* Step 1: Sum WORST_CASE(Omega(n^1),O(n^3))
+ 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)) -> __(activate(X1),activate(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,n____(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 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ 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)) -> __(activate(X1),activate(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,n____(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:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
activate(x){x -> n____(x,y)} =
activate(n____(x,y)) ->^+ __(activate(x),activate(y))
= C[activate(x) = activate(x){}]
** Step 1.b:1: InnermostRuleRemoval WORST_CASE(?,O(n^3))
+ 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)) -> __(activate(X1),activate(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,n____(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:
InnermostRuleRemoval
+ Details:
Arguments of following rules are not normal-forms.
__(X,nil()) -> X
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(nil(),X) -> X
All above mentioned rules can be savely removed.
** Step 1.b:2: DependencyPairs WORST_CASE(?,O(n^3))
+ 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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()
__#(X1,X2) -> c_37()
a#() -> c_38()
activate#(X) -> c_39()
activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
activate#(n__a()) -> c_41(a#())
activate#(n__e()) -> c_42(e#())
activate#(n__i()) -> c_43(i#())
activate#(n__nil()) -> c_44(nil#())
activate#(n__o()) -> c_45(o#())
activate#(n__u()) -> c_46(u#())
e#() -> c_47()
i#() -> c_48()
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isList#(n__nil()) -> c_51()
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isPal#(n__nil()) -> c_58()
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
isPalListKind#(n__a()) -> c_60()
isPalListKind#(n__e()) -> c_61()
isPalListKind#(n__i()) -> c_62()
isPalListKind#(n__nil()) -> c_63()
isPalListKind#(n__o()) -> c_64()
isPalListKind#(n__u()) -> c_65()
isQid#(n__a()) -> c_66()
isQid#(n__e()) -> c_67()
isQid#(n__i()) -> c_68()
isQid#(n__o()) -> c_69()
isQid#(n__u()) -> c_70()
nil#() -> c_71()
o#() -> c_72()
u#() -> c_73()
Weak DPs
and mark the set of starting terms.
** Step 1.b:3: PredecessorEstimation WORST_CASE(?,O(n^3))
+ 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()
__#(X1,X2) -> c_37()
a#() -> c_38()
activate#(X) -> c_39()
activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
activate#(n__a()) -> c_41(a#())
activate#(n__e()) -> c_42(e#())
activate#(n__i()) -> c_43(i#())
activate#(n__nil()) -> c_44(nil#())
activate#(n__o()) -> c_45(o#())
activate#(n__u()) -> c_46(u#())
e#() -> c_47()
i#() -> c_48()
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isList#(n__nil()) -> c_51()
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isPal#(n__nil()) -> c_58()
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
isPalListKind#(n__a()) -> c_60()
isPalListKind#(n__e()) -> c_61()
isPalListKind#(n__i()) -> c_62()
isPalListKind#(n__nil()) -> c_63()
isPalListKind#(n__o()) -> c_64()
isPalListKind#(n__u()) -> c_65()
isQid#(n__a()) -> c_66()
isQid#(n__e()) -> c_67()
isQid#(n__i()) -> c_68()
isQid#(n__o()) -> c_69()
isQid#(n__u()) -> c_70()
nil#() -> c_71()
o#() -> c_72()
u#() -> c_73()
- 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_39/0,c_40/3,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/5,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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
{3,9,12,18,24,27,31,34,36,37,38,39,47,48,51,58,60,61,62,63,64,65,66,67,68,69,70,71,72,73}
by application of
Pre({3,9,12,18,24,27,31,34,36,37,38,39,47,48,51,58,60,61,62,63,64,65,66,67,68,69,70,71,72,73}) = {1,2,4,5
,6,7,8,10,11,13,14,15,16,17,19,20,21,22,23,25,26,28,29,30,32,33,35,40,41,42,43,44,45,46,49,50,52,53,54,55,56
,57,59}.
