V2)) ,activate#(V2)):25 34:W:U13#(tt()) -> c_3() 35:W:U26#(tt()) -> c_9() 36:W:U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) -->_3 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isQid#(n__u()) -> c_73():73 -->_2 isQid#(n__o()) -> c_72():72 -->_2 isQid#(n__i()) -> c_71():71 -->_2 isQid#(n__e()) -> c_70():70 -->_2 isQid#(n__a()) -> c_69():69 -->_3 activate#(X) -> c_42():50 -->_1 U33#(tt()) -> c_12():37 37:W:U33#(tt()) -> c_12() 38:W:U46#(tt()) -> c_18() 39:W:U56#(tt()) -> c_24() 40:W:U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) -->_3 activate#(n__u()) -> c_49(u#()):57 -->_3 activate#(n__o()) -> c_48(o#()):56 -->_3 activate#(n__nil()) -> c_47(nil#()):55 -->_3 activate#(n__i()) -> c_46(i#()):54 -->_3 activate#(n__e()) -> c_45(e#()):53 -->_3 activate#(n__a()) -> c_44(a#()):52 -->_3 activate#(n____(X1,X2)) -> c_43(__#(X1,X2)):51 -->_2 isQid#(n__u()) -> c_73():73 -->_2 isQid#(n__o()) -> c_72():72 -->_2 isQid#(n__i()) -> c_71():71 -->_2 isQid#(n__e()) -> c_70():70 -->_2 isQid#(n__a()) -> c_69():69 -->_3 activate#(X) -> c_42():50 -->_1 U63#(tt()) -> c_27():41 41:W:U63#(tt()) -> c_27() 42:W:U74#(tt()) -> c_31() 43:W:U83#(tt()) -> c_34() 44:W:U92#(tt()) -> c_36() 45:W:__#(X,nil()) -> c_37() 46:W:__#(X1,X2) -> c_38() 47:W:__#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) 48:W:__#(nil(),X) -> c_40() 49:W:a#() -> c_41() 50:W:activate#(X) -> c_42() 51:W:activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) -->_1 __#(X1,X2) -> c_38():46 52:W:activate#(n__a()) -> c_44(a#()) -->_1 a#() -> c_41():49 53:W:activate#(n__e()) -> c_45(e#()) -->_1 e#() -> c_50():58 54:W:activate#(n__i()) -> c_46(i#()) -->_1 i#() -> c_51():59 55:W:activate#(n__nil()) -> c_47(nil#()) -->_1 nil#() -> c_74():74 56:W:activate#(n__o()) -> c_48(o#()) -->_1 o#() -> c_75():75 57:W:activate#(n__u()) -> c_49(u#()) -->_1 u#() -> c_76():76 58:W:e#() -> c_50() 59:W:i#() -> c_51() 60:W:isList#(n__nil()) -> c_54() 61:W:isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) 62:W:isPal#(n__nil()) -> c_61() 63:W:isPalListKind#(n__a()) -> c_63() 64:W:isPalListKind#(n__e()) -> c_64() 65:W:isPalListKind#(n__i()) -> c_65() 66:W:isPalListKind#(n__nil()) -> c_66() 67:W:isPalListKind#(n__o()) -> c_67() 68:W:isPalListKind#(n__u()) -> c_68() 69:W:isQid#(n__a()) -> c_69() 70:W:isQid#(n__e()) -> c_70() 71:W:isQid#(n__i()) -> c_71() 72:W:isQid#(n__o()) -> c_72() 73:W:isQid#(n__u()) -> c_73() 74:W:nil#() -> c_74() 75:W:o#() -> c_75() 76:W:u#() -> c_76() The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 61: isNePal#(n____(I,__(P,I))) -> c_59(U71#(isQid(activate(I)),activate(I),activate(P)) ,isQid#(activate(I)) ,activate#(I) ,activate#(I) ,activate#(P)) 48: __#(nil(),X) -> c_40() 47: __#(__(X,Y),Z) -> c_39(__#(X,__(Y,Z)),__#(Y,Z)) 45: __#(X,nil()) -> c_37() 62: isPal#(n__nil()) -> c_61() 42: U74#(tt()) -> c_31() 43: U83#(tt()) -> c_34() 40: U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) 41: U63#(tt()) -> c_27() 34: U13#(tt()) -> c_3() 39: U56#(tt()) -> c_24() 38: U46#(tt()) -> c_18() 36: U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)) 37: U33#(tt()) -> c_12() 69: isQid#(n__a()) -> c_69() 70: isQid#(n__e()) -> c_70() 71: isQid#(n__i()) -> c_71() 72: isQid#(n__o()) -> c_72() 73: isQid#(n__u()) -> c_73() 35: U26#(tt()) -> c_9() 60: isList#(n__nil()) -> c_54() 44: U92#(tt()) -> c_36() 50: activate#(X) -> c_42() 63: isPalListKind#(n__a()) -> c_63() 64: isPalListKind#(n__e()) -> c_64() 65: isPalListKind#(n__i()) -> c_65() 66: isPalListKind#(n__nil()) -> c_66() 67: isPalListKind#(n__o()) -> c_67() 68: isPalListKind#(n__u()) -> c_68() 51: activate#(n____(X1,X2)) -> c_43(__#(X1,X2)) 46: __#(X1,X2) -> c_38() 52: activate#(n__a()) -> c_44(a#()) 49: a#() -> c_41() 53: activate#(n__e()) -> c_45(e#()) 58: e#() -> c_50() 54: activate#(n__i()) -> c_46(i#()) 59: i#() -> c_51() 55: activate#(n__nil()) -> c_47(nil#()) 74: nil#() -> c_74() 56: activate#(n__o()) -> c_48(o#()) 75: o#() -> c_75() 57: activate#(n__u()) -> c_49(u#()) 76: u#() -> c_76() * Step 7: SimplifyRHS WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P)) U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/4,c_2/3,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/3,c_9/0,c_10/4,c_11/3,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4 ,c_17/3,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/3,c_24/0,c_25/4,c_26/3,c_27/0,c_28/4,c_29/4,c_30/3,c_31/0 ,c_32/4,c_33/3,c_34/0,c_35/3,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/4,c_53/5,c_54/0,c_55/4,c_56/5,c_57/5,c_58/4,c_59/5,c_60/4,c_61/0 ,c_62/4,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: SimplifyRHS + Details: Consider the dependency graph 1:S:U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)):2 2:S:U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)) -->_2 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):30 -->_2 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):29 -->_2 isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):28 3:S:U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):4 4:S:U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):5 5:S:U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)):6 6:S:U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):27 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):26 -->_1 U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)):7 7:S:U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):27 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):26 8:S:U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 9:S:U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):10 10:S:U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):11 11:S:U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)):12 12:S:U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)) ,isList#(activate(V1)) ,activate#(V1) ,activate#(V2)) -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):27 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):26 -->_1 U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)):13 13:S:U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)) -->_2 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):30 -->_2 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):29 -->_2 isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):28 14:S:U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):15 15:S:U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)):16 16:S:U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2)) ,activate#(V2) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)):17 17:S:U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)) ,isNeList#(activate(V1)) ,activate#(V1) ,activate#(V2)) -->_2 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):30 -->_2 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):29 -->_2 isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):28 -->_1 U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)):18 18:S:U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)) -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):27 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):26 19:S:U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 20:S:U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)) ,isPalListKind#(activate(I)) ,activate#(I) ,activate#(P)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)) ,isPal#(activate(P)) ,activate#(P) ,activate#(P)):21 21:S:U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)) ,isPal#(activate(P)) ,activate#(P) ,activate#(P)) -->_2 isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):32 -->_1 U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)):22 22:S:U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 23:S:U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)):24 24:S:U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)) -->_2 isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):31 25:S:U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 26:S:isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):1 27:S:isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):3 28:S:isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):8 29:S:isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):9 30:S:isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V1) ,activate#(V2)):14 31:S:isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):19 32:S:isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)) ,isPalListKind#(activate(V)) ,activate#(V) ,activate#(V)):23 33:S:isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)) -->_2 isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1)) ,activate#(V1) ,activate#(V2)):33 -->_1 U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))) ,isPalListKind#(activate(V2)) ,activate#(V2)):25 Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U31#(tt(),V) -> c_10(isPalListKind#(activate(V))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1))) * Step 8: DecomposeDG WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U31#(tt(),V) -> c_10(isPalListKind#(activate(V))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: DecomposeDG {onSelection = all below first cut in WDG, onUpper = Nothing, onLower = Nothing} + Details: We decompose the input problem according to the dependency graph into the upper component U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) and a lower component U31#(tt(),V) -> c_10(isPalListKind#(activate(V))) U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1))) Further, following extension rules are added to the lower component. U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isPalListKind#(activate(V)) U12#(tt(),V) -> isNeList#(activate(V)) U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt(),V1,V2) -> isList#(activate(V1)) U25#(tt(),V2) -> isList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt(),V1,V2) -> isList#(activate(V1)) U45#(tt(),V2) -> isNeList#(activate(V2)) U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt(),V1,V2) -> isNeList#(activate(V1)) U55#(tt(),V2) -> isList#(activate(V2)) U61#(tt(),V) -> isPalListKind#(activate(V)) U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)) U71#(tt(),I,P) -> isPalListKind#(activate(I)) U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)) U72#(tt(),P) -> isPal#(activate(P)) U73#(tt(),P) -> isPalListKind#(activate(P)) U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)) U81#(tt(),V) -> isPalListKind#(activate(V)) U82#(tt(),V) -> isNePal#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) isList#(V) -> isPalListKind#(activate(V)) isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) isNePal#(V) -> isPalListKind#(activate(V)) isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)) isPal#(V) -> isPalListKind#(activate(V)) ** Step 8.a:1: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {18,21} by application of Pre({18,21}) = {20,28}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 2: U12#(tt(),V) -> c_2(isNeList#(activate(V))) 3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 7: U25#(tt(),V2) -> c_8(isList#(activate(V2))) 8: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 11: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 12: U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) 13: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 16: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) 17: U55#(tt(),V2) -> c_23(isList#(activate(V2))) 18: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) 19: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) 20: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) 21: U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) 22: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 23: U82#(tt(),V) -> c_33(isNePal#(activate(V))) 24: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 25: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 26: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 27: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 28: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 29: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) ** Step 8.a:2: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak DPs: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {26} by application of Pre({26}) = {21}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 2: U12#(tt(),V) -> c_2(isNeList#(activate(V))) 3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 7: U25#(tt(),V2) -> c_8(isList#(activate(V2))) 8: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 11: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 12: U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) 13: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 16: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) 17: U55#(tt(),V2) -> c_23(isList#(activate(V2))) 18: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) 19: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) 20: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 21: U82#(tt(),V) -> c_33(isNePal#(activate(V))) 22: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 23: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 24: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 25: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 26: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 27: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 28: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) 29: U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) ** Step 8.a:3: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak DPs: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {21} by application of Pre({21}) = {20}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 2: U12#(tt(),V) -> c_2(isNeList#(activate(V))) 3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 7: U25#(tt(),V2) -> c_8(isList#(activate(V2))) 8: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 11: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 12: U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) 13: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 16: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) 17: U55#(tt(),V2) -> c_23(isList#(activate(V2))) 18: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) 19: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) 20: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 21: U82#(tt(),V) -> c_33(isNePal#(activate(V))) 22: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 23: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 24: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 25: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 26: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 27: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) 28: U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) 29: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) ** Step 8.a:4: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak DPs: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {20} by application of Pre({20}) = {25}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 2: U12#(tt(),V) -> c_2(isNeList#(activate(V))) 3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 7: U25#(tt(),V2) -> c_8(isList#(activate(V2))) 8: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 11: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 12: U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) 13: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 16: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) 17: U55#(tt(),V2) -> c_23(isList#(activate(V2))) 18: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) 19: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) 20: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 21: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 22: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 23: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 24: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 25: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 26: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) 27: U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) 28: U82#(tt(),V) -> c_33(isNePal#(activate(V))) 29: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) ** Step 8.a:5: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak DPs: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {24} by application of Pre({24}) = {19}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 2: U12#(tt(),V) -> c_2(isNeList#(activate(V))) 3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 7: U25#(tt(),V2) -> c_8(isList#(activate(V2))) 8: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 11: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 12: U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) 13: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 16: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) 17: U55#(tt(),V2) -> c_23(isList#(activate(V2))) 18: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) 19: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) 20: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 21: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 22: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 23: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 24: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 25: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) 26: U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) 27: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 28: U82#(tt(),V) -> c_33(isNePal#(activate(V))) 29: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) ** Step 8.a:6: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) - Weak DPs: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {19} by application of Pre({19}) = {18}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 2: U12#(tt(),V) -> c_2(isNeList#(activate(V))) 3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 7: U25#(tt(),V2) -> c_8(isList#(activate(V2))) 8: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 11: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 12: U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) 13: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 16: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) 17: U55#(tt(),V2) -> c_23(isList#(activate(V2))) 18: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) 19: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) 20: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 21: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 22: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 23: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 24: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) 25: U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) 26: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 27: U82#(tt(),V) -> c_33(isNePal#(activate(V))) 28: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 29: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) ** Step 8.a:7: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) - Weak DPs: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {18} by application of Pre({18}) = {}. Here rules are labelled as follows: 1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 2: U12#(tt(),V) -> c_2(isNeList#(activate(V))) 3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 7: U25#(tt(),V2) -> c_8(isList#(activate(V2))) 8: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 11: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) 12: U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) 13: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) 16: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) 17: U55#(tt(),V2) -> c_23(isList#(activate(V2))) 18: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) 19: isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 20: isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 21: isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 22: isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) 23: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) 24: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) 25: U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) 26: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 27: U82#(tt(),V) -> c_33(isNePal#(activate(V))) 28: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 29: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) ** Step 8.a:8: RemoveWeakSuffixes WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) - Weak DPs: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U82#(tt(),V) -> c_33(isNePal#(activate(V))) isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: RemoveWeakSuffixes + Details: Consider the dependency graph 1:S:U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) -->_1 U12#(tt(),V) -> c_2(isNeList#(activate(V))):2 2:S:U12#(tt(),V) -> c_2(isNeList#(activate(V))) -->_1 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):21 -->_1 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):20 3:S:U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):4 4:S:U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):5 5:S:U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))):6 6:S:U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):19 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):18 -->_1 U25#(tt(),V2) -> c_8(isList#(activate(V2))):7 7:S:U25#(tt(),V2) -> c_8(isList#(activate(V2))) -->_1 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):19 -->_1 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):18 8:S:U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):9 9:S:U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):10 10:S:U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))):11 11:S:U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):19 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):18 -->_1 U45#(tt(),V2) -> c_17(isNeList#(activate(V2))):12 12:S:U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) -->_1 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):21 -->_1 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):20 13:S:U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):14 14:S:U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):15 15:S:U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))):16 16:S:U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) -->_2 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):21 -->_2 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):20 -->_1 U55#(tt(),V2) -> c_23(isList#(activate(V2))):17 17:S:U55#(tt(),V2) -> c_23(isList#(activate(V2))) -->_1 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):19 -->_1 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):18 18:S:isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) -->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):1 19:S:isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):3 20:S:isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):8 21:S:isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):13 22:W:U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) 23:W:U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) -->_1 U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))):24 24:W:U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) -->_2 isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):29 -->_1 U73#(tt(),P) -> c_30(isPalListKind#(activate(P))):25 25:W:U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) 26:W:U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) -->_1 U82#(tt(),V) -> c_33(isNePal#(activate(V))):27 27:W:U82#(tt(),V) -> c_33(isNePal#(activate(V))) -->_1 isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):28 28:W:isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) -->_1 U61#(tt(),V) -> c_25(isPalListKind#(activate(V))):22 29:W:isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) -->_1 U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):26 The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 23: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I))) 24: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P))) 25: U73#(tt(),P) -> c_30(isPalListKind#(activate(P))) 29: isPal#(V) -> c_60(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 26: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 27: U82#(tt(),V) -> c_33(isNePal#(activate(V))) 28: isNePal#(V) -> c_58(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) 22: U61#(tt(),V) -> c_25(isPalListKind#(activate(V))) ** Step 8.a:9: SimplifyRHS WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: SimplifyRHS + Details: Consider the dependency graph 1:S:U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) -->_1 U12#(tt(),V) -> c_2(isNeList#(activate(V))):2 2:S:U12#(tt(),V) -> c_2(isNeList#(activate(V))) -->_1 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):21 -->_1 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):20 3:S:U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):4 4:S:U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):5 5:S:U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))):6 6:S:U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):19 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):18 -->_1 U25#(tt(),V2) -> c_8(isList#(activate(V2))):7 7:S:U25#(tt(),V2) -> c_8(isList#(activate(V2))) -->_1 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):19 -->_1 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):18 8:S:U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):9 9:S:U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):10 10:S:U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))):11 11:S:U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) -->_2 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):19 -->_2 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):18 -->_1 U45#(tt(),V2) -> c_17(isNeList#(activate(V2))):12 12:S:U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) -->_1 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):21 -->_1 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):20 13:S:U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):14 14:S:U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))):15 15:S:U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) ,isPalListKind#(activate(V2))) -->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))):16 16:S:U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) -->_2 isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):21 -->_2 isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):20 -->_1 U55#(tt(),V2) -> c_23(isList#(activate(V2))):17 17:S:U55#(tt(),V2) -> c_23(isList#(activate(V2))) -->_1 isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):19 -->_1 isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):18 18:S:isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) -->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):1 19:S:isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):3 20:S:isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):8 21:S:isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))) -->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) ,isPalListKind#(activate(V1))):13 Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) ** Step 8.a:10: UsableRules WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) ** Step 8.a:11: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 6 + 4*x1 + 3*x2 p(U12) = 2*x1 p(U13) = 4*x1 p(U21) = 4*x2 p(U22) = 6 + 3*x2 + 4*x3 p(U23) = 7 p(U24) = 6 + x2 + 2*x3 p(U25) = 0 p(U26) = 6 p(U31) = 1 p(U32) = 2*x2 p(U33) = 4 p(U41) = 1 + 5*x1 p(U42) = x2 p(U43) = 6 + x3 p(U44) = 4 + 3*x1 + 2*x2 p(U45) = 0 p(U46) = 2 p(U51) = 1 + 2*x1 p(U52) = 2 + 4*x1 p(U53) = 5 p(U54) = 4 + 7*x1 + 5*x2 + 5*x3 p(U55) = 6 p(U56) = 2 p(U61) = 4*x2 p(U62) = 2 + x1 + x2 p(U63) = 1 + 4*x1 p(U71) = 0 p(U72) = 1 + x2 p(U73) = x2 p(U74) = 0 p(U81) = 2 + x2 p(U82) = 2 p(U83) = 1 + 2*x1 p(U91) = 2 + 5*x1 p(U92) = 4 p(__) = 6 + x1 + x2 p(a) = 2 p(activate) = x1 p(e) = 0 p(i) = 0 p(isList) = 0 p(isNeList) = 0 p(isNePal) = x1 p(isPal) = 4 + x1 p(isPalListKind) = 1 p(isQid) = 7 p(n____) = 6 + x1 + x2 p(n__a) = 2 p(n__e) = 0 p(n__i) = 0 p(n__nil) = 0 p(n__o) = 2 p(n__u) = 0 p(nil) = 0 p(o) = 2 p(tt) = 0 p(u) = 0 p(U11#) = 2*x2 p(U12#) = 2*x2 p(U13#) = 1 p(U21#) = 4 + 2*x2 + 2*x3 p(U22#) = 2*x2 + 2*x3 p(U23#) = 2*x2 + 2*x3 p(U24#) = 2*x2 + 2*x3 p(U25#) = 2*x2 p(U26#) = 0 p(U31#) = 0 p(U32#) = 1 + x1 p(U33#) = x1 p(U41#) = 5 + 2*x2 + 2*x3 p(U42#) = 2*x2 + 2*x3 p(U43#) = 2*x2 + 2*x3 p(U44#) = 2*x2 + 2*x3 p(U45#) = 2*x2 p(U46#) = 1 + 2*x1 p(U51#) = 6 + 2*x2 + 2*x3 p(U52#) = 4 + 2*x2 + 2*x3 p(U53#) = 2 + 2*x2 + 2*x3 p(U54#) = 2 + 2*x2 + 2*x3 p(U55#) = 2*x2 p(U56#) = 2 + 4*x1 p(U61#) = x2 p(U62#) = 2 p(U63#) = 1 p(U71#) = 2 + x3 p(U72#) = x1 p(U73#) = 