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: __#(X1,X2) -> c_37()
38: a#() -> c_38()
39: activate#(X) -> c_39()
40: activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
41: activate#(n__a()) -> c_41(a#())
42: activate#(n__e()) -> c_42(e#())
43: activate#(n__i()) -> c_43(i#())
44: activate#(n__nil()) -> c_44(nil#())
45: activate#(n__o()) -> c_45(o#())
46: activate#(n__u()) -> c_46(u#())
47: e#() -> c_47()
48: i#() -> c_48()
49: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
50: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
51: isList#(n__nil()) -> c_51()
52: isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
53: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
54: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
55: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
56: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P))
57: isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
58: isPal#(n__nil()) -> c_58()
59: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
60: isPalListKind#(n__a()) -> c_60()
61: isPalListKind#(n__e()) -> c_61()
62: isPalListKind#(n__i()) -> c_62()
63: isPalListKind#(n__nil()) -> c_63()
64: isPalListKind#(n__o()) -> c_64()
65: isPalListKind#(n__u()) -> c_65()
66: isQid#(n__a()) -> c_66()
67: isQid#(n__e()) -> c_67()
68: isQid#(n__i()) -> c_68()
69: isQid#(n__o()) -> c_69()
70: isQid#(n__u()) -> c_70()
71: nil#() -> c_71()
72: o#() -> c_72()
73: u#() -> c_73()
** Step 1.b:4: PredecessorEstimation WORST_CASE(?,O(n^3))
+ 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_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
activate#(n__a()) -> c_41(a#())
activate#(n__e()) -> c_42(e#())
activate#(n__i()) -> c_43(i#())
activate#(n__nil()) -> c_44(nil#())
activate#(n__o()) -> c_45(o#())
activate#(n__u()) -> c_46(u#())
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__#(X1,X2) -> c_37()
a#() -> c_38()
activate#(X) -> c_39()
e#() -> c_47()
i#() -> c_48()
isList#(n__nil()) -> c_51()
isPal#(n__nil()) -> c_58()
isPalListKind#(n__a()) -> c_60()
isPalListKind#(n__e()) -> c_61()
isPalListKind#(n__i()) -> c_62()
isPalListKind#(n__nil()) -> c_63()
isPalListKind#(n__o()) -> c_64()
isPalListKind#(n__u()) -> c_65()
isQid#(n__a()) -> c_66()
isQid#(n__e()) -> c_67()
isQid#(n__i()) -> c_68()
isQid#(n__o()) -> c_69()
isQid#(n__u()) -> c_70()
nil#() -> c_71()
o#() -> c_72()
u#() -> c_73()
- 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_39/0,c_40/3,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/5,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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
{29,30,31,32,33,34}
by application of
Pre({29,30,31,32,33,34}) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,35
,36,37,38,39,40,41,42,43}.
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_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
29: activate#(n__a()) -> c_41(a#())
30: activate#(n__e()) -> c_42(e#())
31: activate#(n__i()) -> c_43(i#())
32: activate#(n__nil()) -> c_44(nil#())
33: activate#(n__o()) -> c_45(o#())
34: activate#(n__u()) -> c_46(u#())
35: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
36: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
37: isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
38: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
39: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
40: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
41: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P))
42: isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
43: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
44: U13#(tt()) -> c_3()
45: U26#(tt()) -> c_9()
46: U33#(tt()) -> c_12()
47: U46#(tt()) -> c_18()
48: U56#(tt()) -> c_24()
49: U63#(tt()) -> c_27()
50: U74#(tt()) -> c_31()
51: U83#(tt()) -> c_34()
52: U92#(tt()) -> c_36()
53: __#(X1,X2) -> c_37()
54: a#() -> c_38()
55: activate#(X) -> c_39()
56: e#() -> c_47()
57: i#() -> c_48()
58: isList#(n__nil()) -> c_51()
59: isPal#(n__nil()) -> c_58()
60: isPalListKind#(n__a()) -> c_60()
61: isPalListKind#(n__e()) -> c_61()
62: isPalListKind#(n__i()) -> c_62()
63: isPalListKind#(n__nil()) -> c_63()
64: isPalListKind#(n__o()) -> c_64()
65: isPalListKind#(n__u()) -> c_65()
66: isQid#(n__a()) -> c_66()
67: isQid#(n__e()) -> c_67()
68: isQid#(n__i()) -> c_68()
69: isQid#(n__o()) -> c_69()
70: isQid#(n__u()) -> c_70()
71: nil#() -> c_71()
72: o#() -> c_72()
73: u#() -> c_73()
** Step 1.b:5: RemoveWeakSuffixes WORST_CASE(?,O(n^3))
+ 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_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__#(X1,X2) -> c_37()
a#() -> c_38()
activate#(X) -> c_39()
activate#(n__a()) -> c_41(a#())
activate#(n__e()) -> c_42(e#())
activate#(n__i()) -> c_43(i#())
activate#(n__nil()) -> c_44(nil#())
activate#(n__o()) -> c_45(o#())
activate#(n__u()) -> c_46(u#())
e#() -> c_47()
i#() -> c_48()
isList#(n__nil()) -> c_51()
isPal#(n__nil()) -> c_58()
isPalListKind#(n__a()) -> c_60()
isPalListKind#(n__e()) -> c_61()
isPalListKind#(n__i()) -> c_62()
isPalListKind#(n__nil()) -> c_63()
isPalListKind#(n__o()) -> c_64()
isPalListKind#(n__u()) -> c_65()
isQid#(n__a()) -> c_66()
isQid#(n__e()) -> c_67()
isQid#(n__i()) -> c_68()
isQid#(n__o()) -> c_69()
isQid#(n__u()) -> c_70()
nil#() -> c_71()
o#() -> c_72()
u#() -> c_73()
- 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_39/0,c_40/3,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/5,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V)):2
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
2:S:U12#(tt(),V) -> c_2(U13#(isNeList(activate(V))),isNeList#(activate(V)),activate#(V))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):33
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_2 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(X) -> c_39():49
-->_1 U13#(tt()) -> c_3():38
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_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
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_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
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_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
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_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):30
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):29
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)):7
-->_2 isList#(n__nil()) -> c_51():58
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
7:S:U25#(tt(),V2) -> c_8(U26#(isList(activate(V2))),isList#(activate(V2)),activate#(V2))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):30
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):29
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_2 isList#(n__nil()) -> c_51():58
-->_3 activate#(X) -> c_39():49
-->_1 U26#(tt()) -> c_9():39
8:S:U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
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,activate#(V)
,activate#(V))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)):9
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
9:S:U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_2 isQid#(n__u()) -> c_70():70
-->_2 isQid#(n__o()) -> c_69():69
-->_2 isQid#(n__i()) -> c_68():68
-->_2 isQid#(n__e()) -> c_67():67
-->_2 isQid#(n__a()) -> c_66():66
-->_3 activate#(X) -> c_39():49
-->_1 U33#(tt()) -> c_12():40
10: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_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):11
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
11:S:U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
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,activate#(V1)
,activate#(V2))
-->_5 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):12
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
12:S:U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
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,activate#(V1)
,activate#(V2))
-->_5 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2)):13
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
13: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_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):30
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):29
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)):14
-->_2 isList#(n__nil()) -> c_51():58
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
14:S:U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):33
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_2 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(X) -> c_39():49
-->_1 U46#(tt()) -> c_18():41
15: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_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):16
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
16:S:U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
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,activate#(V1)
,activate#(V2))
-->_5 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
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,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):17
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
17:S:U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
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,activate#(V1)
,activate#(V2))
-->_5 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
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,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2)):18
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
18:S:U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
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,activate#(V1)
,activate#(V2))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):33
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_2 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)):19
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
19:S:U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):30
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):29
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_2 isList#(n__nil()) -> c_51():58
-->_3 activate#(X) -> c_39():49
-->_1 U56#(tt()) -> c_24():42
20:S:U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)):21
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
21:S:U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_2 isQid#(n__u()) -> c_70():70
-->_2 isQid#(n__o()) -> c_69():69
-->_2 isQid#(n__i()) -> c_68():68
-->_2 isQid#(n__e()) -> c_67():67
-->_2 isQid#(n__a()) -> c_66():66
-->_3 activate#(X) -> c_39():49
-->_1 U63#(tt()) -> c_27():43
22: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_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P))
,isPal#(activate(P))
,activate#(P)
,activate#(P)):23
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
23:S:U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P))
,isPal#(activate(P))
,activate#(P)
,activate#(P))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):36
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)):24
-->_2 isPal#(n__nil()) -> c_58():59
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
24:S:U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_3 activate#(X) -> c_39():49
-->_1 U74#(tt()) -> c_31():44
25:S:U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)):26
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