1 + 4*x1 + x2 p(U74#) = 4*x1 p(U81#) = 4 + x1 p(U82#) = 0 p(U83#) = 0 p(U91#) = x2 p(U92#) = x1 p(__#) = x1 p(a#) = 2 p(activate#) = 1 p(e#) = 0 p(i#) = 1 p(isList#) = 2*x1 p(isNeList#) = 2*x1 p(isNePal#) = 0 p(isPal#) = x1 p(isPalListKind#) = x1 p(isQid#) = 1 p(nil#) = 4 p(o#) = 2 p(u#) = 0 p(c_1) = x1 p(c_2) = x1 p(c_3) = 0 p(c_4) = x1 p(c_5) = x1 p(c_6) = x1 p(c_7) = x1 + x2 p(c_8) = x1 p(c_9) = 1 p(c_10) = 1 p(c_11) = x2 + x3 p(c_12) = 1 p(c_13) = x1 p(c_14) = x1 p(c_15) = x1 p(c_16) = x1 + x2 p(c_17) = x1 p(c_18) = 1 p(c_19) = 1 + x1 p(c_20) = 1 + x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 4 p(c_25) = 1 p(c_26) = 2 + x2 p(c_27) = 0 p(c_28) = x2 p(c_29) = x1 + x2 p(c_30) = x1 p(c_31) = 1 p(c_32) = 0 p(c_33) = 0 p(c_34) = 4 p(c_35) = 0 p(c_36) = 2 p(c_37) = 0 p(c_38) = 0 p(c_39) = x1 p(c_40) = 1 p(c_41) = 1 p(c_42) = 4 p(c_43) = 4 p(c_44) = 1 + x1 p(c_45) = 1 p(c_46) = 2 p(c_47) = 0 p(c_48) = 1 + x1 p(c_49) = 4 p(c_50) = 4 p(c_51) = 1 p(c_52) = x1 p(c_53) = 4 + x1 p(c_54) = 0 p(c_55) = 2 + x1 p(c_56) = 5 + x1 p(c_57) = 4 + x1 p(c_58) = 1 + x1 p(c_59) = x5 p(c_60) = 0 p(c_61) = 4 p(c_62) = x2 p(c_63) = 0 p(c_64) = 1 p(c_65) = 1 p(c_66) = 0 p(c_67) = 1 p(c_68) = 4 p(c_69) = 1 p(c_70) = 0 p(c_71) = 1 p(c_72) = 0 p(c_73) = 1 p(c_74) = 0 p(c_75) = 0 p(c_76) = 4 Following rules are strictly oriented: U21#(tt(),V1,V2) = 4 + 2*V1 + 2*V2 > 2*V1 + 2*V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U41#(tt(),V1,V2) = 5 + 2*V1 + 2*V2 > 2*V1 + 2*V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U51#(tt(),V1,V2) = 6 + 2*V1 + 2*V2 > 5 + 2*V1 + 2*V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 4 + 2*V1 + 2*V2 > 3 + 2*V1 + 2*V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = 2 + 2*V1 + 2*V2 > 2*V1 + 2*V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) isList#(n____(V1,V2)) = 12 + 2*V1 + 2*V2 > 8 + 2*V1 + 2*V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 12 + 2*V1 + 2*V2 > 10 + 2*V1 + 2*V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 12 + 2*V1 + 2*V2 > 10 + 2*V1 + 2*V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = 2*V >= 2*V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) = 2*V >= 2*V = c_2(isNeList#(activate(V))) U22#(tt(),V1,V2) = 2*V1 + 2*V2 >= 2*V1 + 2*V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = 2*V1 + 2*V2 >= 2*V1 + 2*V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = 2*V1 + 2*V2 >= 2*V1 + 2*V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) = 2*V2 >= 2*V2 = c_8(isList#(activate(V2))) U42#(tt(),V1,V2) = 2*V1 + 2*V2 >= 2*V1 + 2*V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = 2*V1 + 2*V2 >= 2*V1 + 2*V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = 2*V1 + 2*V2 >= 2*V1 + 2*V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) = 2*V2 >= 2*V2 = c_17(isNeList#(activate(V2))) U53#(tt(),V1,V2) = 2 + 2*V1 + 2*V2 >= 2 + 2*V1 + 2*V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U55#(tt(),V2) = 2*V2 >= 2*V2 = c_23(isList#(activate(V2))) isList#(V) = 2*V >= 2*V = c_52(U11#(isPalListKind(activate(V)),activate(V))) __(X,nil()) = 6 + X >= X = X __(X1,X2) = 6 + X1 + X2 >= 6 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 12 + X + Y + Z >= 12 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 6 + X >= X = X a() = 2 >= 2 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 6 + X1 + X2 >= 6 + X1 + X2 = __(X1,X2) activate(n__a()) = 2 >= 2 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__nil()) = 0 >= 0 = nil() activate(n__o()) = 2 >= 2 = o() activate(n__u()) = 0 >= 0 = u() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() nil() = 0 >= 0 = n__nil() o() = 2 >= 2 = n__o() u() = 0 >= 0 = n__u() ** Step 8.a:12: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) - Weak DPs: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 2*x1 p(U12) = 4 p(U13) = 0 p(U21) = 4 + 4*x1 + 2*x3 p(U22) = 4*x1 p(U23) = 2 + x1 p(U24) = 0 p(U25) = 4 + 4*x1 p(U26) = 0 p(U31) = 1 p(U32) = 2 p(U33) = 5 p(U41) = 5 p(U42) = 4 + x1 + x2 p(U43) = 1 + 4*x1 + 5*x2 + 6*x3 p(U44) = 0 p(U45) = 2 p(U46) = 0 p(U51) = 0 p(U52) = 6*x2 p(U53) = 4*x2 p(U54) = 0 p(U55) = 0 p(U56) = 1 p(U61) = 4*x1 + x2 p(U62) = 2*x1 p(U63) = 0 p(U71) = 1 + x2 + 4*x3 p(U72) = 0 p(U73) = 2 + 4*x2 p(U74) = 4 p(U81) = 1 + x1 p(U82) = x2 p(U83) = 1 p(U91) = x1 + 6*x2 p(U92) = 2 p(__) = 1 + x1 + x2 p(a) = 0 p(activate) = x1 p(e) = 6 p(i) = 2 p(isList) = 0 p(isNeList) = 0 p(isNePal) = 0 p(isPal) = 2 + x1 p(isPalListKind) = 0 p(isQid) = 0 p(n____) = 1 + x1 + x2 p(n__a) = 0 p(n__e) = 6 p(n__i) = 2 p(n__nil) = 0 p(n__o) = 0 p(n__u) = 0 p(nil) = 0 p(o) = 0 p(tt) = 0 p(u) = 0 p(U11#) = 4*x2 p(U12#) = 4*x2 p(U13#) = x1 p(U21#) = 1 + 4*x2 + 4*x3 p(U22#) = 1 + 4*x2 + 4*x3 p(U23#) = 1 + 4*x2 + 4*x3 p(U24#) = 1 + 4*x2 + 4*x3 p(U25#) = 1 + 4*x2 p(U26#) = x1 p(U31#) = 0 p(U32#) = 1 + x2 p(U33#) = 0 p(U41#) = 4 + 4*x2 + 4*x3 p(U42#) = 4 + 4*x2 + 4*x3 p(U43#) = 4 + 4*x2 + 4*x3 p(U44#) = 4 + 4*x2 + 4*x3 p(U45#) = 4 + 4*x2 p(U46#) = 1 p(U51#) = 4*x2 + 4*x3 p(U52#) = 4*x2 + 4*x3 p(U53#) = 4*x2 + 4*x3 p(U54#) = 4*x2 + 4*x3 p(U55#) = 4*x2 p(U56#) = 2 p(U61#) = 4*x2 p(U62#) = 1 + 2*x1 + 4*x2 p(U63#) = 1 p(U71#) = 2 p(U72#) = 1 + 4*x2 p(U73#) = 4*x1 p(U74#) = 4 p(U81#) = 0 p(U82#) = x2 p(U83#) = 2 p(U91#) = 1 + x1 p(U92#) = 2 + x1 p(__#) = 1 + x2 p(a#) = 1 p(activate#) = 0 p(e#) = 1 p(i#) = 1 p(isList#) = 4*x1 p(isNeList#) = 4*x1 p(isNePal#) = 2 p(isPal#) = 1 + x1 p(isPalListKind#) = 4 + x1 p(isQid#) = x1 p(nil#) = 0 p(o#) = 1 p(u#) = 2 p(c_1) = x1 p(c_2) = x1 p(c_3) = 4 p(c_4) = x1 p(c_5) = x1 p(c_6) = x1 p(c_7) = x1 + x2 p(c_8) = x1 p(c_9) = 4 p(c_10) = 1 p(c_11) = 1 + x3 p(c_12) = 1 p(c_13) = x1 p(c_14) = x1 p(c_15) = x1 p(c_16) = x1 + x2 p(c_17) = 2 + x1 p(c_18) = 1 p(c_19) = x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 0 p(c_25) = 0 p(c_26) = 0 p(c_27) = 4 p(c_28) = 1 + x1 + x2 p(c_29) = x1 + x2 p(c_30) = 1 p(c_31) = 4 p(c_32) = 2 + x1 + x2 p(c_33) = 1 p(c_34) = 4 p(c_35) = 1 p(c_36) = 1 p(c_37) = 0 p(c_38) = 4 p(c_39) = 4 + x2 p(c_40) = 1 p(c_41) = 4 p(c_42) = 4 p(c_43) = 2 + x1 p(c_44) = 2 p(c_45) = 1 + x1 p(c_46) = 4 p(c_47) = 1 p(c_48) = 2 + x1 p(c_49) = 0 p(c_50) = 0 p(c_51) = 0 p(c_52) = x1 p(c_53) = x1 p(c_54) = 0 p(c_55) = 0 p(c_56) = x1 p(c_57) = x1 p(c_58) = 2 + x2 p(c_59) = 1 + x3 p(c_60) = 4 + x1 p(c_61) = 1 p(c_62) = x2 p(c_63) = 4 p(c_64) = 4 p(c_65) = 0 p(c_66) = 1 p(c_67) = 4 p(c_68) = 1 p(c_69) = 0 p(c_70) = 1 p(c_71) = 1 p(c_72) = 0 p(c_73) = 1 p(c_74) = 1 p(c_75) = 0 p(c_76) = 1 Following rules are strictly oriented: U25#(tt(),V2) = 1 + 4*V2 > 4*V2 = c_8(isList#(activate(V2))) U45#(tt(),V2) = 4 + 4*V2 > 2 + 4*V2 = c_17(isNeList#(activate(V2))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = 4*V >= 4*V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) = 4*V >= 4*V = c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) = 1 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) = 1 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = 1 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = 1 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U41#(tt(),V1,V2) = 4 + 4*V1 + 4*V2 >= 4 + 4*V1 + 4*V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) = 4 + 4*V1 + 4*V2 >= 4 + 4*V1 + 4*V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = 4 + 4*V1 + 4*V2 >= 4 + 4*V1 + 4*V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = 4 + 4*V1 + 4*V2 >= 4 + 4*V1 + 4*V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U51#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) = 4*V2 >= 4*V2 = c_23(isList#(activate(V2))) isList#(V) = 4*V >= 4*V = c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) = 4 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + 4*V1 + 4*V2 >= 4 + 4*V1 + 4*V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 1 + X >= X = X __(X1,X2) = 1 + X1 + X2 >= 1 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 2 + X + Y + Z >= 2 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 1 + X >= X = X a() = 0 >= 0 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 1 + X1 + X2 >= 1 + X1 + X2 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 6 >= 6 = e() activate(n__i()) = 2 >= 2 = i() activate(n__nil()) = 0 >= 0 = nil() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() e() = 6 >= 6 = n__e() i() = 2 >= 2 = n__i() nil() = 0 >= 0 = n__nil() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() ** Step 8.a:13: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) - Weak DPs: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 5 p(U12) = 3 p(U13) = 2*x1 p(U21) = 2 + x2 p(U22) = 3 p(U23) = 4*x3 p(U24) = 0 p(U25) = 1 + 2*x1 + 4*x2 p(U26) = 4 + x1 p(U31) = 1 p(U32) = 0 p(U33) = 1 p(U41) = 6*x3 p(U42) = 1 + 3*x2 + 6*x3 p(U43) = 4 + x1 + x2 p(U44) = 4 + x2 + 2*x3 p(U45) = 1 + 2*x1 p(U46) = 2*x1 p(U51) = 4 + x1 p(U52) = 4*x3 p(U53) = 2*x1 + 4*x3 p(U54) = 3*x1 + 5*x2 p(U55) = 0 p(U56) = 0 p(U61) = 1 + x1 p(U62) = 1 + x2 p(U63) = 0 p(U71) = 4*x1 + 2*x3 p(U72) = 1 + 4*x2 p(U73) = 0 p(U74) = 1 p(U81) = 1 p(U82) = 2*x2 p(U83) = 0 p(U91) = 6 p(U92) = 0 p(__) = 4 + x1 + x2 p(a) = 0 p(activate) = x1 p(e) = 0 p(i) = 0 p(isList) = 2 p(isNeList) = 0 p(isNePal) = x1 p(isPal) = 0 p(isPalListKind) = 0 p(isQid) = 0 p(n____) = 4 + x1 + x2 p(n__a) = 0 p(n__e) = 0 p(n__i) = 0 p(n__nil) = 4 p(n__o) = 1 p(n__u) = 1 p(nil) = 4 p(o) = 1 p(tt) = 4 p(u) = 1 p(U11#) = x2 p(U12#) = x2 p(U13#) = 1 p(U21#) = 4 + x2 + x3 p(U22#) = 2 + x2 + x3 p(U23#) = 2 + x2 + x3 p(U24#) = x2 + x3 p(U25#) = x2 p(U26#) = 0 p(U31#) = 1 + x1 + x2 p(U32#) = x1 p(U33#) = 4 + x1 p(U41#) = x2 + x3 p(U42#) = x2 + x3 p(U43#) = x2 + x3 p(U44#) = x2 + x3 p(U45#) = x2 p(U46#) = 2 p(U51#) = 4 + x2 + x3 p(U52#) = 1 + x2 + x3 p(U53#) = 1 + x2 + x3 p(U54#) = 1 + x2 + x3 p(U55#) = x2 p(U56#) = 2*x1 p(U61#) = 4 p(U62#) = 2*x1 p(U63#) = 4 p(U71#) = 4 + x1 + x2 + 2*x3 p(U72#) = 2 + x2 p(U73#) = 0 p(U74#) = 4 p(U81#) = 1 + x1 + 2*x2 p(U82#) = 2 + 4*x1 + 4*x2 p(U83#) = 2 + 2*x1 p(U91#) = 1 + x1 + 4*x2 p(U92#) = 4 + x1 p(__#) = 2 p(a#) = 2 p(activate#) = 1 + 2*x1 p(e#) = 1 p(i#) = 1 p(isList#) = x1 p(isNeList#) = x1 p(isNePal#) = 2*x1 p(isPal#) = 1 p(isPalListKind#) = 1 p(isQid#) = x1 p(nil#) = 1 p(o#) = 0 p(u#) = 1 p(c_1) = x1 p(c_2) = x1 p(c_3) = 0 p(c_4) = x1 p(c_5) = x1 p(c_6) = x1 p(c_7) = x1 + x2 p(c_8) = x1 p(c_9) = 4 p(c_10) = x1 p(c_11) = 4 p(c_12) = 1 p(c_13) = x1 p(c_14) = x1 p(c_15) = x1 p(c_16) = x1 + x2 p(c_17) = x1 p(c_18) = 4 p(c_19) = x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = 1 + x1 + x2 p(c_23) = x1 p(c_24) = 4 p(c_25) = x1 p(c_26) = 1 + x1 + x3 p(c_27) = 0 p(c_28) = 2 p(c_29) = 2 + x2 p(c_30) = 4 + x1 p(c_31) = 1 p(c_32) = 0 p(c_33) = x1 p(c_34) = 1 p(c_35) = 0 p(c_36) = 1 p(c_37) = 2 p(c_38) = 0 p(c_39) = 0 p(c_40) = 1 p(c_41) = 1 p(c_42) = 0 p(c_43) = 2 p(c_44) = 1 + x1 p(c_45) = 1 p(c_46) = 0 p(c_47) = x1 p(c_48) = 1 + x1 p(c_49) = 1 p(c_50) = 2 p(c_51) = 1 p(c_52) = x1 p(c_53) = x1 p(c_54) = 0 p(c_55) = 1 + x1 p(c_56) = x1 p(c_57) = x1 p(c_58) = x1 + x2 p(c_59) = x4 p(c_60) = 1 + x2 p(c_61) = 1 p(c_62) = x1 p(c_63) = 0 p(c_64) = 1 p(c_65) = 0 p(c_66) = 1 p(c_67) = 4 p(c_68) = 0 p(c_69) = 2 p(c_70) = 0 p(c_71) = 2 p(c_72) = 1 p(c_73) = 0 p(c_74) = 0 p(c_75) = 0 p(c_76) = 2 Following rules are strictly oriented: U23#(tt(),V1,V2) = 2 + V1 + V2 > V1 + V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = V >= V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) = V >= V = c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) = 4 + V1 + V2 >= 2 + V1 + V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) = 2 + V1 + V2 >= 2 + V1 + V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) = V2 >= V2 = c_8(isList#(activate(V2))) U41#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) = V2 >= V2 = c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) = 4 + V1 + V2 >= 1 + V1 + V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) = V2 >= V2 = c_23(isList#(activate(V2))) isList#(V) = V >= V = c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) = 4 + V1 + V2 >= 4 + V1 + V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + V1 + V2 >= V1 + V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + V1 + V2 >= 4 + V1 + V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 8 + X >= X = X __(X1,X2) = 4 + X1 + X2 >= 4 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 8 + X + Y + Z >= 8 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 8 + X >= X = X a() = 0 >= 0 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 4 + X1 + X2 >= 4 + X1 + X2 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__nil()) = 4 >= 4 = nil() activate(n__o()) = 1 >= 1 = o() activate(n__u()) = 1 >= 1 = u() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() nil() = 4 >= 4 = n__nil() o() = 1 >= 1 = n__o() u() = 1 >= 1 = n__u() ** Step 8.a:14: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) - Weak DPs: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 6 + 4*x1 + 2*x2 p(U12) = 4*x1 + 4*x2 p(U13) = 3 p(U21) = 4*x1 + 4*x2 p(U22) = 6 p(U23) = 5 + 2*x2 + x3 p(U24) = 0 p(U25) = 2 p(U26) = 2 + x1 p(U31) = 1 + x2 p(U32) = 2 p(U33) = 1 + x1 p(U41) = 4 p(U42) = 0 p(U43) = 0 p(U44) = 0 p(U45) = 0 p(U46) = 0 p(U51) = 2 p(U52) = 3 + x2 p(U53) = 3 + x1 + 7*x3 p(U54) = 5 + 2*x1 + 2*x2 + 2*x3 p(U55) = 6 p(U56) = 3 + 2*x1 p(U61) = 0 p(U62) = 4*x1 p(U63) = x1 p(U71) = 1 + x1 p(U72) = 2 + 4*x1 p(U73) = 0 p(U74) = 1 p(U81) = 1 + x1 + x2 p(U82) = 4*x1 + 2*x2 p(U83) = 1 p(U91) = 2 + 3*x1 p(U92) = x1 p(__) = 4 + x1 + x2 p(a) = 0 p(activate) = x1 p(e) = 0 p(i) = 0 p(isList) = 0 p(isNeList) = 0 p(isNePal) = 4 + x1 p(isPal) = 1 p(isPalListKind) = 2*x1 p(isQid) = 4 + 6*x1 p(n____) = 4 + x1 + x2 p(n__a) = 0 p(n__e) = 0 p(n__i) = 0 p(n__nil) = 0 p(n__o) = 0 p(n__u) = 0 p(nil) = 0 p(o) = 0 p(tt) = 0 p(u) = 0 p(U11#) = x2 p(U12#) = x2 p(U13#) = 2 + x1 p(U21#) = 4 + x2 + x3 p(U22#) = 4 + x2 + x3 p(U23#) = 2 + x2 + x3 p(U24#) = x2 + x3 p(U25#) = x2 p(U26#) = 0 p(U31#) = 1 + x1 + x2 p(U32#) = 4*x2 p(U33#) = 0 p(U41#) = x2 + x3 p(U42#) = x2 + x3 p(U43#) = x2 + x3 p(U44#) = x2 + x3 p(U45#) = x2 p(U46#) = 4 p(U51#) = 1 + x2 + x3 p(U52#) = 1 + x2 + x3 p(U53#) = 1 + x2 + x3 p(U54#) = 1 + x2 + x3 p(U55#) = 1 + x2 p(U56#) = 2 p(U61#) = x1 p(U62#) = 1 + 2*x2 p(U63#) = 4 p(U71#) = 1 + 2*x3 p(U72#) = 2 + x1 + x2 p(U73#) = 1 + x1 p(U74#) = 1 p(U81#) = 2 + 4*x2 p(U82#) = 1 + 2*x2 p(U83#) = 0 p(U91#) = 0 p(U92#) = 2 + 2*x1 p(__#) = x2 p(a#) = 0 p(activate#) = 1 + x1 p(e#) = 0 p(i#) = 0 p(isList#) = x1 p(isNeList#) = x1 p(isNePal#) = 1 + x1 p(isPal#) = 0 