26:S:U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P)):35
-->_2 isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):34
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(X) -> c_39():49
-->_1 U83#(tt()) -> c_34():45
27:S:U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_3 activate#(X) -> c_39():49
-->_1 U92#(tt()) -> c_36():46
28:S:activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_2 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_2 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_2 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_2 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_2 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(X) -> c_39():49
-->_2 activate#(X) -> c_39():49
-->_1 __#(X1,X2) -> c_37():47
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_2 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
29:S:isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):1
30:S:isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_5 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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
31:S:isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):8
32:S:isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_5 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):10
33:S:isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_5 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):15
34:S:isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):20
35:S:isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P))
-->_5 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_5 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_5 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_5 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_5 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_5 activate#(n__a()) -> c_41(a#()):50
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isQid#(n__u()) -> c_70():70
-->_2 isQid#(n__o()) -> c_69():69
-->_2 isQid#(n__i()) -> c_68():68
-->_2 isQid#(n__e()) -> c_67():67
-->_2 isQid#(n__a()) -> c_66():66
-->_5 activate#(X) -> c_39():49
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P)):22
36:S:isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):25
37:S:isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
-->_4 activate#(n__u()) -> c_46(u#()):55
-->_3 activate#(n__u()) -> c_46(u#()):55
-->_4 activate#(n__o()) -> c_45(o#()):54
-->_3 activate#(n__o()) -> c_45(o#()):54
-->_4 activate#(n__nil()) -> c_44(nil#()):53
-->_3 activate#(n__nil()) -> c_44(nil#()):53
-->_4 activate#(n__i()) -> c_43(i#()):52
-->_3 activate#(n__i()) -> c_43(i#()):52
-->_4 activate#(n__e()) -> c_42(e#()):51
-->_3 activate#(n__e()) -> c_42(e#()):51
-->_4 activate#(n__a()) -> c_41(a#()):50
-->_3 activate#(n__a()) -> c_41(a#()):50
-->_2 isPalListKind#(n__u()) -> c_65():65
-->_2 isPalListKind#(n__o()) -> c_64():64
-->_2 isPalListKind#(n__nil()) -> c_63():63
-->_2 isPalListKind#(n__i()) -> c_62():62
-->_2 isPalListKind#(n__e()) -> c_61():61
-->_2 isPalListKind#(n__a()) -> c_60():60
-->_4 activate#(X) -> c_39():49
-->_3 activate#(X) -> c_39():49
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2)))
,isPalListKind#(activate(V2))
,activate#(V2)):27
38:W:U13#(tt()) -> c_3()
39:W:U26#(tt()) -> c_9()
40:W:U33#(tt()) -> c_12()
41:W:U46#(tt()) -> c_18()
42:W:U56#(tt()) -> c_24()
43:W:U63#(tt()) -> c_27()
44:W:U74#(tt()) -> c_31()
45:W:U83#(tt()) -> c_34()
46:W:U92#(tt()) -> c_36()
47:W:__#(X1,X2) -> c_37()
48:W:a#() -> c_38()
49:W:activate#(X) -> c_39()
50:W:activate#(n__a()) -> c_41(a#())
-->_1 a#() -> c_38():48
51:W:activate#(n__e()) -> c_42(e#())
-->_1 e#() -> c_47():56
52:W:activate#(n__i()) -> c_43(i#())
-->_1 i#() -> c_48():57
53:W:activate#(n__nil()) -> c_44(nil#())
-->_1 nil#() -> c_71():71
54:W:activate#(n__o()) -> c_45(o#())
-->_1 o#() -> c_72():72
55:W:activate#(n__u()) -> c_46(u#())
-->_1 u#() -> c_73():73
56:W:e#() -> c_47()
57:W:i#() -> c_48()
58:W:isList#(n__nil()) -> c_51()
59:W:isPal#(n__nil()) -> c_58()
60:W:isPalListKind#(n__a()) -> c_60()
61:W:isPalListKind#(n__e()) -> c_61()
62:W:isPalListKind#(n__i()) -> c_62()
63:W:isPalListKind#(n__nil()) -> c_63()
64:W:isPalListKind#(n__o()) -> c_64()
65:W:isPalListKind#(n__u()) -> c_65()
66:W:isQid#(n__a()) -> c_66()
67:W:isQid#(n__e()) -> c_67()
68:W:isQid#(n__i()) -> c_68()
69:W:isQid#(n__o()) -> c_69()
70:W:isQid#(n__u()) -> c_70()
71:W:nil#() -> c_71()
72:W:o#() -> c_72()
73:W:u#() -> c_73()
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
59: isPal#(n__nil()) -> c_58()
44: U74#(tt()) -> c_31()
45: U83#(tt()) -> c_34()
43: U63#(tt()) -> c_27()
38: U13#(tt()) -> c_3()
42: U56#(tt()) -> c_24()
41: U46#(tt()) -> c_18()
40: U33#(tt()) -> c_12()
66: isQid#(n__a()) -> c_66()
67: isQid#(n__e()) -> c_67()
68: isQid#(n__i()) -> c_68()
69: isQid#(n__o()) -> c_69()
70: isQid#(n__u()) -> c_70()
39: U26#(tt()) -> c_9()
58: isList#(n__nil()) -> c_51()
46: U92#(tt()) -> c_36()
47: __#(X1,X2) -> c_37()
49: activate#(X) -> c_39()
60: isPalListKind#(n__a()) -> c_60()
61: isPalListKind#(n__e()) -> c_61()
62: isPalListKind#(n__i()) -> c_62()
63: isPalListKind#(n__nil()) -> c_63()
64: isPalListKind#(n__o()) -> c_64()
65: isPalListKind#(n__u()) -> c_65()
50: activate#(n__a()) -> c_41(a#())
48: a#() -> c_38()
51: activate#(n__e()) -> c_42(e#())
56: e#() -> c_47()
52: activate#(n__i()) -> c_43(i#())
57: i#() -> c_48()
53: activate#(n__nil()) -> c_44(nil#())
71: nil#() -> c_71()
54: activate#(n__o()) -> c_45(o#())
72: o#() -> c_72()
55: activate#(n__u()) -> c_46(u#())
73: u#() -> c_73()