p(isPalListKind#) = 0 p(isQid#) = 1 p(nil#) = 1 p(o#) = 0 p(u#) = 4 p(c_1) = x1 p(c_2) = x1 p(c_3) = 0 p(c_4) = x1 p(c_5) = x1 p(c_6) = x1 p(c_7) = x1 + x2 p(c_8) = x1 p(c_9) = 2 p(c_10) = 1 p(c_11) = 0 p(c_12) = 1 p(c_13) = x1 p(c_14) = x1 p(c_15) = x1 p(c_16) = x1 + x2 p(c_17) = x1 p(c_18) = 4 p(c_19) = x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 0 p(c_25) = 4 p(c_26) = x2 p(c_27) = 4 p(c_28) = 1 + x2 p(c_29) = x2 p(c_30) = 4 p(c_31) = 2 p(c_32) = 1 + x1 + x2 p(c_33) = 0 p(c_34) = 1 p(c_35) = 1 p(c_36) = 0 p(c_37) = 0 p(c_38) = 4 p(c_39) = 1 p(c_40) = 0 p(c_41) = 1 p(c_42) = 2 p(c_43) = 1 + x1 p(c_44) = 4 + x1 p(c_45) = 2 + x1 p(c_46) = 4 + x1 p(c_47) = x1 p(c_48) = 0 p(c_49) = 2 p(c_50) = 0 p(c_51) = 4 p(c_52) = x1 p(c_53) = x1 p(c_54) = 4 p(c_55) = 0 p(c_56) = 4 + x1 p(c_57) = 3 + x1 p(c_58) = 2 + x2 p(c_59) = 1 + x4 p(c_60) = 0 p(c_61) = 1 p(c_62) = x2 p(c_63) = 1 p(c_64) = 1 p(c_65) = 1 p(c_66) = 0 p(c_67) = 0 p(c_68) = 0 p(c_69) = 0 p(c_70) = 1 p(c_71) = 1 p(c_72) = 0 p(c_73) = 1 p(c_74) = 0 p(c_75) = 2 p(c_76) = 0 Following rules are strictly oriented: U22#(tt(),V1,V2) = 4 + V1 + V2 > 2 + V1 + V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U55#(tt(),V2) = 1 + V2 > V2 = c_23(isList#(activate(V2))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = V >= V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) = V >= V = c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) = 4 + V1 + V2 >= 4 + V1 + V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = 2 + V1 + V2 >= V1 + V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) = V2 >= V2 = c_8(isList#(activate(V2))) U41#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) = V2 >= V2 = c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) isList#(V) = V >= V = c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) = 4 + V1 + V2 >= 4 + V1 + V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + V1 + V2 >= 4 + V1 + V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + V1 + V2 >= 4 + V1 + V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 4 + X >= X = X __(X1,X2) = 4 + X1 + X2 >= 4 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 8 + X + Y + Z >= 8 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 4 + X >= X = X a() = 0 >= 0 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 4 + X1 + X2 >= 4 + X1 + X2 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__nil()) = 0 >= 0 = nil() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() nil() = 0 >= 0 = n__nil() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() ** Step 8.a:15: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) - Weak DPs: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 3*x1 + 7*x2 p(U12) = 0 p(U13) = 2 + x1 p(U21) = 2 + x2 p(U22) = x2 + 4*x3 p(U23) = 2 + 2*x1 p(U24) = 2 + x1 + 2*x2 p(U25) = 1 + x1 p(U26) = 7 + x1 p(U31) = 3 + 4*x1 p(U32) = 0 p(U33) = 4 p(U41) = 1 p(U42) = 0 p(U43) = 5*x2 + x3 p(U44) = 2 + x1 + x3 p(U45) = 2*x2 p(U46) = 4 p(U51) = 5 + x1 + 6*x2 + 2*x3 p(U52) = 2 + 4*x1 p(U53) = 1 + 6*x3 p(U54) = 2 + 6*x2 + 4*x3 p(U55) = 3 p(U56) = 4 + x1 p(U61) = x2 p(U62) = 1 + x1 + 4*x2 p(U63) = 1 + 4*x1 p(U71) = 1 + 2*x2 p(U72) = 0 p(U73) = 4 + x2 p(U74) = 0 p(U81) = 1 + x1 p(U82) = 2 + 4*x1 + x2 p(U83) = 1 + x1 p(U91) = 1 + 5*x1 + 2*x2 p(U92) = 0 p(__) = 1 + x1 + x2 p(a) = 0 p(activate) = x1 p(e) = 1 p(i) = 0 p(isList) = 4 p(isNeList) = x1 p(isNePal) = 4 p(isPal) = 2 p(isPalListKind) = 1 p(isQid) = 2 p(n____) = 1 + x1 + x2 p(n__a) = 0 p(n__e) = 1 p(n__i) = 0 p(n__nil) = 0 p(n__o) = 0 p(n__u) = 0 p(nil) = 0 p(o) = 0 p(tt) = 0 p(u) = 0 p(U11#) = x2 p(U12#) = x2 p(U13#) = 0 p(U21#) = 1 + x2 + x3 p(U22#) = 1 + x2 + x3 p(U23#) = 1 + x2 + x3 p(U24#) = 1 + x2 + x3 p(U25#) = x2 p(U26#) = 2 p(U31#) = 1 + x1 p(U32#) = 1 + 4*x1 p(U33#) = 1 p(U41#) = 1 + x2 + x3 p(U42#) = 1 + x2 + x3 p(U43#) = 1 + x2 + x3 p(U44#) = 1 + x2 + x3 p(U45#) = 1 + x2 p(U46#) = x1 p(U51#) = 1 + x2 + x3 p(U52#) = x2 + x3 p(U53#) = x2 + x3 p(U54#) = x2 + x3 p(U55#) = x2 p(U56#) = 0 p(U61#) = 2*x2 p(U62#) = 4 + 4*x2 p(U63#) = 4 + x1 p(U71#) = 1 + x2 p(U72#) = 4 p(U73#) = x2 p(U74#) = 1 + 2*x1 p(U81#) = 1 + 4*x2 p(U82#) = 0 p(U83#) = 0 p(U91#) = 1 + x1 p(U92#) = 2*x1 p(__#) = 0 p(a#) = 1 p(activate#) = 0 p(e#) = 1 p(i#) = 4 p(isList#) = x1 p(isNeList#) = x1 p(isNePal#) = x1 p(isPal#) = 0 p(isPalListKind#) = 0 p(isQid#) = 1 + x1 p(nil#) = 0 p(o#) = 0 p(u#) = 2 p(c_1) = x1 p(c_2) = x1 p(c_3) = 4 p(c_4) = x1 p(c_5) = x1 p(c_6) = x1 p(c_7) = x1 + x2 p(c_8) = x1 p(c_9) = 1 p(c_10) = 4 p(c_11) = x2 p(c_12) = 0 p(c_13) = x1 p(c_14) = x1 p(c_15) = x1 p(c_16) = x1 + x2 p(c_17) = 1 + x1 p(c_18) = 0 p(c_19) = 1 + x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 0 p(c_25) = x1 p(c_26) = 1 + x3 p(c_27) = 0 p(c_28) = 1 p(c_29) = x1 p(c_30) = 4 p(c_31) = 1 p(c_32) = 1 + x1 p(c_33) = 4 p(c_34) = 0 p(c_35) = 1 p(c_36) = 2 p(c_37) = 0 p(c_38) = 1 p(c_39) = 0 p(c_40) = 0 p(c_41) = 1 p(c_42) = 0 p(c_43) = x1 p(c_44) = 0 p(c_45) = x1 p(c_46) = 2 p(c_47) = 1 p(c_48) = 2 p(c_49) = 4 p(c_50) = 4 p(c_51) = 0 p(c_52) = x1 p(c_53) = x1 p(c_54) = 1 p(c_55) = 1 p(c_56) = x1 p(c_57) = x1 p(c_58) = 0 p(c_59) = 1 + x1 + x4 p(c_60) = x1 p(c_61) = 4 p(c_62) = 4 p(c_63) = 0 p(c_64) = 2 p(c_65) = 0 p(c_66) = 4 p(c_67) = 0 p(c_68) = 0 p(c_69) = 1 p(c_70) = 1 p(c_71) = 0 p(c_72) = 4 p(c_73) = 4 p(c_74) = 1 p(c_75) = 0 p(c_76) = 0 Following rules are strictly oriented: U24#(tt(),V1,V2) = 1 + V1 + V2 > V1 + V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = V >= V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) = V >= V = c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U25#(tt(),V2) = V2 >= V2 = c_8(isList#(activate(V2))) U41#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) = 1 + V2 >= 1 + V2 = c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) = V2 >= V2 = c_23(isList#(activate(V2))) isList#(V) = V >= V = c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) = 1 + V1 + V2 >= 1 + V1 + V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 1 + V1 + V2 >= 1 + V1 + V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 1 + V1 + V2 >= 1 + V1 + V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 1 + X >= X = X __(X1,X2) = 1 + X1 + X2 >= 1 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 2 + X + Y + Z >= 2 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 1 + X >= X = X a() = 0 >= 0 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 1 + X1 + X2 >= 1 + X1 + X2 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 1 >= 1 = e() activate(n__i()) = 0 >= 0 = i() activate(n__nil()) = 0 >= 0 = nil() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() e() = 1 >= 1 = n__e() i() = 0 >= 0 = n__i() nil() = 0 >= 0 = n__nil() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() ** Step 8.a:16: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) - Weak DPs: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 2*x2 p(U12) = 3 + x1 + x2 p(U13) = 1 + 5*x1 p(U21) = 6 + 4*x2 p(U22) = 1 + x2 p(U23) = x2 p(U24) = 2*x1 + x2 + 7*x3 p(U25) = 1 + 2*x1 + 4*x2 p(U26) = 2 + 4*x1 p(U31) = 0 p(U32) = x1 + 4*x2 p(U33) = 6 + 2*x1 p(U41) = x1 + 4*x2 + 6*x3 p(U42) = x1 + 6*x2 p(U43) = x2 p(U44) = 5 + x1 p(U45) = 4 p(U46) = 4 p(U51) = 0 p(U52) = 2 + 2*x3 p(U53) = 5*x2 p(U54) = 3 + x1 p(U55) = 6 + 3*x2 p(U56) = 0 p(U61) = 4 + x1 + x2 p(U62) = 1 p(U63) = 4 + 2*x1 p(U71) = 1 + x3 p(U72) = 4*x1 p(U73) = x2 p(U74) = 2*x1 p(U81) = 1 + x1 + 2*x2 p(U82) = 2 + x1 + 2*x2 p(U83) = 1 + x1 p(U91) = 1 + x1 p(U92) = 0 p(__) = 4 + x1 + x2 p(a) = 1 p(activate) = x1 p(e) = 0 p(i) = 0 p(isList) = 0 p(isNeList) = 2 p(isNePal) = 0 p(isPal) = 2 p(isPalListKind) = 0 p(isQid) = 2*x1 p(n____) = 4 + x1 + x2 p(n__a) = 1 p(n__e) = 0 p(n__i) = 0 p(n__nil) = 0 p(n__o) = 2 p(n__u) = 2 p(nil) = 0 p(o) = 2 p(tt) = 0 p(u) = 2 p(U11#) = x2 p(U12#) = x2 p(U13#) = 0 p(U21#) = 1 + x2 + x3 p(U22#) = 1 + x2 + x3 p(U23#) = 1 + x2 + x3 p(U24#) = x2 + x3 p(U25#) = x2 p(U26#) = 0 p(U31#) = 1 + x2 p(U32#) = 1 p(U33#) = 0 p(U41#) = 3 + x2 + x3 p(U42#) = 2 + x2 + x3 p(U43#) = 2 + x2 + x3 p(U44#) = 2 + x2 + x3 p(U45#) = x2 p(U46#) = 4 p(U51#) = 4 + x2 + x3 p(U52#) = 4 + x2 + x3 p(U53#) = 4 + x2 + x3 p(U54#) = x2 + x3 p(U55#) = x2 p(U56#) = x1 p(U61#) = x1 p(U62#) = 2*x2 p(U63#) = 1 p(U71#) = 0 p(U72#) = x1 p(U73#) = 0 p(U74#) = 4 p(U81#) = 2*x1 p(U82#) = 1 p(U83#) = 0 p(U91#) = 1 p(U92#) = x1 p(__#) = 4*x2 p(a#) = 1 p(activate#) = 4 + 4*x1 p(e#) = 1 p(i#) = 0 p(isList#) = x1 p(isNeList#) = x1 p(isNePal#) = 2 p(isPal#) = 2 p(isPalListKind#) = 0 p(isQid#) = 1 p(nil#) = 1 p(o#) = 1 p(u#) = 0 p(c_1) = x1 p(c_2) = x1 p(c_3) = 0 p(c_4) = x1 p(c_5) = x1 p(c_6) = 1 + x1 p(c_7) = x1 + x2 p(c_8) = x1 p(c_9) = 2 p(c_10) = 1 p(c_11) = 1 + x1 p(c_12) = 0 p(c_13) = x1 p(c_14) = x1 p(c_15) = x1 p(c_16) = 2 + x1 + x2 p(c_17) = x1 p(c_18) = 0 p(c_19) = x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 1 p(c_25) = 4 p(c_26) = x1 + x3 p(c_27) = 1 p(c_28) = 0 p(c_29) = 1 p(c_30) = x1 p(c_31) = 0 p(c_32) = 1 p(c_33) = 0 p(c_34) = 0 p(c_35) = 1 p(c_36) = 0 p(c_37) = 1 p(c_38) = 0 p(c_39) = 1 p(c_40) = 1 p(c_41) = 0 p(c_42) = 1 p(c_43) = 4 p(c_44) = 4 + x1 p(c_45) = 1 p(c_46) = x1 p(c_47) = 4 + x1 p(c_48) = x1 p(c_49) = 1 p(c_50) = 0 p(c_51) = 1 p(c_52) = x1 p(c_53) = 1 + x1 p(c_54) = 0 p(c_55) = 0 p(c_56) = x1 p(c_57) = x1 p(c_58) = 1 p(c_59) = x2 + x3 + x5 p(c_60) = 1 p(c_61) = 1 p(c_62) = 1 + x2 p(c_63) = 0 p(c_64) = 4 p(c_65) = 0 p(c_66) = 0 p(c_67) = 2 p(c_68) = 1 p(c_69) = 0 p(c_70) = 0 p(c_71) = 4 p(c_72) = 0 p(c_73) = 1 p(c_74) = 2 p(c_75) = 1 p(c_76) = 1 Following rules are strictly oriented: U53#(tt(),V1,V2) = 4 + V1 + V2 > V1 + V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = V >= V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) = V >= V = c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) = V2 >= V2 = c_8(isList#(activate(V2))) U41#(tt(),V1,V2) = 3 + V1 + V2 >= 2 + V1 + V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) = 2 + V1 + V2 >= 2 + V1 + V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = 2 + V1 + V2 >= 2 + V1 + V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = 2 + V1 + V2 >= 2 + V1 + V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) = V2 >= V2 = c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) = 4 + V1 + V2 >= 4 + V1 + V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 4 + V1 + V2 >= 4 + V1 + V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) = V2 >= V2 = c_23(isList#(activate(V2))) isList#(V) = V >= V = c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) = 4 + V1 + V2 >= 2 + V1 + V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + V1 + V2 >= 3 + V1 + V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + V1 + V2 >= 4 + V1 + V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 4 + X >= X = X __(X1,X2) = 4 + X1 + X2 >= 4 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 8 + X + Y + Z >= 8 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 4 + X >= X = X a() = 1 >= 1 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 4 + X1 + X2 >= 4 + X1 + X2 = __(X1,X2) activate(n__a()) = 1 >= 1 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__nil()) = 0 >= 0 = nil() activate(n__o()) = 2 >= 2 = o() activate(n__u()) = 2 >= 2 = u() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() nil() = 0 >= 0 = n__nil() o() = 2 >= 2 = n__o() u() = 2 >= 2 = n__u() ** Step 8.a:17: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) - Weak DPs: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = x1 p(U12) = 1 + x1 p(U13) = 1 p(U21) = 4 + x3 p(U22) = 6 + 4*x1 + 3*x2 + 5*x3 p(U23) = 1 + 4*x2 + 2*x3 p(U24) = 0 p(U25) = x1 p(U26) = 1 + 4*x1 p(U31) = 0 p(U32) = 0 p(U33) = 2 + 3*x1 p(U41) = 6 + x1 + 4*x2 + x3 p(U42) = 5 + 5*x2 p(U43) = 6 + 4*x1 p(U44) = 4*x2 p(U45) = x1 p(U46) = 0 p(U51) = 4*x1 + 4*x3 p(U52) = 6 + 4*x2 + x3 p(U53) = 3 + 2*x1 + 5*x2 p(U54) = 5 + 7*x2 + 4*x3 p(U55) = x1 p(U56) = 2*x1 p(U61) = 1 + x2 p(U62) = x2 p(U63) = 4 + 2*x1 p(U71) = x1 p(U72) = 0 p(U73) = 4 p(U74) = 4 p(U81) = 4*x1 p(U82) = x1 p(U83) = x1 p(U91) = 1 + x1 + 6*x2 p(U92) = 2 + 4*x1 p(__) = 2 + x1 + x2 p(a) = 0 p(activate) = x1 p(e) = 0 p(i) = 7 p(isList) = 0 p(isNeList) = 6*x1 p(isNePal) = 1 + 2*x1 p(isPal) = 4 p(isPalListKind) = 0 p(isQid) = 4 p(n____) = 2 + x1 + x2 p(n__a) = 0 p(n__e) = 0 p(n__i) = 7 p(n__nil) = 1 p(n__o) = 2 p(n__u) = 0 p(nil) = 1 p(o) = 2 p(tt) = 0 p(u) = 0 p(U11#) = 4*x2 p(U12#) = 4*x2 p(U13#) = 0 p(U21#) = 7 + 4*x2 + 4*x3 p(U22#) = 7 + 4*x2 + 4*x3 p(U23#) = 7 + 4*x2 + 4*x3 p(U24#) = 7 + 4*x2 + 4*x3 p(U25#) = 2 + 4*x2 p(U26#) = 1 + 2*x1 p(U31#) = 0 p(U32#) = 1 p(U33#) = 0 p(U41#) = 1 + 4*x2 + 4*x3 p(U42#) = 1 + 4*x2 + 4*x3 p(U43#) = 4*x2 + 4*x3 p(U44#) = 4*x2 + 4*x3 p(U45#) = 4*x2 p(U46#) = 1 p(U51#) = 4*x2 + 4*x3 p(U52#) = 4*x2 + 4*x3 p(U53#) = 4*x2 + 4*x3 p(U54#) = 4*x2 + 4*x3 p(U55#) = 4*x2 p(U56#) = 1 + x1 p(U61#) = 0 p(U62#) = 1 + x1 + 4*x2 p(U63#) = 2*x1 p(U71#) = 1 p(U72#) = 4*x2 p(U73#) = 0 p(U74#) = 1 p(U81#) = 2*x1 + 2*x2 p(U82#) = x2 p(U83#) = 4*x1 p(U91#) = 4 + 4*x2 p(U92#) = 2 p(__#) = 1 + x1 p(a#) = 1 p(activate#) = 0 p(e#) = 2 p(i#) = 1 p(isList#) = 4*x1 p(isNeList#) = 4*x1 p(isNePal#) = 4 p(isPal#) = 2 + 4*x1 p(isPalListKind#) = 1 + 2*x1 p(isQid#) = 1 p(nil#) = 0 p(o#) = 0 p(u#) = 4 p(c_1) = x1 p(c_2) = x1 p(c_3) = 0 p(c_4) = x1 p(c_5) = x1 p(c_6) = x1 p(c_7) = 4 + x1 + x2 p(c_8) = x1 p(c_9) = 1 p(c_10) = 1 p(c_11) = 1 + x3 p(c_12) = 1 p(c_13) = x1 p(c_14) = x1 p(c_15) = x1 p(c_16) = x1 + x2 p(c_17) = x1 p(c_18) = 1 p(c_19) = x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 1 p(c_25) = 2 + x1 p(c_26) = 4 p(c_27) = 1 p(c_28) = 1 p(c_29) = 2 + x1 + x2 p(c_30) = 0 p(c_31) = 4 p(c_32) = 0 p(c_33) = 1 p(c_34) = 1 p(c_35) = 0 p(c_36) = 1 p(c_37) = 0 p(c_38) = 0 p(c_39) = 4 p(c_40) = 4 p(c_41) = 1 p(c_42) = 1 p(c_43) = 2 p(c_44) = 0 p(c_45) = 4 p(c_46) = 0 p(c_47) = 1 + x1 p(c_48) = x1 p(c_49) = 1 p(c_50) = 4 p(c_51) = 1 p(c_52) = x1 p(c_53) = 1 + x1 p(c_54) = 0 p(c_55) = x2 p(c_56) = 7 + x1 p(c_57) = x1 p(c_58) = 1 + x1 p(c_59) = 1 p(c_60) = 1 p(c_61) = 0 p(c_62) = 1 + x2 p(c_63) = 0 p(c_64) = 0 p(c_65) = 1 p(c_66) = 1 p(c_67) = 0 p(c_68) = 4 p(c_69) = 0 p(c_70) = 1 p(c_71) = 1 p(c_72) = 2 p(c_73) = 4 p(c_74) = 1 p(c_75) = 0 p(c_76) = 2 Following rules are strictly oriented: U42#(tt(),V1,V2) = 1 + 4*V1 + 4*V2 > 4*V1 + 4*V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = 4*V >= 4*V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) = 4*V >= 4*V = c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) = 7 + 4*V1 + 4*V2 >= 7 + 4*V1 + 4*V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) = 7 + 4*V1 + 4*V2 >= 7 + 4*V1 + 4*V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = 7 + 4*V1 + 4*V2 >= 7 + 4*V1 + 4*V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = 7 + 4*V1 + 4*V2 >= 6 + 4*V1 + 4*V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) = 2 + 4*V2 >= 4*V2 = c_8(isList#(activate(V2))) U41#(tt(),V1,V2) = 1 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) = 4*V2 >= 4*V2 = c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) = 4*V2 >= 4*V2 = c_23(isList#(activate(V2))) isList#(V) = 4*V >= 4*V = c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) = 8 + 4*V1 + 4*V2 >= 8 + 4*V1 + 4*V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 8 + 4*V1 + 4*V2 >= 8 + 4*V1 + 4*V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 8 + 4*V1 + 4*V2 >= 4*V1 + 4*V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 3 + X >= X = X __(X1,X2) = 2 + X1 + X2 >= 2 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 4 + X + Y + Z >= 4 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 3 + X >= X = X a() = 0 >= 0 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 2 + X1 + X2 >= 2 + X1 + X2 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 7 >= 7 = i() activate(n__nil()) = 1 >= 1 = nil() activate(n__o()) = 2 >= 2 = o() activate(n__u()) = 0 >= 0 = u() e() = 0 >= 0 = n__e() i() = 7 >= 7 = n__i() nil() = 1 >= 1 = n__nil() o() = 2 >= 2 = n__o() u() = 0 >= 0 = n__u() ** Step 8.a:18: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) - Weak DPs: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 2*x1 + 4*x2 p(U12) = 0 p(U13) = 2 p(U21) = 2 p(U22) = 3 + 2*x2 + x3 p(U23) = 3*x2 + 5*x3 p(U24) = 1 + 4*x2 p(U25) = 1 + 3*x1 p(U26) = x1 p(U31) = 5 + 2*x2 p(U32) = 2 + x1 p(U33) = 1 p(U41) = 2 + x1 + 2*x2 p(U42) = x1 + x3 p(U43) = 6 + x1 + 6*x2 p(U44) = 4 + x1 + x2 + 3*x3 p(U45) = 0 p(U46) = 6 p(U51) = x1 + x3 p(U52) = 2 + 2*x1 + 2*x2 p(U53) = 3 + 2*x3 p(U54) = 0 p(U55) = 4*x2 p(U56) = 2 p(U61) = 2 + 2*x2 p(U62) = x1 + x2 p(U63) = 1 + 4*x1 p(U71) = x2 + 2*x3 p(U72) = 0 p(U73) = 1 + x1 + 4*x2 p(U74) = 2 + 2*x1 p(U81) = 2 p(U82) = 1 p(U83) = 0 p(U91) = 7 + x1 + 2*x2 p(U92) = 3 p(__) = 4 + x1 + x2 p(a) = 1 p(activate) = x1 p(e) = 0 p(i) = 0 p(isList) = 1 + 2*x1 p(isNeList) = 0 p(isNePal) = 4 p(isPal) = 2 p(isPalListKind) = 2*x1 p(isQid) = 4 p(n____) = 4 + x1 + x2 p(n__a) = 1 p(n__e) = 0 p(n__i) = 0 p(n__nil) = 0 p(n__o) = 4 p(n__u) = 4 p(nil) = 0 p(o) = 4 p(tt) = 4 p(u) = 4 p(U11#) = x2 p(U12#) = x2 p(U13#) = 1 + x1 p(U21#) = 4 + x2 + x3 p(U22#) = 2 + x2 + x3 p(U23#) = x2 + x3 p(U24#) = x2 + x3 p(U25#) = x2 p(U26#) = x1 p(U31#) = 1 + 4*x2 p(U32#) = 1 p(U33#) = 4 p(U41#) = 3 + x2 + x3 p(U42#) = 3 + x2 + x3 p(U43#) = 3 + x2 + x3 p(U44#) = 2 + x2 + x3 p(U45#) = x2 p(U46#) = 4 p(U51#) = 1 + x2 + x3 p(U52#) = 1 + x2 + x3 p(U53#) = x2 + x3 p(U54#) = x2 + x3 p(U55#) = x2 p(U56#) = x1 p(U61#) = x1 + 4*x2 p(U62#) = x1 p(U63#) = 1 + 4*x1 p(U71#) = 4*x1 + 4*x2 p(U72#) = x2 p(U73#) = x2 p(U74#) = 1 p(U81#) = 4 + x1 p(U82#) = 1 + 4*x1 + 4*x2 p(U83#) = 0 p(U91#) = 0 p(U92#) = 1 + x1 p(__#) = 2*x1 + x2 p(a#) = 0 p(activate#) = 1 + 4*x1 p(e#) = 4 p(i#) = 4 p(isList#) = x1 p(isNeList#) = x1 p(isNePal#) = 0 p(isPal#) = 1 + x1 p(isPalListKind#) = 1 p(isQid#) = 2 + 2*x1 p(nil#) = 0 p(o#) = 1 p(u#) = 1 p(c_1) = x1 p(c_2) = x1 p(c_3) = 0 p(c_4) = 2 + x1 p(c_5) = x1 p(c_6) = x1 p(c_7) = x1 + x2 p(c_8) = x1 p(c_9) = 0 p(c_10) = 4 p(c_11) = x2 p(c_12) = 1 p(c_13) = x1 p(c_14) = x1 p(c_15) = x1 p(c_16) = x1 + x2 p(c_17) = x1 p(c_18) = 0 p(c_19) = x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 2 p(c_25) = 1 + x1 p(c_26) = 0 p(c_27) = 0 p(c_28) = 2 + x2 p(c_29) = 1 + x1 + x2 p(c_30) = x1 p(c_31) = 1 p(c_32) = 4 p(c_33) = 4 p(c_34) = 1 p(c_35) = 2 p(c_36) = 1 p(c_37) = 2 p(c_38) = 0 p(c_39) = 0 p(c_40) = 1 p(c_41) = 0 p(c_42) = 1 p(c_43) = x1 p(c_44) = 2 p(c_45) = 1 p(c_46) = 2 + x1 p(c_47) = 1 p(c_48) = 0 p(c_49) = 0 p(c_50) = 1 p(c_51) = 2 p(c_52) = x1 p(c_53) = x1 p(c_54) = 1 p(c_55) = 1 p(c_56) = x1 p(c_57) = 2 + x1 p(c_58) = x1 p(c_59) = x2 p(c_60) = x1 p(c_61) = 0 p(c_62) = 0 p(c_63) = 2 p(c_64) = 0 p(c_65) = 4 p(c_66) = 1 p(c_67) = 1 p(c_68) = 1 p(c_69) = 1 p(c_70) = 0 p(c_71) = 0 p(c_72) = 0 p(c_73) = 0 p(c_74) = 0 p(c_75) = 1 p(c_76) = 0 Following rules are strictly oriented: U43#(tt(),V1,V2) = 3 + V1 + V2 > 2 + V1 + V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = 2 + V1 + V2 > V1 + V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = V >= V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) = V >= V = c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) = 4 + V1 + V2 >= 4 + V1 + V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) = 2 + V1 + V2 >= V1 + V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) = V2 >= V2 = c_8(isList#(activate(V2))) U41#(tt(),V1,V2) = 3 + V1 + V2 >= 3 + V1 + V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) = 3 + V1 + V2 >= 3 + V1 + V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U45#(tt(),V2) = V2 >= V2 = c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) = 1 + V1 + V2 >= 1 + V1 + V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 1 + V1 + V2 >= V1 + V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) = V2 >= V2 = c_23(isList#(activate(V2))) isList#(V) = V >= V = c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) = 4 + V1 + V2 >= 4 + V1 + V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + V1 + V2 >= 3 + V1 + V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 4 + V1 + V2 >= 3 + V1 + V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 4 + X >= X = X __(X1,X2) = 4 + X1 + X2 >= 4 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 8 + X + Y + Z >= 8 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 4 + X >= X = X a() = 1 >= 1 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 4 + X1 + X2 >= 4 + X1 + X2 = __(X1,X2) activate(n__a()) = 1 >= 1 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__nil()) = 0 >= 0 = nil() activate(n__o()) = 4 >= 4 = o() activate(n__u()) = 4 >= 4 = u() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() nil() = 0 >= 0 = n__nil() o() = 4 >= 4 = n__o() u() = 4 >= 4 = n__u() ** Step 8.a:19: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) - Weak DPs: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 4*x1 p(U12) = x1 p(U13) = 1 + 2*x1 p(U21) = 1 + 5*x1 + x3 p(U22) = 2 p(U23) = 4 + 5*x2 p(U24) = 2 + 4*x1 + 5*x3 p(U25) = 2 + x2 p(U26) = 4*x1 p(U31) = 4 p(U32) = 4 + 4*x1 + 2*x2 p(U33) = 1 + 4*x1 p(U41) = 2 + 4*x1 p(U42) = 7 + 4*x1 + 4*x2 p(U43) = 5*x1 + 2*x3 p(U44) = 3 + 4*x1 + 3*x3 p(U45) = 1 + x1 p(U46) = 4 + 2*x1 p(U51) = 2 + 4*x2 + 5*x3 p(U52) = 1 + 2*x1 + 2*x2 + 3*x3 p(U53) = 1 + 3*x1 + 2*x2 + 2*x3 p(U54) = 4 + 4*x1 + x2 p(U55) = 4 + 3*x1 p(U56) = 1 + x1 p(U61) = 2 + 2*x1 p(U62) = 1 p(U63) = 2 + x1 p(U71) = 2*x1 p(U72) = 1 + 2*x1 + 2*x2 p(U73) = 4 p(U74) = x1 p(U81) = 1 p(U82) = 4*x1 p(U83) = 0 p(U91) = 2 + 2*x1 + 2*x2 p(U92) = 2 + 5*x1 p(__) = 4 + x1 + x2 p(a) = 0 p(activate) = x1 p(e) = 1 p(i) = 1 p(isList) = 0 p(isNeList) = 3 p(isNePal) = x1 p(isPal) = 0 p(isPalListKind) = 1 p(isQid) = 1 p(n____) = 4 + x1 + x2 p(n__a) = 0 p(n__e) = 1 p(n__i) = 1 p(n__nil) = 2 p(n__o) = 3 p(n__u) = 4 p(nil) = 2 p(o) = 3 p(tt) = 0 p(u) = 4 p(U11#) = 2*x2 p(U12#) = 2*x2 p(U13#) = 1 + x1 p(U21#) = 5 + 2*x2 + 2*x3 p(U22#) = 5 + 2*x2 + 2*x3 p(U23#) = 5 + 2*x2 + 2*x3 p(U24#) = 4 + 2*x2 + 2*x3 p(U25#) = 1 + 2*x2 p(U26#) = 0 p(U31#) = 0 p(U32#) = 1 p(U33#) = 4 p(U41#) = 4 + 2*x2 + 2*x3 p(U42#) = 4 + 2*x2 + 2*x3 p(U43#) = 2 + 2*x2 + 2*x3 p(U44#) = 1 + 2*x2 + 2*x3 p(U45#) = 2*x2 p(U46#) = 1 p(U51#) = 2 + 2*x2 + 2*x3 p(U52#) = 2 + 2*x2 + 2*x3 p(U53#) = 2 + 2*x2 + 2*x3 p(U54#) = 2 + 2*x2 + 2*x3 p(U55#) = 2 + 2*x2 p(U56#) = 1 + 2*x1 p(U61#) = 4 + 4*x1 p(U62#) = 1 + x1 p(U63#) = 1 p(U71#) = 2 + 2*x1 p(U72#) = x1 p(U73#) = 2*x1 p(U74#) = 1 p(U81#) = 4 p(U82#) = 1 + 2*x1 p(U83#) = 0 p(U91#) = 2 + 2*x1 p(U92#) = 2 p(__#) = 2 + x1 + x2 p(a#) = 4 p(activate#) = 0 p(e#) = 1 p(i#) = 0 p(isList#) = 1 + 2*x1 p(isNeList#) = 2*x1 p(isNePal#) = 0 p(isPal#) = 1 + 4*x1 p(isPalListKind#) = 0 p(isQid#) = 2*x1 p(nil#) = 0 p(o#) = 0 p(u#) = 4 p(c_1) = x1 p(c_2) = x1 p(c_3) = 0 p(c_4) = x1 p(c_5) = x1 p(c_6) = 1 + x1 p(c_7) = 2 + x1 + x2 p(c_8) = x1 p(c_9) = 0 p(c_10) = 1 p(c_11) = 0 p(c_12) = 0 p(c_13) = x1 p(c_14) = x1 p(c_15) = x1 p(c_16) = x1 + x2 p(c_17) = x1 p(c_18) = 2 p(c_19) = x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 4 p(c_25) = 2 p(c_26) = 0 p(c_27) = 0 p(c_28) = x2 p(c_29) = 0 p(c_30) = 1 p(c_31) = 0 p(c_32) = 0 p(c_33) = 1 p(c_34) = 0 p(c_35) = 0 p(c_36) = 1 p(c_37) = 0 p(c_38) = 1 p(c_39) = 1 p(c_40) = 2 p(c_41) = 0 p(c_42) = 4 p(c_43) = 0 p(c_44) = 0 p(c_45) = 0 p(c_46) = 0 p(c_47) = 1 p(c_48) = 1 p(c_49) = 0 p(c_50) = 0 p(c_51) = 1 p(c_52) = x1 p(c_53) = x1 p(c_54) = 1 p(c_55) = 4 p(c_56) = 4 + x1 p(c_57) = x1 p(c_58) = 1 + x1 + x2 p(c_59) = x2 + x4 + x5 p(c_60) = 1 + x2 p(c_61) = 0 p(c_62) = x2 p(c_63) = 1 p(c_64) = 2 p(c_65) = 0 p(c_66) = 0 p(c_67) = 0 p(c_68) = 1 p(c_69) = 1 p(c_70) = 0 p(c_71) = 0 p(c_72) = 2 p(c_73) = 0 p(c_74) = 1 p(c_75) = 4 p(c_76) = 1 Following rules are strictly oriented: isList#(V) = 1 + 2*V > 2*V = c_52(U11#(isPalListKind(activate(V)),activate(V))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = 2*V >= 2*V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) = 2*V >= 2*V = c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) = 5 + 2*V1 + 2*V2 >= 5 + 2*V1 + 2*V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) = 5 + 2*V1 + 2*V2 >= 5 + 2*V1 + 2*V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = 5 + 2*V1 + 2*V2 >= 5 + 2*V1 + 2*V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = 4 + 2*V1 + 2*V2 >= 4 + 2*V1 + 2*V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) = 1 + 2*V2 >= 1 + 2*V2 = c_8(isList#(activate(V2))) U41#(tt(),V1,V2) = 4 + 2*V1 + 2*V2 >= 4 + 2*V1 + 2*V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) = 4 + 2*V1 + 2*V2 >= 2 + 2*V1 + 2*V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = 2 + 2*V1 + 2*V2 >= 1 + 2*V1 + 2*V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = 1 + 2*V1 + 2*V2 >= 1 + 2*V1 + 2*V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) = 2*V2 >= 2*V2 = c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) = 2 + 2*V1 + 2*V2 >= 2 + 2*V1 + 2*V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 2 + 2*V1 + 2*V2 >= 2 + 2*V1 + 2*V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) = 2 + 2*V1 + 2*V2 >= 2 + 2*V1 + 2*V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = 2 + 2*V1 + 2*V2 >= 2 + 2*V1 + 2*V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) = 2 + 2*V2 >= 1 + 2*V2 = c_23(isList#(activate(V2))) isList#(n____(V1,V2)) = 9 + 2*V1 + 2*V2 >= 5 + 2*V1 + 2*V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 8 + 2*V1 + 2*V2 >= 8 + 2*V1 + 2*V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 8 + 2*V1 + 2*V2 >= 2 + 2*V1 + 2*V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 6 + X >= X = X __(X1,X2) = 4 + X1 + X2 >= 4 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 8 + X + Y + Z >= 8 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 6 + X >= X = X a() = 0 >= 0 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 4 + X1 + X2 >= 4 + X1 + X2 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 1 >= 1 = e() activate(n__i()) = 1 >= 1 = i() activate(n__nil()) = 2 >= 2 = nil() activate(n__o()) = 3 >= 3 = o() activate(n__u()) = 4 >= 4 = u() e() = 1 >= 1 = n__e() i() = 1 >= 1 = n__i() nil() = 2 >= 2 = n__nil() o() = 3 >= 3 = n__o() u() = 4 >= 4 = n__u() ** Step 8.a:20: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) - Weak DPs: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 2 + x1 + 4*x2 p(U12) = x2 p(U13) = 0 p(U21) = 1 + x1 + 4*x2 p(U22) = 2 + x2 p(U23) = 2 + 2*x1 + x2 + 2*x3 p(U24) = 5 + x1 + 7*x3 p(U25) = 1 p(U26) = 5 + x1 p(U31) = 0 p(U32) = 2 + 4*x2 p(U33) = 0 p(U41) = 0 p(U42) = 3 + 4*x2 + x3 p(U43) = x1 + 2*x2 + 2*x3 p(U44) = 1 + 2*x1 + 4*x3 p(U45) = 0 p(U46) = x1 p(U51) = 6 + 2*x1 + 2*x2 p(U52) = 1 + x2 p(U53) = 5 + 6*x2 + 2*x3 p(U54) = 2 + 7*x2 + x3 p(U55) = 4*x1 + 2*x2 p(U56) = 4 + 4*x1 p(U61) = 4*x1 p(U62) = 2*x1 p(U63) = 4 p(U71) = 2*x1 p(U72) = 4 + x1 p(U73) = 2 + x1 p(U74) = x1 p(U81) = 0 p(U82) = 2 + x2 p(U83) = 2 p(U91) = x1 + 2*x2 p(U92) = 2 p(__) = 2 + x1 + x2 p(a) = 0 p(activate) = x1 p(e) = 0 p(i) = 1 p(isList) = 0 p(isNeList) = 1 p(isNePal) = 2 p(isPal) = 2 + 2*x1 p(isPalListKind) = 4 + 4*x1 p(isQid) = 1 + 4*x1 p(n____) = 2 + x1 + x2 p(n__a) = 0 p(n__e) = 0 p(n__i) = 1 p(n__nil) = 0 p(n__o) = 0 p(n__u) = 1 p(nil) = 0 p(o) = 0 p(tt) = 0 p(u) = 1 p(U11#) = 1 + 4*x2 p(U12#) = 4*x2 p(U13#) = x1 p(U21#) = 3 + 4*x2 + 4*x3 p(U22#) = 3 + 4*x2 + 4*x3 p(U23#) = 2 + 4*x2 + 4*x3 p(U24#) = 2 + 4*x2 + 4*x3 p(U25#) = 1 + 4*x2 p(U26#) = 4*x1 p(U31#) = 0 p(U32#) = x1 p(U33#) = 4 p(U41#) = 5 + 4*x2 + 4*x3 p(U42#) = 4 + 4*x2 + 4*x3 p(U43#) = 3 + 4*x2 + 4*x3 p(U44#) = 1 + 4*x2 + 4*x3 p(U45#) = 4*x2 p(U46#) = 1 + x1 p(U51#) = 4 + 4*x2 + 4*x3 p(U52#) = 2 + 4*x2 + 4*x3 p(U53#) = 1 + 4*x2 + 4*x3 p(U54#) = 1 + 4*x2 + 4*x3 p(U55#) = 1 + 4*x2 p(U56#) = x1 p(U61#) = 4 + 4*x2 p(U62#) = 0 p(U63#) = 0 p(U71#) = 1 + 4*x1 + x3 p(U72#) = 2 + 2*x2 p(U73#) = 4 p(U74#) = x1 p(U81#) = 2 + x1 + 4*x2 p(U82#) = 1 + x2 p(U83#) = 2 p(U91#) = 4 + x1 + x2 p(U92#) = 1 + 4*x1 p(__#) = x2 p(a#) = 0 p(activate#) = 1 + x1 p(e#) = 4 p(i#) = 0 p(isList#) = 1 + 4*x1 p(isNeList#) = 4*x1 p(isNePal#) = 4 + 4*x1 p(isPal#) = x1 p(isPalListKind#) = 0 p(isQid#) = 1 p(nil#) = 0 p(o#) = 0 p(u#) = 0 p(c_1) = x1 p(c_2) = x1 p(c_3) = 0 p(c_4) = x1 p(c_5) = 1 + x1 p(c_6) = x1 p(c_7) = x1 + x2 p(c_8) = x1 p(c_9) = 2 p(c_10) = 1 p(c_11) = 1 p(c_12) = 0 p(c_13) = x1 p(c_14) = x1 p(c_15) = 2 + x1 p(c_16) = x1 + x2 p(c_17) = x1 p(c_18) = 1 p(c_19) = 1 + x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 0 p(c_25) = 4 + x1 p(c_26) = 2 + x1 + x2 + x3 p(c_27) = 0 p(c_28) = 1 p(c_29) = 1 + x1 + x2 p(c_30) = 1 p(c_31) = 2 p(c_32) = 1 p(c_33) = 0 p(c_34) = 0 p(c_35) = 2 p(c_36) = 1 p(c_37) = 1 p(c_38) = 4 p(c_39) = 1 + x2 p(c_40) = 1 p(c_41) = 2 p(c_42) = 4 p(c_43) = x1 p(c_44) = 4 p(c_45) = 0 p(c_46) = 0 p(c_47) = 2 + x1 p(c_48) = 4 + x1 p(c_49) = 1 + x1 p(c_50) = 0 p(c_51) = 2 p(c_52) = x1 p(c_53) = 6 + x1 p(c_54) = 0 p(c_55) = 0 p(c_56) = x1 p(c_57) = 3 + x1 p(c_58) = 4 + x1 p(c_59) = x2 p(c_60) = 1 p(c_61) = 1 p(c_62) = x2 p(c_63) = 0 p(c_64) = 4 p(c_65) = 0 p(c_66) = 0 p(c_67) = 0 p(c_68) = 0 p(c_69) = 4 p(c_70) = 0 p(c_71) = 2 p(c_72) = 4 p(c_73) = 1 p(c_74) = 2 p(c_75) = 0 p(c_76) = 4 Following rules are strictly oriented: U11#(tt(),V) = 1 + 4*V > 4*V = c_1(U12#(isPalListKind(activate(V)),activate(V))) Following rules are (at-least) weakly oriented: U12#(tt(),V) = 4*V >= 4*V = c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) = 3 + 4*V1 + 4*V2 >= 3 + 4*V1 + 4*V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) = 3 + 4*V1 + 4*V2 >= 3 + 4*V1 + 4*V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = 2 + 4*V1 + 4*V2 >= 2 + 4*V1 + 4*V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = 2 + 4*V1 + 4*V2 >= 2 + 4*V1 + 4*V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) = 1 + 4*V2 >= 1 + 4*V2 = c_8(isList#(activate(V2))) U41#(tt(),V1,V2) = 5 + 4*V1 + 4*V2 >= 4 + 4*V1 + 4*V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) = 4 + 4*V1 + 4*V2 >= 3 + 4*V1 + 4*V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = 3 + 4*V1 + 4*V2 >= 3 + 4*V1 + 4*V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = 1 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) = 4*V2 >= 4*V2 = c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) = 4 + 4*V1 + 4*V2 >= 3 + 4*V1 + 4*V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 2 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) = 1 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = 1 + 4*V1 + 4*V2 >= 1 + 4*V1 + 4*V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) = 1 + 4*V2 >= 1 + 4*V2 = c_23(isList#(activate(V2))) isList#(V) = 1 + 4*V >= 1 + 4*V = c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) = 9 + 4*V1 + 4*V2 >= 9 + 4*V1 + 4*V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 8 + 4*V1 + 4*V2 >= 5 + 4*V1 + 4*V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 8 + 4*V1 + 4*V2 >= 7 + 4*V1 + 4*V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 2 + X >= X = X __(X1,X2) = 2 + X1 + X2 >= 2 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 4 + X + Y + Z >= 4 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 2 + X >= X = X a() = 0 >= 0 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 2 + X1 + X2 >= 2 + X1 + X2 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 1 >= 1 = i() activate(n__nil()) = 0 >= 0 = nil() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 1 >= 1 = u() e() = 0 >= 0 = n__e() i() = 1 >= 1 = n__i() nil() = 0 >= 0 = n__nil() o() = 0 >= 0 = n__o() u() = 1 >= 1 = n__u() ** Step 8.a:21: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U12#(tt(),V) -> c_2(isNeList#(activate(V))) - Weak DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_4) = {1}, uargs(c_5) = {1}, uargs(c_6) = {1}, uargs(c_7) = {1,2}, uargs(c_8) = {1}, uargs(c_13) = {1}, uargs(c_14) = {1}, uargs(c_15) = {1}, uargs(c_16) = {1,2}, uargs(c_17) = {1}, uargs(c_19) = {1}, uargs(c_20) = {1}, uargs(c_21) = {1}, uargs(c_22) = {1,2}, uargs(c_23) = {1}, uargs(c_52) = {1}, uargs(c_53) = {1}, uargs(c_56) = {1}, uargs(c_57) = {1} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 0 p(U12) = 6 + 6*x2 p(U13) = 7 + x1 p(U21) = x1 + 4*x2 p(U22) = x1 p(U23) = 1 + x1 + 3*x3 p(U24) = 4 + x1 p(U25) = 0 p(U26) = 2 + 4*x1 p(U31) = 7*x2 p(U32) = 5 + x1 + x2 p(U33) = 4 p(U41) = x2 p(U42) = 4 + 2*x1 + 5*x3 p(U43) = 2 p(U44) = 1 + x1 + 5*x3 p(U45) = 4*x1 p(U46) = x1 p(U51) = x1 + 4*x3 p(U52) = 2 + 6*x2 + 2*x3 p(U53) = 2 + 3*x3 p(U54) = 0 p(U55) = 2*x1 p(U56) = 2*x1 p(U61) = 4 + 4*x1 p(U62) = 0 p(U63) = 4 p(U71) = 2 p(U72) = 2 + x1 p(U73) = 1 p(U74) = x1 p(U81) = x2 p(U82) = 1 + 4*x2 p(U83) = 2 + 4*x1 p(U91) = 6 + x1 p(U92) = 6 + 2*x1 p(__) = 2 + x1 + x2 p(a) = 0 p(activate) = x1 p(e) = 0 p(i) = 0 p(isList) = 1 p(isNeList) = 1 + 2*x1 p(isNePal) = 2 + x1 p(isPal) = 1 p(isPalListKind) = 0 p(isQid) = 0 p(n____) = 2 + x1 + x2 p(n__a) = 0 p(n__e) = 0 p(n__i) = 0 p(n__nil) = 0 p(n__o) = 0 p(n__u) = 4 p(nil) = 0 p(o) = 0 p(tt) = 0 p(u) = 4 p(U11#) = 1 + 4*x2 p(U12#) = 1 + 4*x2 p(U13#) = 2 p(U21#) = 3 + 4*x2 + 4*x3 p(U22#) = 3 + 4*x2 + 4*x3 p(U23#) = 3 + 4*x2 + 4*x3 p(U24#) = 3 + 4*x2 + 4*x3 p(U25#) = 2 + 4*x2 p(U26#) = 4 p(U31#) = x1 p(U32#) = 1 + x1 + x2 p(U33#) = 2 + x1 p(U41#) = 6 + 4*x2 + 4*x3 p(U42#) = 6 + 4*x2 + 4*x3 p(U43#) = 4 + 4*x2 + 4*x3 p(U44#) = 2 + 4*x2 + 4*x3 p(U45#) = 1 + 4*x2 p(U46#) = 2 + x1 p(U51#) = 7 + 4*x2 + 4*x3 p(U52#) = 7 + 4*x2 + 4*x3 p(U53#) = 7 + 4*x2 + 4*x3 p(U54#) = 7 + 4*x2 + 4*x3 p(U55#) = 7 + 4*x2 p(U56#) = 0 p(U61#) = 1 + x1 + 4*x2 p(U62#) = 1 p(U63#) = 0 p(U71#) = 1 p(U72#) = 1 + 2*x2 p(U73#) = 2*x1 p(U74#) = 0 p(U81#) = 4 p(U82#) = 2 + x1 + x2 p(U83#) = x1 p(U91#) = 1 + x1 p(U92#) = 4 p(__#) = 1 + 2*x2 p(a#) = 1 p(activate#) = 4 p(e#) = 2 p(i#) = 0 p(isList#) = 1 + 4*x1 p(isNeList#) = 4*x1 p(isNePal#) = 1 + x1 p(isPal#) = 0 p(isPalListKind#) = 2 + x1 p(isQid#) = 0 p(nil#) = 0 p(o#) = 0 p(u#) = 0 p(c_1) = x1 p(c_2) = x1 p(c_3) = 2 p(c_4) = x1 p(c_5) = x1 p(c_6) = x1 p(c_7) = x1 + x2 p(c_8) = x1 p(c_9) = 1 p(c_10) = 1 p(c_11) = x2 p(c_12) = 4 p(c_13) = x1 p(c_14) = 1 + x1 p(c_15) = x1 p(c_16) = x1 + x2 p(c_17) = x1 p(c_18) = 0 p(c_19) = x1 p(c_20) = x1 p(c_21) = x1 p(c_22) = x1 + x2 p(c_23) = x1 p(c_24) = 2 p(c_25) = 2 p(c_26) = 1 + x1 + x2 p(c_27) = 1 p(c_28) = x1 + x2 p(c_29) = x1 p(c_30) = x1 p(c_31) = 4 p(c_32) = 4 p(c_33) = 0 p(c_34) = 1 p(c_35) = 2 + x1 p(c_36) = 2 p(c_37) = 0 p(c_38) = 1 p(c_39) = 1 + x2 p(c_40) = 1 p(c_41) = 1 p(c_42) = 0 p(c_43) = 0 p(c_44) = 0 p(c_45) = 0 p(c_46) = 1 + x1 p(c_47) = 1 p(c_48) = 4 p(c_49) = 2 p(c_50) = 4 p(c_51) = 2 p(c_52) = x1 p(c_53) = 6 + x1 p(c_54) = 0 p(c_55) = 1 + x2 p(c_56) = x1 p(c_57) = x1 p(c_58) = 0 p(c_59) = 4 p(c_60) = x1 + x2 p(c_61) = 2 p(c_62) = x2 p(c_63) = 2 p(c_64) = 1 p(c_65) = 1 p(c_66) = 1 p(c_67) = 0 p(c_68) = 0 p(c_69) = 0 p(c_70) = 0 p(c_71) = 1 p(c_72) = 0 p(c_73) = 0 p(c_74) = 2 p(c_75) = 0 p(c_76) = 2 Following rules are strictly oriented: U12#(tt(),V) = 1 + 4*V > 4*V = c_2(isNeList#(activate(V))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = 1 + 4*V >= 1 + 4*V = c_1(U12#(isPalListKind(activate(V)),activate(V))) U21#(tt(),V1,V2) = 3 + 4*V1 + 4*V2 >= 3 + 4*V1 + 4*V2 = c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) = 3 + 4*V1 + 4*V2 >= 3 + 4*V1 + 4*V2 = c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) = 3 + 4*V1 + 4*V2 >= 3 + 4*V1 + 4*V2 = c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) = 3 + 4*V1 + 4*V2 >= 3 + 4*V1 + 4*V2 = c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) = 2 + 4*V2 >= 1 + 4*V2 = c_8(isList#(activate(V2))) U41#(tt(),V1,V2) = 6 + 4*V1 + 4*V2 >= 6 + 4*V1 + 4*V2 = c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) = 6 + 4*V1 + 4*V2 >= 5 + 4*V1 + 4*V2 = c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) = 4 + 4*V1 + 4*V2 >= 2 + 4*V1 + 4*V2 = c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) = 2 + 4*V1 + 4*V2 >= 2 + 4*V1 + 4*V2 = c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) = 1 + 4*V2 >= 4*V2 = c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) = 7 + 4*V1 + 4*V2 >= 7 + 4*V1 + 4*V2 = c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) = 7 + 4*V1 + 4*V2 >= 7 + 4*V1 + 4*V2 = c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) = 7 + 4*V1 + 4*V2 >= 7 + 4*V1 + 4*V2 = c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) = 7 + 4*V1 + 4*V2 >= 7 + 4*V1 + 4*V2 = c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) = 7 + 4*V2 >= 1 + 4*V2 = c_23(isList#(activate(V2))) isList#(V) = 1 + 4*V >= 1 + 4*V = c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) = 9 + 4*V1 + 4*V2 >= 9 + 4*V1 + 4*V2 = c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 8 + 4*V1 + 4*V2 >= 6 + 4*V1 + 4*V2 = c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) = 8 + 4*V1 + 4*V2 >= 7 + 4*V1 + 4*V2 = c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) __(X,nil()) = 2 + X >= X = X __(X1,X2) = 2 + X1 + X2 >= 2 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 4 + X + Y + Z >= 4 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 2 + X >= X = X a() = 0 >= 0 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 2 + X1 + X2 >= 2 + X1 + X2 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__nil()) = 0 >= 0 = nil() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 4 >= 4 = u() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() nil() = 0 >= 0 = n__nil() o() = 0 >= 0 = n__o() u() = 4 >= 4 = n__u() ** Step 8.a:22: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak DPs: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))) U12#(tt(),V) -> c_2(isNeList#(activate(V))) U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U25#(tt(),V2) -> c_8(isList#(activate(V2))) U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))) U45#(tt(),V2) -> c_17(isNeList#(activate(V2))) U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))) U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))) U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))) U55#(tt(),V2) -> c_23(isList#(activate(V2))) isList#(V) -> c_52(U11#(isPalListKind(activate(V)),activate(V))) isList#(n____(V1,V2)) -> c_53(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_56(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))) isNeList#(n____(V1,V2)) -> c_57(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/1,c_14/1,c_15/1,c_16/2 ,c_17/1,c_18/0,c_19/1,c_20/1,c_21/1,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/1,c_53/1,c_54/0,c_55/2,c_56/1,c_57/1,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). ** Step 8.b:1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U31#(tt(),V) -> c_10(isPalListKind#(activate(V))) U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1))) - Weak DPs: U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isPalListKind#(activate(V)) U12#(tt(),V) -> isNeList#(activate(V)) U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt(),V1,V2) -> isList#(activate(V1)) U25#(tt(),V2) -> isList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt(),V1,V2) -> isList#(activate(V1)) U45#(tt(),V2) -> isNeList#(activate(V2)) U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt(),V1,V2) -> isNeList#(activate(V1)) U55#(tt(),V2) -> isList#(activate(V2)) U61#(tt(),V) -> isPalListKind#(activate(V)) U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)) U71#(tt(),I,P) -> isPalListKind#(activate(I)) U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)) U72#(tt(),P) -> isPal#(activate(P)) U73#(tt(),P) -> isPalListKind#(activate(P)) U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)) U81#(tt(),V) -> isPalListKind#(activate(V)) U82#(tt(),V) -> isNePal#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) isList#(V) -> isPalListKind#(activate(V)) isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) isNePal#(V) -> isPalListKind#(activate(V)) isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)) isPal#(V) -> isPalListKind#(activate(V)) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_10) = {1}, uargs(c_35) = {1}, uargs(c_55) = {1,2}, uargs(c_62) = {1,2} Following symbols are considered usable: {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53# ,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList# ,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 0 p(U12) = 0 p(U13) = 0 p(U21) = 0 p(U22) = 0 p(U23) = 0 p(U24) = 2*x2 p(U25) = 0 p(U26) = 0 p(U31) = 0 p(U32) = 2 p(U33) = 0 p(U41) = 0 p(U42) = 0 p(U43) = 0 p(U44) = 0 p(U45) = 0 p(U46) = 0 p(U51) = 0 p(U52) = 0 p(U53) = 0 p(U54) = 0 p(U55) = 0 p(U56) = 0 p(U61) = 0 p(U62) = 2 p(U63) = 0 p(U71) = 0 p(U72) = 0 p(U73) = 0 p(U74) = 2 p(U81) = 1 p(U82) = 0 p(U83) = 3 p(U91) = 0 p(U92) = 0 p(__) = 0 p(a) = 0 p(activate) = 0 p(e) = 0 p(i) = 0 p(isList) = 0 p(isNeList) = 0 p(isNePal) = 0 p(isPal) = 0 p(isPalListKind) = 0 p(isQid) = 0 p(n____) = 0 p(n__a) = 0 p(n__e) = 0 p(n__i) = 0 p(n__nil) = 0 p(n__o) = 0 p(n__u) = 0 p(nil) = 0 p(o) = 0 p(tt) = 0 p(u) = 0 p(U11#) = 2 p(U12#) = 2 p(U13#) = 0 p(U21#) = 2 p(U22#) = 2 p(U23#) = 2 p(U24#) = 2 p(U25#) = 2 p(U26#) = 0 p(U31#) = 1 p(U32#) = 0 p(U33#) = 0 p(U41#) = 2 p(U42#) = 2 p(U43#) = 2 p(U44#) = 2 p(U45#) = 2 p(U46#) = 0 p(U51#) = 2 p(U52#) = 2 p(U53#) = 2 p(U54#) = 2 p(U55#) = 2 p(U56#) = 0 p(U61#) = 0 p(U62#) = 0 p(U63#) = 0 p(U71#) = 3 + 2*x1 + 2*x2 p(U72#) = 0 p(U73#) = 0 p(U74#) = 0 p(U81#) = 0 p(U82#) = 0 p(U83#) = 0 p(U91#) = 0 p(U92#) = 0 p(__#) = 2*x1 p(a#) = 0 p(activate#) = 2*x1 p(e#) = 0 p(i#) = 0 p(isList#) = 2 p(isNeList#) = 2 p(isNePal#) = 0 p(isPal#) = 0 p(isPalListKind#) = 0 p(isQid#) = 0 p(nil#) = 0 p(o#) = 0 p(u#) = 0 p(c_1) = 0 p(c_2) = x1 p(c_3) = 0 p(c_4) = x1 p(c_5) = 0 p(c_6) = x2 p(c_7) = 0 p(c_8) = 0 p(c_9) = 0 p(c_10) = x1 p(c_11) = x1 p(c_12) = 0 p(c_13) = 0 p(c_14) = x1 + x2 p(c_15) = 0 p(c_16) = 0 p(c_17) = x1 p(c_18) = 0 p(c_19) = x1 p(c_20) = 0 p(c_21) = 0 p(c_22) = 0 p(c_23) = 0 p(c_24) = 0 p(c_25) = 0 p(c_26) = 0 p(c_27) = 2 p(c_28) = 0 p(c_29) = 0 p(c_30) = 0 p(c_31) = 0 p(c_32) = 0 p(c_33) = 0 p(c_34) = 2 p(c_35) = x1 p(c_36) = 0 p(c_37) = 0 p(c_38) = 0 p(c_39) = 0 p(c_40) = 0 p(c_41) = 0 p(c_42) = 0 p(c_43) = x1 p(c_44) = x1 p(c_45) = 0 p(c_46) = 0 p(c_47) = 0 p(c_48) = 0 p(c_49) = x1 p(c_50) = 0 p(c_51) = 0 p(c_52) = 0 p(c_53) = 0 p(c_54) = 2 p(c_55) = x1 + x2 p(c_56) = 2 + x1 p(c_57) = 2 p(c_58) = 2 p(c_59) = x2 + x4 p(c_60) = 2 p(c_61) = 0 p(c_62) = x1 + x2 p(c_63) = 0 p(c_64) = 0 p(c_65) = 0 p(c_66) = 0 p(c_67) = 0 p(c_68) = 0 p(c_69) = 0 p(c_70) = 0 p(c_71) = 0 p(c_72) = 0 p(c_73) = 0 p(c_74) = 0 p(c_75) = 0 p(c_76) = 0 Following rules are strictly oriented: U31#(tt(),V) = 1 > 0 = c_10(isPalListKind#(activate(V))) isNeList#(V) = 2 > 1 = c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = 2 >= 2 = U12#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) = 2 >= 0 = isPalListKind#(activate(V)) U12#(tt(),V) = 2 >= 2 = isNeList#(activate(V)) U21#(tt(),V1,V2) = 2 >= 2 = U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt(),V1,V2) = 2 >= 0 = isPalListKind#(activate(V1)) U22#(tt(),V1,V2) = 2 >= 2 = U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt(),V1,V2) = 2 >= 0 = isPalListKind#(activate(V2)) U23#(tt(),V1,V2) = 2 >= 2 = U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt(),V1,V2) = 2 >= 0 = isPalListKind#(activate(V2)) U24#(tt(),V1,V2) = 2 >= 2 = U25#(isList(activate(V1)),activate(V2)) U24#(tt(),V1,V2) = 2 >= 2 = isList#(activate(V1)) U25#(tt(),V2) = 2 >= 2 = isList#(activate(V2)) U41#(tt(),V1,V2) = 2 >= 2 = U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt(),V1,V2) = 2 >= 0 = isPalListKind#(activate(V1)) U42#(tt(),V1,V2) = 