** Step 1.b:6: SimplifyRHS WORST_CASE(?,O(n^3))
+ 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_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_39/0,c_40/3,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/5,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):33
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_2 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):30
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):29
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):30
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):29
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V)):9
9:S:U32#(tt(),V) -> c_11(U33#(isQid(activate(V))),isQid#(activate(V)),activate#(V))
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
10: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):11
11: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):12
12: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2)):13
13: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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):30
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):29
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2)):14
14:S:U45#(tt(),V2) -> c_17(U46#(isNeList(activate(V2))),isNeList#(activate(V2)),activate#(V2))
-->_2 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):33
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_2 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
15: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):16
16: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):17
17: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2)):18
18: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_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):33
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_2 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2)):19
19:S:U55#(tt(),V2) -> c_23(U56#(isList(activate(V2))),isList#(activate(V2)),activate#(V2))
-->_2 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):30
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):29
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
20: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V)):21
21:S:U62#(tt(),V) -> c_26(U63#(isQid(activate(V))),isQid#(activate(V)),activate#(V))
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
22: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P))
,isPal#(activate(P))
,activate#(P)
,activate#(P)):23
23:S:U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P))
,isPal#(activate(P))
,activate#(P)
,activate#(P))
-->_2 isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):36
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P)):24
24:S:U73#(tt(),P) -> c_30(U74#(isPalListKind(activate(P))),isPalListKind#(activate(P)),activate#(P))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
25: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V)):26
26:S:U82#(tt(),V) -> c_33(U83#(isNePal(activate(V))),isNePal#(activate(V)),activate#(V))
-->_2 isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P)):35
-->_2 isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):34
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
27:S:U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2))),isPalListKind#(activate(V2)),activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
28:S:activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_2 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
29:S:isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):1
30:S:isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_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
31:S:isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):8
32:S:isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):10
33:S:isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):15
34:S:isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):20
35:S:isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,isQid#(activate(I))
,activate#(I)
,activate#(I)
,activate#(P))
-->_5 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P)):22
36:S:isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):25
37:S:isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_3 activate#(n____(X1,X2)) -> c_40(__#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):28
-->_1 U91#(tt(),V2) -> c_35(U92#(isPalListKind(activate(V2)))
,isPalListKind#(activate(V2))
,activate#(V2)):27
Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V))
U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2))
U32#(tt(),V) -> c_11(activate#(V))
U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2))
U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2))
U62#(tt(),V) -> c_26(activate#(V))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
** Step 1.b:7: Decompose WORST_CASE(?,O(n^3))
+ 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(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(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(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(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(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(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(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(isNePal#(activate(V)),activate#(V))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
+ Details:
We analyse the complexity of following sub-problems (R) and (S).
Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
Problem (R)
- 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(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(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(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(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(isList#(activate(V2)),activate#(V2))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
- Weak DPs:
U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U62#(tt(),V) -> c_26(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(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(isNePal#(activate(V)),activate#(V))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1
,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1
,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1
,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4
,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0,c_62/0,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}
- 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}
Problem (S)
- Strict DPs:
U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U62#(tt(),V) -> c_26(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(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(isNePal#(activate(V)),activate#(V))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
- Weak DPs:
U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U12#(tt(),V) -> c_2(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(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(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(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(isList#(activate(V2)),activate#(V2))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1
,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1
,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1
,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4
,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0,c_62/0,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}
- 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}
*** Step 1.b:7.a:1: DecomposeDG WORST_CASE(?,O(n^3))
+ 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(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(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(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(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(isList#(activate(V2)),activate#(V2))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
- Weak DPs:
U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U62#(tt(),V) -> c_26(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(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(isNePal#(activate(V)),activate#(V))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = Just someStrategy, 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))
,activate#(V)
,activate#(V))
U12#(tt(),V) -> c_2(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(isList#(activate(V2)),activate#(V2))
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(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(isList#(activate(V2)),activate#(V2))
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))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
and a lower component
U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U32#(tt(),V) -> c_11(activate#(V))
U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U62#(tt(),V) -> c_26(activate#(V))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
Further, following extension rules are added to the lower component.
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
U25#(tt(),V2) -> isList#(activate(V2))
U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(activate(V2))
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> activate#(V)
U82#(tt(),V) -> isNePal#(activate(V))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(V) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> 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)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) -> activate#(V)
isPal#(V) -> isPalListKind#(activate(V))
**** Step 1.b:7.a:1.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
+ 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(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(isList#(activate(V2)),activate#(V2))
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(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(isList#(activate(V2)),activate#(V2))
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))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
18: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P))
Consider the set of all dependency pairs
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(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(isList#(activate(V2)),activate#(V2))
8: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
11: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2))
12: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2))
13: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
16: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2))
17: U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2))
18: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P))
19: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P))
20: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
21: U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
22: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
23: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
24: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
25: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
26: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
27: isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
Processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
SPACE(?,?)on application of the dependency pairs
{18}
These cover all (indirect) predecessors of dependency pairs
{18,19,20,21,26,27}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