2 >= 2 = U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt(),V1,V2) = 2 >= 0 = isPalListKind#(activate(V2)) U43#(tt(),V1,V2) = 2 >= 2 = U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt(),V1,V2) = 2 >= 0 = isPalListKind#(activate(V2)) U44#(tt(),V1,V2) = 2 >= 2 = U45#(isList(activate(V1)),activate(V2)) U44#(tt(),V1,V2) = 2 >= 2 = isList#(activate(V1)) U45#(tt(),V2) = 2 >= 2 = isNeList#(activate(V2)) U51#(tt(),V1,V2) = 2 >= 2 = U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt(),V1,V2) = 2 >= 0 = isPalListKind#(activate(V1)) U52#(tt(),V1,V2) = 2 >= 2 = U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt(),V1,V2) = 2 >= 0 = isPalListKind#(activate(V2)) U53#(tt(),V1,V2) = 2 >= 2 = U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt(),V1,V2) = 2 >= 0 = isPalListKind#(activate(V2)) U54#(tt(),V1,V2) = 2 >= 2 = U55#(isNeList(activate(V1)),activate(V2)) U54#(tt(),V1,V2) = 2 >= 2 = isNeList#(activate(V1)) U55#(tt(),V2) = 2 >= 2 = isList#(activate(V2)) U61#(tt(),V) = 0 >= 0 = isPalListKind#(activate(V)) U71#(tt(),I,P) = 3 + 2*I >= 0 = U72#(isPalListKind(activate(I)),activate(P)) U71#(tt(),I,P) = 3 + 2*I >= 0 = isPalListKind#(activate(I)) U72#(tt(),P) = 0 >= 0 = U73#(isPal(activate(P)),activate(P)) U72#(tt(),P) = 0 >= 0 = isPal#(activate(P)) U73#(tt(),P) = 0 >= 0 = isPalListKind#(activate(P)) U81#(tt(),V) = 0 >= 0 = U82#(isPalListKind(activate(V)),activate(V)) U81#(tt(),V) = 0 >= 0 = isPalListKind#(activate(V)) U82#(tt(),V) = 0 >= 0 = isNePal#(activate(V)) U91#(tt(),V2) = 0 >= 0 = c_35(isPalListKind#(activate(V2))) isList#(V) = 2 >= 2 = U11#(isPalListKind(activate(V)),activate(V)) isList#(V) = 2 >= 0 = isPalListKind#(activate(V)) isList#(n____(V1,V2)) = 2 >= 2 = U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList#(n____(V1,V2)) = 2 >= 0 = isPalListKind#(activate(V1)) isNeList#(n____(V1,V2)) = 2 >= 2 = U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) = 2 >= 2 = U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) = 2 >= 0 = isPalListKind#(activate(V1)) isNePal#(V) = 0 >= 0 = U61#(isPalListKind(activate(V)),activate(V)) isNePal#(V) = 0 >= 0 = isPalListKind#(activate(V)) isPal#(V) = 0 >= 0 = U81#(isPalListKind(activate(V)),activate(V)) isPal#(V) = 0 >= 0 = isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) = 0 >= 0 = c_62(U91#(isPalListKind(activate(V1)),activate(V2)),isPalListKind#(activate(V1))) ** Step 8.b:2: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1))) - Weak DPs: U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isPalListKind#(activate(V)) U12#(tt(),V) -> isNeList#(activate(V)) U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt(),V1,V2) -> isList#(activate(V1)) U25#(tt(),V2) -> isList#(activate(V2)) U31#(tt(),V) -> c_10(isPalListKind#(activate(V))) U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt(),V1,V2) -> isList#(activate(V1)) U45#(tt(),V2) -> isNeList#(activate(V2)) U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt(),V1,V2) -> isNeList#(activate(V1)) U55#(tt(),V2) -> isList#(activate(V2)) U61#(tt(),V) -> isPalListKind#(activate(V)) U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)) U71#(tt(),I,P) -> isPalListKind#(activate(I)) U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)) U72#(tt(),P) -> isPal#(activate(P)) U73#(tt(),P) -> isPalListKind#(activate(P)) U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)) U81#(tt(),V) -> isPalListKind#(activate(V)) U82#(tt(),V) -> isNePal#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) isList#(V) -> isPalListKind#(activate(V)) isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) isNePal#(V) -> isPalListKind#(activate(V)) isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)) isPal#(V) -> isPalListKind#(activate(V)) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(c_10) = {1}, uargs(c_35) = {1}, uargs(c_55) = {1,2}, uargs(c_62) = {1,2} Following symbols are considered usable: {U11,U12,U13,U21,U22,U23,U24,U25,U26,__,a,activate,e,i,isList,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24# ,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71# ,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal# ,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = [1] x2 + [0] p(U12) = [0] p(U13) = [0] p(U21) = [1] x2 + [1] x3 + [7] p(U22) = [1] x3 + [7] p(U23) = [1] x3 + [6] p(U24) = [1] x3 + [4] p(U25) = [4] p(U26) = [1] p(U31) = [7] p(U32) = [2] x2 + [0] p(U33) = [7] p(U41) = [1] x1 + [1] x2 + [4] x3 + [3] p(U42) = [4] x1 + [1] x2 + [4] p(U43) = [4] x1 + [4] x2 + [2] p(U44) = [4] x1 + [2] x3 + [4] p(U45) = [1] p(U46) = [0] p(U51) = [3] x1 + [6] x2 + [3] p(U52) = [0] p(U53) = [1] x3 + [4] p(U54) = [4] x2 + [0] p(U55) = [5] p(U56) = [4] p(U61) = [4] x2 + [4] p(U62) = [2] x1 + [4] x2 + [2] p(U63) = [0] p(U71) = [4] x1 + [2] p(U72) = [3] x1 + [6] p(U73) = [1] x1 + [2] x2 + [0] p(U74) = [0] p(U81) = [1] p(U82) = [2] x1 + [2] x2 + [1] p(U83) = [0] p(U91) = [4] x1 + [1] x2 + [0] p(U92) = [4] x1 + [0] p(__) = [1] x1 + [1] x2 + [7] p(a) = [0] p(activate) = [1] x1 + [0] p(e) = [1] p(i) = [2] p(isList) = [1] x1 + [0] p(isNeList) = [4] p(isNePal) = [1] x1 + [0] p(isPal) = [0] p(isPalListKind) = [2] p(isQid) = [2] x1 + [0] p(n____) = [1] x1 + [1] x2 + [7] p(n__a) = [0] p(n__e) = [1] p(n__i) = [2] p(n__nil) = [0] p(n__o) = [0] p(n__u) = [0] p(nil) = [0] p(o) = [0] p(tt) = [0] p(u) = [0] p(U11#) = [2] x2 + [0] p(U12#) = [2] x2 + [0] p(U13#) = [1] p(U21#) = [2] x2 + [2] x3 + [2] p(U22#) = [2] x2 + [2] x3 + [0] p(U23#) = [2] x2 + [2] x3 + [0] p(U24#) = [2] x2 + [2] x3 + [0] p(U25#) = [2] x2 + [0] p(U26#) = [1] x1 + [1] p(U31#) = [1] x2 + [0] p(U32#) = [4] x1 + [1] x2 + [1] p(U33#) = [4] p(U41#) = [2] x2 + [2] x3 + [1] p(U42#) = [2] x2 + [2] x3 + [1] p(U43#) = [2] x2 + [2] x3 + [1] p(U44#) = [2] x2 + [2] x3 + [1] p(U45#) = [2] x1 + [2] x2 + [0] p(U46#) = [2] p(U51#) = [2] x2 + [2] x3 + [7] p(U52#) = [2] x2 + [2] x3 + [7] p(U53#) = [2] x2 + [2] x3 + [4] p(U54#) = [2] x2 + [2] x3 + [0] p(U55#) = [2] x2 + [0] p(U56#) = [4] p(U61#) = [2] x2 + [1] p(U62#) = [0] p(U63#) = [0] p(U71#) = [1] x2 + [5] x3 + [6] p(U72#) = [5] x2 + [6] p(U73#) = [1] x2 + [2] p(U74#) = [1] x1 + [0] p(U81#) = [5] x2 + [1] p(U82#) = [5] x2 + [1] p(U83#) = [1] x1 + [2] p(U91#) = [1] x2 + [0] p(U92#) = [4] p(__#) = [1] x2 + [1] p(a#) = [4] p(activate#) = [4] x1 + [4] p(e#) = [2] p(i#) = [0] p(isList#) = [2] x1 + [0] p(isNeList#) = [2] x1 + [0] p(isNePal#) = [5] x1 + [1] p(isPal#) = [5] x1 + [1] p(isPalListKind#) = [1] x1 + [0] p(isQid#) = [1] x1 + [1] p(nil#) = [1] p(o#) = [1] p(u#) = [4] p(c_1) = [1] x1 + [0] p(c_2) = [1] x1 + [1] p(c_3) = [2] p(c_4) = [1] x2 + [0] p(c_5) = [0] p(c_6) = [1] x1 + [1] x2 + [1] p(c_7) = [1] x1 + [0] p(c_8) = [1] p(c_9) = [0] p(c_10) = [1] x1 + [0] p(c_11) = [2] x1 + [1] x2 + [2] x3 + [4] p(c_12) = [0] p(c_13) = [1] x1 + [4] p(c_14) = [2] x2 + [1] p(c_15) = [1] x2 + [4] p(c_16) = [0] p(c_17) = [4] x1 + [2] p(c_18) = [1] p(c_19) = [4] x2 + [2] p(c_20) = [1] x2 + [0] p(c_21) = [1] x1 + [4] x2 + [1] p(c_22) = [4] x1 + [0] p(c_23) = [1] x1 + [1] p(c_24) = [4] p(c_25) = [2] p(c_26) = [1] x1 + [1] x2 + [1] x3 + [2] p(c_27) = [2] p(c_28) = [1] x1 + [0] p(c_29) = [1] x1 + [1] p(c_30) = [0] p(c_31) = [4] p(c_32) = [2] x1 + [4] p(c_33) = [2] p(c_34) = [0] p(c_35) = [1] x1 + [0] p(c_36) = [0] p(c_37) = [0] p(c_38) = [4] p(c_39) = [0] p(c_40) = [1] p(c_41) = [0] p(c_42) = [0] p(c_43) = [1] p(c_44) = [1] x1 + [1] p(c_45) = [4] x1 + [2] p(c_46) = [1] p(c_47) = [1] x1 + [2] p(c_48) = [0] p(c_49) = [4] x1 + [1] p(c_50) = [4] p(c_51) = [0] p(c_52) = [0] p(c_53) = [4] p(c_54) = [0] p(c_55) = [1] x1 + [1] x2 + [0] p(c_56) = [2] x1 + [1] x2 + [2] p(c_57) = [4] x1 + [1] p(c_58) = [2] x2 + [2] p(c_59) = [1] x2 + [1] x3 + [4] x4 + [2] x5 + [4] p(c_60) = [4] x1 + [1] x2 + [4] p(c_61) = [1] p(c_62) = [1] x1 + [1] x2 + [0] p(c_63) = [4] p(c_64) = [0] p(c_65) = [0] p(c_66) = [0] p(c_67) = [4] p(c_68) = [0] p(c_69) = [1] p(c_70) = [0] p(c_71) = [4] p(c_72) = [1] p(c_73) = [0] p(c_74) = [0] p(c_75) = [2] p(c_76) = [0] Following rules are strictly oriented: isPalListKind#(n____(V1,V2)) = [1] V1 + [1] V2 + [7] > [1] V1 + [1] V2 + [0] = c_62(U91#(isPalListKind(activate(V1)),activate(V2)),isPalListKind#(activate(V1))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = [2] V + [0] >= [2] V + [0] = U12#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) = [2] V + [0] >= [1] V + [0] = isPalListKind#(activate(V)) U12#(tt(),V) = [2] V + [0] >= [2] V + [0] = isNeList#(activate(V)) U21#(tt(),V1,V2) = [2] V1 + [2] V2 + [2] >= [2] V1 + [2] V2 + [0] = U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt(),V1,V2) = [2] V1 + [2] V2 + [2] >= [1] V1 + [0] = isPalListKind#(activate(V1)) U22#(tt(),V1,V2) = [2] V1 + [2] V2 + [0] >= [2] V1 + [2] V2 + [0] = U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt(),V1,V2) = [2] V1 + [2] V2 + [0] >= [1] V2 + [0] = isPalListKind#(activate(V2)) U23#(tt(),V1,V2) = [2] V1 + [2] V2 + [0] >= [2] V1 + [2] V2 + [0] = U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt(),V1,V2) = [2] V1 + [2] V2 + [0] >= [1] V2 + [0] = isPalListKind#(activate(V2)) U24#(tt(),V1,V2) = [2] V1 + [2] V2 + [0] >= [2] V2 + [0] = U25#(isList(activate(V1)),activate(V2)) U24#(tt(),V1,V2) = [2] V1 + [2] V2 + [0] >= [2] V1 + [0] = isList#(activate(V1)) U25#(tt(),V2) = [2] V2 + [0] >= [2] V2 + [0] = isList#(activate(V2)) U31#(tt(),V) = [1] V + [0] >= [1] V + [0] = c_10(isPalListKind#(activate(V))) U41#(tt(),V1,V2) = [2] V1 + [2] V2 + [1] >= [2] V1 + [2] V2 + [1] = U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt(),V1,V2) = [2] V1 + [2] V2 + [1] >= [1] V1 + [0] = isPalListKind#(activate(V1)) U42#(tt(),V1,V2) = [2] V1 + [2] V2 + [1] >= [2] V1 + [2] V2 + [1] = U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt(),V1,V2) = [2] V1 + [2] V2 + [1] >= [1] V2 + [0] = isPalListKind#(activate(V2)) U43#(tt(),V1,V2) = [2] V1 + [2] V2 + [1] >= [2] V1 + [2] V2 + [1] = U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt(),V1,V2) = [2] V1 + [2] V2 + [1] >= [1] V2 + [0] = isPalListKind#(activate(V2)) U44#(tt(),V1,V2) = [2] V1 + [2] V2 + [1] >= [2] V1 + [2] V2 + [0] = U45#(isList(activate(V1)),activate(V2)) U44#(tt(),V1,V2) = [2] V1 + [2] V2 + [1] >= [2] V1 + [0] = isList#(activate(V1)) U45#(tt(),V2) = [2] V2 + [0] >= [2] V2 + [0] = isNeList#(activate(V2)) U51#(tt(),V1,V2) = [2] V1 + [2] V2 + [7] >= [2] V1 + [2] V2 + [7] = U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt(),V1,V2) = [2] V1 + [2] V2 + [7] >= [1] V1 + [0] = isPalListKind#(activate(V1)) U52#(tt(),V1,V2) = [2] V1 + [2] V2 + [7] >= [2] V1 + [2] V2 + [4] = U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt(),V1,V2) = [2] V1 + [2] V2 + [7] >= [1] V2 + [0] = isPalListKind#(activate(V2)) U53#(tt(),V1,V2) = [2] V1 + [2] V2 + [4] >= [2] V1 + [2] V2 + [0] = U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt(),V1,V2) = [2] V1 + [2] V2 + [4] >= [1] V2 + [0] = isPalListKind#(activate(V2)) U54#(tt(),V1,V2) = [2] V1 + [2] V2 + [0] >= [2] V2 + [0] = U55#(isNeList(activate(V1)),activate(V2)) U54#(tt(),V1,V2) = [2] V1 + [2] V2 + [0] >= [2] V1 + [0] = isNeList#(activate(V1)) U55#(tt(),V2) = [2] V2 + [0] >= [2] V2 + [0] = isList#(activate(V2)) U61#(tt(),V) = [2] V + [1] >= [1] V + [0] = isPalListKind#(activate(V)) U71#(tt(),I,P) = [1] I + [5] P + [6] >= [5] P + [6] = U72#(isPalListKind(activate(I)),activate(P)) U71#(tt(),I,P) = [1] I + [5] P + [6] >= [1] I + [0] = isPalListKind#(activate(I)) U72#(tt(),P) = [5] P + [6] >= [1] P + [2] = U73#(isPal(activate(P)),activate(P)) U72#(tt(),P) = [5] P + [6] >= [5] P + [1] = isPal#(activate(P)) U73#(tt(),P) = [1] P + [2] >= [1] P + [0] = isPalListKind#(activate(P)) U81#(tt(),V) = [5] V + [1] >= [5] V + [1] = U82#(isPalListKind(activate(V)),activate(V)) U81#(tt(),V) = [5] V + [1] >= [1] V + [0] = isPalListKind#(activate(V)) U82#(tt(),V) = [5] V + [1] >= [5] V + [1] = isNePal#(activate(V)) U91#(tt(),V2) = [1] V2 + [0] >= [1] V2 + [0] = c_35(isPalListKind#(activate(V2))) isList#(V) = [2] V + [0] >= [2] V + [0] = U11#(isPalListKind(activate(V)),activate(V)) isList#(V) = [2] V + [0] >= [1] V + [0] = isPalListKind#(activate(V)) isList#(n____(V1,V2)) = [2] V1 + [2] V2 + [14] >= [2] V1 + [2] V2 + [2] = U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList#(n____(V1,V2)) = [2] V1 + [2] V2 + [14] >= [1] V1 + [0] = isPalListKind#(activate(V1)) isNeList#(V) = [2] V + [0] >= [2] V + [0] = c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isNeList#(n____(V1,V2)) = [2] V1 + [2] V2 + [14] >= [2] V1 + [2] V2 + [1] = U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) = [2] V1 + [2] V2 + [14] >= [2] V1 + [2] V2 + [7] = U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) = [2] V1 + [2] V2 + [14] >= [1] V1 + [0] = isPalListKind#(activate(V1)) isNePal#(V) = [5] V + [1] >= [2] V + [1] = U61#(isPalListKind(activate(V)),activate(V)) isNePal#(V) = [5] V + [1] >= [1] V + [0] = isPalListKind#(activate(V)) isPal#(V) = [5] V + [1] >= [5] V + [1] = U81#(isPalListKind(activate(V)),activate(V)) isPal#(V) = [5] V + [1] >= [1] V + [0] = isPalListKind#(activate(V)) U11(tt(),V) = [1] V + [0] >= [0] = U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) = [0] >= [0] = U13(isNeList(activate(V))) U13(tt()) = [0] >= [0] = tt() U21(tt(),V1,V2) = [1] V1 + [1] V2 + [7] >= [1] V2 + [7] = U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) = [1] V2 + [7] >= [1] V2 + [6] = U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) = [1] V2 + [6] >= [1] V2 + [4] = U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) = [1] V2 + [4] >= [4] = U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) = [4] >= [1] = U26(isList(activate(V2))) U26(tt()) = [1] >= [0] = tt() __(X,nil()) = [1] X + [7] >= [1] X + [0] = X __(X1,X2) = [1] X1 + [1] X2 + [7] >= [1] X1 + [1] X2 + [7] = n____(X1,X2) __(__(X,Y),Z) = [1] X + [1] Y + [1] Z + [14] >= [1] X + [1] Y + [1] Z + [14] = __(X,__(Y,Z)) __(nil(),X) = [1] X + [7] >= [1] X + [0] = X a() = [0] >= [0] = n__a() activate(X) = [1] X + [0] >= [1] X + [0] = X activate(n____(X1,X2)) = [1] X1 + [1] X2 + [7] >= [1] X1 + [1] X2 + [7] = __(X1,X2) activate(n__a()) = [0] >= [0] = a() activate(n__e()) = [1] >= [1] = e() activate(n__i()) = [2] >= [2] = i() activate(n__nil()) = [0] >= [0] = nil() activate(n__o()) = [0] >= [0] = o() activate(n__u()) = [0] >= [0] = u() e() = [1] >= [1] = n__e() i() = [2] >= [2] = n__i() isList(V) = [1] V + [0] >= [1] V + [0] = U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) = [1] V1 + [1] V2 + [7] >= [1] V1 + [1] V2 + [7] = U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) = [0] >= [0] = tt() nil() = [0] >= [0] = n__nil() o() = [0] >= [0] = n__o() u() = [0] >= [0] = n__u() ** Step 8.b:3: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))) - Weak DPs: U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isPalListKind#(activate(V)) U12#(tt(),V) -> isNeList#(activate(V)) U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt(),V1,V2) -> isList#(activate(V1)) U25#(tt(),V2) -> isList#(activate(V2)) U31#(tt(),V) -> c_10(isPalListKind#(activate(V))) U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt(),V1,V2) -> isList#(activate(V1)) U45#(tt(),V2) -> isNeList#(activate(V2)) U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt(),V1,V2) -> isNeList#(activate(V1)) U55#(tt(),V2) -> isList#(activate(V2)) U61#(tt(),V) -> isPalListKind#(activate(V)) U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)) U71#(tt(),I,P) -> isPalListKind#(activate(I)) U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)) U72#(tt(),P) -> isPal#(activate(P)) U73#(tt(),P) -> isPalListKind#(activate(P)) U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)) U81#(tt(),V) -> isPalListKind#(activate(V)) U82#(tt(),V) -> isNePal#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) isList#(V) -> isPalListKind#(activate(V)) isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) isNePal#(V) -> isPalListKind#(activate(V)) isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)) isPal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(c_10) = {1}, uargs(c_35) = {1}, uargs(c_55) = {1,2}, uargs(c_62) = {1,2} Following symbols are considered usable: {__,a,activate,e,i,nil,o,u,U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32#,U33#,U41#,U42#,U43#,U44# ,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81#,U82#,U83#,U91#,U92#,__#,a# ,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o#,u#} TcT has computed the following interpretation: p(U11) = 0 p(U12) = 0 p(U13) = 1 + x1 p(U21) = 0 p(U22) = 0 p(U23) = 0 p(U24) = 0 p(U25) = 0 p(U26) = 0 p(U31) = 2*x1 p(U32) = 0 p(U33) = x1 p(U41) = 0 p(U42) = 2 p(U43) = 0 p(U44) = 0 p(U45) = 0 p(U46) = 0 p(U51) = 0 p(U52) = 0 p(U53) = 0 p(U54) = 0 p(U55) = 0 p(U56) = 0 p(U61) = 0 p(U62) = 0 p(U63) = 0 p(U71) = 0 p(U72) = 0 p(U73) = 0 p(U74) = 0 p(U81) = 0 p(U82) = 0 p(U83) = 0 p(U91) = 0 p(U92) = 0 p(__) = 2 + x1 + x2 p(a) = 0 p(activate) = x1 p(e) = 0 p(i) = 0 p(isList) = 0 p(isNeList) = 1 + x1 p(isNePal) = 0 p(isPal) = 0 p(isPalListKind) = 1 p(isQid) = 2*x1 p(n____) = 2 + x1 + x2 p(n__a) = 0 p(n__e) = 0 p(n__i) = 0 p(n__nil) = 3 p(n__o) = 0 p(n__u) = 0 p(nil) = 3 p(o) = 0 p(tt) = 0 p(u) = 0 p(U11#) = 3*x2 p(U12#) = 3*x2 p(U13#) = 0 p(U21#) = 3*x2 + 3*x3 p(U22#) = 3*x2 + 3*x3 p(U23#) = 3*x2 + 3*x3 p(U24#) = 3*x2 + 3*x3 p(U25#) = 3*x2 p(U26#) = 0 p(U31#) = 2*x2 p(U32#) = 0 p(U33#) = 0 p(U41#) = 3*x2 + 3*x3 p(U42#) = 3*x2 + 3*x3 p(U43#) = 3*x2 + 3*x3 p(U44#) = 3*x2 + 3*x3 p(U45#) = 3*x2 p(U46#) = 0 p(U51#) = 3 + 3*x2 + 3*x3 p(U52#) = 2 + 3*x2 + 3*x3 p(U53#) = 3*x2 + 3*x3 p(U54#) = 3*x2 + 3*x3 p(U55#) = 3*x2 p(U56#) = 0 p(U61#) = 2*x2 p(U62#) = 0 p(U63#) = 0 p(U71#) = 2*x2 + 2*x3 p(U72#) = 2*x2 p(U73#) = 2*x2 p(U74#) = 0 p(U81#) = 2*x2 p(U82#) = 2*x2 p(U83#) = 0 p(U91#) = 1 + x2 p(U92#) = 0 p(__#) = 0 p(a#) = 0 p(activate#) = 0 p(e#) = 0 p(i#) = 0 p(isList#) = 3*x1 p(isNeList#) = 3*x1 p(isNePal#) = 2*x1 p(isPal#) = 2*x1 p(isPalListKind#) = x1 p(isQid#) = 0 p(nil#) = 0 p(o#) = 0 p(u#) = 0 p(c_1) = 0 p(c_2) = 0 p(c_3) = 0 p(c_4) = 0 p(c_5) = x2 p(c_6) = x2 p(c_7) = 0 p(c_8) = x1 p(c_9) = 0 p(c_10) = x1 p(c_11) = 0 p(c_12) = 0 p(c_13) = 0 p(c_14) = x2 p(c_15) = x1 p(c_16) = x1 p(c_17) = 0 p(c_18) = 0 p(c_19) = 0 p(c_20) = 0 p(c_21) = 0 p(c_22) = 0 p(c_23) = 0 p(c_24) = 0 p(c_25) = 0 p(c_26) = 0 p(c_27) = 0 p(c_28) = x2 p(c_29) = 0 p(c_30) = 0 p(c_31) = 0 p(c_32) = x2 p(c_33) = 0 p(c_34) = 0 p(c_35) = x1 p(c_36) = 0 p(c_37) = 0 p(c_38) = 0 p(c_39) = 0 p(c_40) = 0 p(c_41) = 0 p(c_42) = 0 p(c_43) = x1 p(c_44) = x1 p(c_45) = x1 p(c_46) = 0 p(c_47) = 0 p(c_48) = 0 p(c_49) = 0 p(c_50) = 0 p(c_51) = 0 p(c_52) = 0 p(c_53) = 0 p(c_54) = 0 p(c_55) = x1 + x2 p(c_56) = 0 p(c_57) = 0 p(c_58) = x2 p(c_59) = 2 p(c_60) = 0 p(c_61) = 0 p(c_62) = 1 + x1 + x2 p(c_63) = 0 p(c_64) = 0 p(c_65) = 0 p(c_66) = 0 p(c_67) = 0 p(c_68) = 0 p(c_69) = 0 p(c_70) = 0 p(c_71) = 0 p(c_72) = 0 p(c_73) = 0 p(c_74) = 0 p(c_75) = 0 p(c_76) = 0 Following rules are strictly oriented: U91#(tt(),V2) = 1 + V2 > V2 = c_35(isPalListKind#(activate(V2))) Following rules are (at-least) weakly oriented: U11#(tt(),V) = 3*V >= 3*V = U12#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) = 3*V >= V = isPalListKind#(activate(V)) U12#(tt(),V) = 3*V >= 3*V = isNeList#(activate(V)) U21#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt(),V1,V2) = 3*V1 + 3*V2 >= V1 = isPalListKind#(activate(V1)) U22#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt(),V1,V2) = 3*V1 + 3*V2 >= V2 = isPalListKind#(activate(V2)) U23#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt(),V1,V2) = 3*V1 + 3*V2 >= V2 = isPalListKind#(activate(V2)) U24#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V2 = U25#(isList(activate(V1)),activate(V2)) U24#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 = isList#(activate(V1)) U25#(tt(),V2) = 3*V2 >= 3*V2 = isList#(activate(V2)) U31#(tt(),V) = 2*V >= V = c_10(isPalListKind#(activate(V))) U41#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt(),V1,V2) = 3*V1 + 3*V2 >= V1 = isPalListKind#(activate(V1)) U42#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt(),V1,V2) = 3*V1 + 3*V2 >= V2 = isPalListKind#(activate(V2)) U43#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt(),V1,V2) = 3*V1 + 3*V2 >= V2 = isPalListKind#(activate(V2)) U44#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V2 = U45#(isList(activate(V1)),activate(V2)) U44#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 = isList#(activate(V1)) U45#(tt(),V2) = 3*V2 >= 3*V2 = isNeList#(activate(V2)) U51#(tt(),V1,V2) = 3 + 3*V1 + 3*V2 >= 2 + 3*V1 + 3*V2 = U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt(),V1,V2) = 3 + 3*V1 + 3*V2 >= V1 = isPalListKind#(activate(V1)) U52#(tt(),V1,V2) = 2 + 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt(),V1,V2) = 2 + 3*V1 + 3*V2 >= V2 = isPalListKind#(activate(V2)) U53#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt(),V1,V2) = 3*V1 + 3*V2 >= V2 = isPalListKind#(activate(V2)) U54#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V2 = U55#(isNeList(activate(V1)),activate(V2)) U54#(tt(),V1,V2) = 3*V1 + 3*V2 >= 3*V1 = isNeList#(activate(V1)) U55#(tt(),V2) = 3*V2 >= 3*V2 = isList#(activate(V2)) U61#(tt(),V) = 2*V >= V = isPalListKind#(activate(V)) U71#(tt(),I,P) = 2*I + 2*P >= 2*P = U72#(isPalListKind(activate(I)),activate(P)) U71#(tt(),I,P) = 2*I + 2*P >= I = isPalListKind#(activate(I)) U72#(tt(),P) = 2*P >= 2*P = U73#(isPal(activate(P)),activate(P)) U72#(tt(),P) = 2*P >= 2*P = isPal#(activate(P)) U73#(tt(),P) = 2*P >= P = isPalListKind#(activate(P)) U81#(tt(),V) = 2*V >= 2*V = U82#(isPalListKind(activate(V)),activate(V)) U81#(tt(),V) = 2*V >= V = isPalListKind#(activate(V)) U82#(tt(),V) = 2*V >= 2*V = isNePal#(activate(V)) isList#(V) = 3*V >= 3*V = U11#(isPalListKind(activate(V)),activate(V)) isList#(V) = 3*V >= V = isPalListKind#(activate(V)) isList#(n____(V1,V2)) = 6 + 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList#(n____(V1,V2)) = 6 + 3*V1 + 3*V2 >= V1 = isPalListKind#(activate(V1)) isNeList#(V) = 3*V >= 3*V = c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isNeList#(n____(V1,V2)) = 6 + 3*V1 + 3*V2 >= 3*V1 + 3*V2 = U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) = 6 + 3*V1 + 3*V2 >= 3 + 3*V1 + 3*V2 = U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) = 6 + 3*V1 + 3*V2 >= V1 = isPalListKind#(activate(V1)) isNePal#(V) = 2*V >= 2*V = U61#(isPalListKind(activate(V)),activate(V)) isNePal#(V) = 2*V >= V = isPalListKind#(activate(V)) isPal#(V) = 2*V >= 2*V = U81#(isPalListKind(activate(V)),activate(V)) isPal#(V) = 2*V >= V = isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) = 2 + V1 + V2 >= 2 + V1 + V2 = c_62(U91#(isPalListKind(activate(V1)),activate(V2)),isPalListKind#(activate(V1))) __(X,nil()) = 5 + X >= X = X __(X1,X2) = 2 + X1 + X2 >= 2 + X1 + X2 = n____(X1,X2) __(__(X,Y),Z) = 4 + X + Y + Z >= 4 + X + Y + Z = __(X,__(Y,Z)) __(nil(),X) = 5 + X >= X = X a() = 0 >= 0 = n__a() activate(X) = X >= X = X activate(n____(X1,X2)) = 2 + X1 + X2 >= 2 + X1 + X2 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__nil()) = 3 >= 3 = nil() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() nil() = 3 >= 3 = n__nil() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() ** Step 8.b:4: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak DPs: U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isPalListKind#(activate(V)) U12#(tt(),V) -> isNeList#(activate(V)) U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)) U24#(tt(),V1,V2) -> isList#(activate(V1)) U25#(tt(),V2) -> isList#(activate(V2)) U31#(tt(),V) -> c_10(isPalListKind#(activate(V))) U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)) U44#(tt(),V1,V2) -> isList#(activate(V1)) U45#(tt(),V2) -> isNeList#(activate(V2)) U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)) U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)) U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)) U54#(tt(),V1,V2) -> isNeList#(activate(V1)) U55#(tt(),V2) -> isList#(activate(V2)) U61#(tt(),V) -> isPalListKind#(activate(V)) U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)) U71#(tt(),I,P) -> isPalListKind#(activate(I)) U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)) U72#(tt(),P) -> isPal#(activate(P)) U73#(tt(),P) -> isPalListKind#(activate(P)) U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)) U81#(tt(),V) -> isPalListKind#(activate(V)) U82#(tt(),V) -> isNePal#(activate(V)) U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) isList#(V) -> isPalListKind#(activate(V)) isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(V) -> c_55(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))) isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) isNePal#(V) -> isPalListKind#(activate(V)) isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)) isPal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> c_62(U91#(isPalListKind(activate(V1)),activate(V2)) ,isPalListKind#(activate(V1))) - Weak TRS: U11(tt(),V) -> U12(isPalListKind(activate(V)),activate(V)) U12(tt(),V) -> U13(isNeList(activate(V))) U13(tt()) -> tt() U21(tt(),V1,V2) -> U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) U22(tt(),V1,V2) -> U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) U23(tt(),V1,V2) -> U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) U24(tt(),V1,V2) -> U25(isList(activate(V1)),activate(V2)) U25(tt(),V2) -> U26(isList(activate(V2))) U26(tt()) -> tt() U31(tt(),V) -> U32(isPalListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isQid(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isList(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNeList(activate(V2))) U46(tt()) -> tt() U51(tt(),V1,V2) -> U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) U52(tt(),V1,V2) -> U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) U53(tt(),V1,V2) -> U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) U54(tt(),V1,V2) -> U55(isNeList(activate(V1)),activate(V2)) U55(tt(),V2) -> U56(isList(activate(V2))) U56(tt()) -> tt() U61(tt(),V) -> U62(isPalListKind(activate(V)),activate(V)) U62(tt(),V) -> U63(isQid(activate(V))) U63(tt()) -> tt() U71(tt(),I,P) -> U72(isPalListKind(activate(I)),activate(P)) U72(tt(),P) -> U73(isPal(activate(P)),activate(P)) U73(tt(),P) -> U74(isPalListKind(activate(P))) U74(tt()) -> tt() U81(tt(),V) -> U82(isPalListKind(activate(V)),activate(V)) U82(tt(),V) -> U83(isNePal(activate(V))) U83(tt()) -> tt() U91(tt(),V2) -> U92(isPalListKind(activate(V2))) U92(tt()) -> tt() __(X,nil()) -> X __(X1,X2) -> n____(X1,X2) __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X a() -> n__a() activate(X) -> X activate(n____(X1,X2)) -> __(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__nil()) -> nil() activate(n__o()) -> o() activate(n__u()) -> u() e() -> n__e() i() -> n__i() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n____(V1,V2)) -> U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) isList(n__nil()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(I),activate(P)) isPal(V) -> U81(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n____(V1,V2)) -> U91(isPalListKind(activate(V1)),activate(V2)) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() o() -> n__o() u() -> n__u() - Signature: {U11/2,U12/2,U13/1,U21/3,U22/3,U23/3,U24/3,U25/2,U26/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1 ,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/3,U72/2,U73/2,U74/1,U81/2,U82/2,U83/1,U91/2,U92/1 ,__/2,a/0,activate/1,e/0,i/0,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,nil/0,o/0,u/0 ,U11#/2,U12#/2,U13#/1,U21#/3,U22#/3,U23#/3,U24#/3,U25#/2,U26#/1,U31#/2,U32#/2,U33#/1,U41#/3,U42#/3,U43#/3 ,U44#/3,U45#/2,U46#/1,U51#/3,U52#/3,U53#/3,U54#/3,U55#/2,U56#/1,U61#/2,U62#/2,U63#/1,U71#/3,U72#/2,U73#/2 ,U74#/1,U81#/2,U82#/2,U83#/1,U91#/2,U92#/1,__#/2,a#/0,activate#/1,e#/0,i#/0,isList#/1,isNeList#/1,isNePal#/1 ,isPal#/1,isPalListKind#/1,isQid#/1,nil#/0,o#/0,u#/0} / {n____/2,n__a/0,n__e/0,n__i/0,n__nil/0,n__o/0,n__u/0 ,tt/0,c_1/2,c_2/1,c_3/0,c_4/2,c_5/2,c_6/2,c_7/2,c_8/1,c_9/0,c_10/1,c_11/3,c_12/0,c_13/2,c_14/2,c_15/2,c_16/2 ,c_17/1,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2,c_23/1,c_24/0,c_25/1,c_26/3,c_27/0,c_28/2,c_29/2,c_30/1,c_31/0 ,c_32/2,c_33/1,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/2,c_40/0,c_41/0,c_42/0,c_43/1,c_44/1,c_45/1,c_46/1 ,c_47/1,c_48/1,c_49/1,c_50/0,c_51/0,c_52/2,c_53/2,c_54/0,c_55/2,c_56/2,c_57/2,c_58/2,c_59/5,c_60/2,c_61/0 ,c_62/2,c_63/0,c_64/0,c_65/0,c_66/0,c_67/0,c_68/0,c_69/0,c_70/0,c_71/0,c_72/0,c_73/0,c_74/0,c_75/0,c_76/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U13#,U21#,U22#,U23#,U24#,U25#,U26#,U31#,U32# ,U33#,U41#,U42#,U43#,U44#,U45#,U46#,U51#,U52#,U53#,U54#,U55#,U56#,U61#,U62#,U63#,U71#,U72#,U73#,U74#,U81# ,U82#,U83#,U91#,U92#,__#,a#,activate#,e#,i#,isList#,isNeList#,isNePal#,isPal#,isPalListKind#,isQid#,nil#,o# ,u#} and constructors {n____,n__a,n__e,n__i,n__nil,n__o,n__u,tt} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^2))