***** Step 1.b:7.a:1.a:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
+ 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(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(isList#(activate(V2)),activate#(V2))
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(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(isList#(activate(V2)),activate#(V2))
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))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
The following argument positions are considered usable:
uargs(c_1) = {1,2},
uargs(c_2) = {1},
uargs(c_4) = {1,2},
uargs(c_5) = {1,2},
uargs(c_6) = {1,2},
uargs(c_7) = {1,2},
uargs(c_8) = {1},
uargs(c_13) = {1,2},
uargs(c_14) = {1,2},
uargs(c_15) = {1,2},
uargs(c_16) = {1,2},
uargs(c_17) = {1},
uargs(c_19) = {1,2},
uargs(c_20) = {1,2},
uargs(c_21) = {1,2},
uargs(c_22) = {1,2},
uargs(c_23) = {1},
uargs(c_28) = {1,2},
uargs(c_29) = {1,2},
uargs(c_32) = {1,2},
uargs(c_33) = {1},
uargs(c_49) = {1,2},
uargs(c_50) = {1,2},
uargs(c_53) = {1,2},
uargs(c_54) = {1,2},
uargs(c_56) = {1},
uargs(c_57) = {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 0] x2 + [0]
[1 0] [0]
p(U12) = [0 0] x2 + [0]
[0 1] [0]
p(U13) = [0 1] x1 + [1]
[0 1] [0]
p(U21) = [0 0] x2 + [1]
[1 0] [1]
p(U22) = [0]
[1]
p(U23) = [1]
[1]
p(U24) = [0 0] x3 + [0]
[1 1] [1]
p(U25) = [0]
[0]
p(U26) = [0]
[1]
p(U31) = [1 0] x2 + [0]
[0 0] [1]
p(U32) = [1 0] x2 + [1]
[0 0] [0]
p(U33) = [0 1] x1 + [0]
[1 0] [0]
p(U41) = [1]
[0]
p(U42) = [1 0] x2 + [0]
[1 0] [1]
p(U43) = [0 0] x3 + [1]
[1 0] [0]
p(U44) = [0 0] x2 + [0]
[1 0] [1]
p(U45) = [1]
[1]
p(U46) = [0]
[0]
p(U51) = [1]
[1]
p(U52) = [1]
[1]
p(U53) = [1 0] x2 + [1]
[1 0] [0]
p(U54) = [0]
[0]
p(U55) = [0 0] x1 + [0 0] x2 + [1]
[0 1] [1 0] [0]
p(U56) = [1]
[1]
p(U61) = [0]
[0]
p(U62) = [0]
[1]
p(U63) = [0 1] x1 + [0]
[1 0] [0]
p(U71) = [0 0] x3 + [0]
[1 0] [0]
p(U72) = [1]
[0]
p(U73) = [0 0] x2 + [0]
[1 0] [1]
p(U74) = [1]
[0]
p(U81) = [1]
[0]
p(U82) = [1]
[0]
p(U83) = [1 0] x1 + [0]
[1 1] [0]
p(U91) = [0 0] x2 + [1]
[1 0] [1]
p(U92) = [0]
[1]
p(__) = [1 1] x1 + [1 0] x2 + [0]
[0 0] [0 0] [1]
p(a) = [0]
[0]
p(activate) = [1 0] x1 + [0]
[0 1] [0]
p(e) = [1]
[0]
p(i) = [0]
[1]
p(isList) = [1 0] x1 + [0]
[1 0] [0]
p(isNeList) = [0 0] x1 + [0]
[0 1] [1]
p(isNePal) = [1]
[1]
p(isPal) = [0]
[0]
p(isPalListKind) = [0]
[0]
p(isQid) = [1 1] x1 + [0]
[0 1] [1]
p(n____) = [1 1] x1 + [1 0] x2 + [0]
[0 0] [0 0] [1]
p(n__a) = [0]
[0]
p(n__e) = [1]
[0]
p(n__i) = [0]
[1]
p(n__nil) = [1]
[0]
p(n__o) = [0]
[1]
p(n__u) = [0]
[0]
p(nil) = [1]
[0]
p(o) = [0]
[1]
p(tt) = [0]
[0]
p(u) = [0]
[0]
p(U11#) = [1 0] x2 + [0]
[1 1] [1]
p(U12#) = [1 0] x2 + [0]
[0 0] [1]
p(U13#) = [0]
[0]
p(U21#) = [1 1] x2 + [1 0] x3 + [0]
[1 0] [0 0] [1]
p(U22#) = [1 0] x2 + [1 0] x3 + [0]
[1 0] [0 0] [0]
p(U23#) = [1 0] x2 + [1 0] x3 + [0]
[1 1] [1 0] [1]
p(U24#) = [1 0] x2 + [1 0] x3 + [0]
[0 1] [0 0] [1]
p(U25#) = [1 0] x2 + [0]
[1 0] [1]
p(U26#) = [0]
[0]
p(U31#) = [0]
[0]
p(U32#) = [0]
[0]
p(U33#) = [0]
[0]
p(U41#) = [1 0] x2 + [1 0] x3 + [0]
[0 0] [1 0] [0]
p(U42#) = [1 0] x2 + [1 0] x3 + [0]
[0 0] [1 1] [0]
p(U43#) = [1 0] x2 + [1 0] x3 + [0]
[1 0] [1 1] [1]
p(U44#) = [1 0] x2 + [1 0] x3 + [0]
[1 1] [1 1] [1]
p(U45#) = [1 0] x2 + [0]
[1 1] [1]
p(U46#) = [0]
[0]
p(U51#) = [1 1] x2 + [1 0] x3 + [0]
[1 1] [1 0] [1]
p(U52#) = [1 0] x2 + [1 0] x3 + [0]
[0 0] [1 1] [0]
p(U53#) = [1 0] x2 + [1 0] x3 + [0]
[0 0] [0 1] [1]
p(U54#) = [1 0] x2 + [1 0] x3 + [0]
[0 1] [1 0] [1]
p(U55#) = [1 0] x2 + [0]
[0 0] [1]
p(U56#) = [0]
[0]
p(U61#) = [0]
[0]
p(U62#) = [0]
[0]
p(U63#) = [0]
[0]
p(U71#) = [0 1] x2 + [1 1] x3 + [1]
[0 0] [1 1] [0]
p(U72#) = [1 1] x2 + [0]
[1 0] [1]
p(U73#) = [0 0] x2 + [0]
[1 0] [1]
p(U74#) = [0]
[0]
p(U81#) = [1 1] x2 + [0]
[1 1] [0]
p(U82#) = [1 1] x2 + [0]
[1 1] [0]
p(U83#) = [0]
[0]
p(U91#) = [0]
[0]
p(U92#) = [0]
[0]
p(__#) = [0]
[0]
p(a#) = [0]
[0]
p(activate#) = [0 0] x1 + [1]
[1 0] [1]
p(e#) = [0]
[0]
p(i#) = [0]
[0]
p(isList#) = [1 0] x1 + [0]
[0 0] [1]
p(isNeList#) = [1 0] x1 + [0]
[1 1] [1]
p(isNePal#) = [1 1] x1 + [0]
[1 1] [1]
p(isPal#) = [1 1] x1 + [0]
[1 1] [1]
p(isPalListKind#) = [0 0] x1 + [0]
[0 1] [0]
p(isQid#) = [0]
[0]
p(nil#) = [0]
[0]
p(o#) = [0]
[0]
p(u#) = [0]
[0]
p(c_1) = [1 0] x1 + [1 0] x2 + [0]
[1 1] [0 0] [0]
p(c_2) = [1 0] x1 + [0]
[0 0] [0]
p(c_3) = [0]
[0]
p(c_4) = [1 0] x1 + [1 0] x2 + [0 0] x4 + [0]
[0 0] [0 0] [1 0] [0]
p(c_5) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_6) = [1 0] x1 + [1 0] x2 + [0]
[1 0] [0 0] [1]
p(c_7) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
p(c_8) = [1 0] x1 + [0 0] x2 + [0]
[1 0] [1 0] [0]
p(c_9) = [0]
[0]
p(c_10) = [0]
[0]
p(c_11) = [0]
[0]
p(c_12) = [0]
[0]
p(c_13) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_14) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_15) = [1 0] x1 + [1 0] x2 + [0]
[1 0] [0 1] [1]
p(c_16) = [1 0] x1 + [1 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 1] [0]
p(c_17) = [1 0] x1 + [0]
[0 1] [0]
p(c_18) = [0]
[0]
p(c_19) = [1 0] x1 + [1 0] x2 + [0]
[1 0] [0 1] [1]
p(c_20) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_21) = [1 0] x1 + [1 0] x2 + [0 0] x4 + [0]
[0 0] [0 1] [1 0] [0]
p(c_22) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 0] [0]
p(c_23) = [1 0] x1 + [0]
[0 0] [0]
p(c_24) = [0]
[0]
p(c_25) = [0]
[0]
p(c_26) = [0]
[0]
p(c_27) = [0]
[0]
p(c_28) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_29) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 0] [0]
p(c_30) = [0]
[0]
p(c_31) = [0]
[0]
p(c_32) = [1 0] x1 + [1 0] x2 + [0]
[1 0] [0 0] [0]
p(c_33) = [1 0] x1 + [0]
[1 0] [0]
p(c_34) = [0]
[0]
p(c_35) = [0]
[0]
p(c_36) = [0]
[0]
p(c_37) = [0]
[0]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [0]
[0]
p(c_41) = [0]
[0]
p(c_42) = [0]
[0]
p(c_43) = [0]
[0]
p(c_44) = [0]
[0]
p(c_45) = [0]
[0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [0]
[0]
p(c_49) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [1]
p(c_50) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_51) = [0]
[0]
p(c_52) = [0]
[0]
p(c_53) = [1 0] x1 + [1 0] x2 + [0 0] x4 + [0 0] x5 + [0]
[0 1] [0 1] [0 1] [1 0] [0]
p(c_54) = [1 0] x1 + [1 0] x2 + [0]
[1 0] [0 0] [0]
p(c_55) = [0]
[0]
p(c_56) = [1 0] x1 + [0]
[1 0] [1]
p(c_57) = [1 0] x1 + [1 0] x2 + [0 0] x3 + [0]
[0 0] [0 1] [0 1] [0]
p(c_58) = [0]
[0]
p(c_59) = [0]
[0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [0]
[0]
p(c_64) = [0]
[0]
p(c_65) = [0]
[0]
p(c_66) = [0]
[0]
p(c_67) = [0]
[0]
p(c_68) = [0]
[0]
p(c_69) = [0]
[0]
p(c_70) = [0]
[0]
p(c_71) = [0]
[0]
p(c_72) = [0]
[0]
p(c_73) = [0]
[0]
Following rules are strictly oriented:
U71#(tt(),I,P) = [0 1] I + [1 1] P + [1]
[0 0] [1 1] [0]
> [1 1] P + [0]
[0 0] [0]
= c_28(U72#(isPalListKind(activate(I)),activate(P)),isPalListKind#(activate(I)),activate#(I),activate#(P))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [1 0] V + [0]
[1 1] [1]
>= [1 0] V + [0]
[1 0] [1]
= c_1(U12#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)),activate#(V),activate#(V))
U12#(tt(),V) = [1 0] V + [0]
[0 0] [1]
>= [1 0] V + [0]
[0 0] [0]
= c_2(isNeList#(activate(V)),activate#(V))
U21#(tt(),V1,V2) = [1 1] V1 + [1 0] V2 + [0]
[1 0] [0 0] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [1]
= c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
U22#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[1 0] [0 0] [0]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
U23#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[1 1] [1 0] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[1 0] [1 0] [1]
= c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
U24#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 1] [0 0] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [1]
= c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)),activate#(V1),activate#(V2))
U25#(tt(),V2) = [1 0] V2 + [0]
[1 0] [1]
>= [1 0] V2 + [0]
[1 0] [1]
= c_8(isList#(activate(V2)),activate#(V2))
U41#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 0] [1 0] [0]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
U42#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 0] [1 1] [0]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
U43#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[1 0] [1 1] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[1 0] [1 1] [1]
= c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
U44#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[1 1] [1 1] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[1 0] [0 0] [1]
= c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)),activate#(V1),activate#(V2))
U45#(tt(),V2) = [1 0] V2 + [0]
[1 1] [1]
>= [1 0] V2 + [0]
[1 1] [1]
= c_17(isNeList#(activate(V2)),activate#(V2))
U51#(tt(),V1,V2) = [1 1] V1 + [1 0] V2 + [0]
[1 1] [1 0] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[1 1] [1 0] [1]
= c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
U52#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 0] [1 1] [0]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
U53#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 1] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 1] [1]
= c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
U54#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 1] [1 0] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [1]
= c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)),activate#(V1),activate#(V2))
U55#(tt(),V2) = [1 0] V2 + [0]
[0 0] [1]
>= [1 0] V2 + [0]
[0 0] [0]
= c_23(isList#(activate(V2)),activate#(V2))
U72#(tt(),P) = [1 1] P + [0]
[1 0] [1]
>= [1 1] P + [0]
[1 0] [1]
= c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P))
U81#(tt(),V) = [1 1] V + [0]
[1 1] [0]
>= [1 1] V + [0]
[1 1] [0]
= c_32(U82#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)),activate#(V),activate#(V))
U82#(tt(),V) = [1 1] V + [0]
[1 1] [0]
>= [1 1] V + [0]
[1 1] [0]
= c_33(isNePal#(activate(V)),activate#(V))
isList#(V) = [1 0] V + [0]
[0 0] [1]
>= [1 0] V + [0]
[0 0] [1]
= c_49(U11#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)),activate#(V),activate#(V))
isList#(n____(V1,V2)) = [1 1] V1 + [1 0] V2 + [0]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 0] V2 + [0]
[1 1] [1 0] [2]
>= [1 0] V1 + [1 0] V2 + [0]
[1 1] [1 0] [2]
= c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 0] V2 + [0]
[1 1] [1 0] [2]
>= [1 1] V1 + [1 0] V2 + [0]
[1 1] [1 0] [0]
= c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(n____(I,n____(P,I))) = [2 1] I + [1 1] P + [1]
[2 1] [1 1] [2]
>= [0 1] I + [1 1] P + [1]
[0 1] [1 1] [2]
= c_56(U71#(isQid(activate(I)),activate(I),activate(P)),activate#(I),activate#(I),activate#(P))
isPal#(V) = [1 1] V + [0]
[1 1] [1]
>= [1 1] V + [0]
[1 1] [1]
= c_57(U81#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)),activate#(V),activate#(V))
__(X1,X2) = [1 1] X1 + [1 0] X2 + [0]
[0 0] [0 0] [1]
>= [1 1] X1 + [1 0] X2 + [0]
[0 0] [0 0] [1]
= n____(X1,X2)
a() = [0]
[0]
>= [0]
[0]
= n__a()
activate(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n____(X1,X2)) = [1 1] X1 + [1 0] X2 + [0]
[0 0] [0 0] [1]
>= [1 1] X1 + [1 0] X2 + [0]
[0 0] [0 0] [1]
= __(activate(X1),activate(X2))
activate(n__a()) = [0]
[0]
>= [0]
[0]
= a()
activate(n__e()) = [1]
[0]
>= [1]
[0]
= e()
activate(n__i()) = [0]
[1]
>= [0]
[1]
= i()
activate(n__nil()) = [1]
[0]
>= [1]
[0]
= nil()
activate(n__o()) = [0]
[1]
>= [0]
[1]
= o()
activate(n__u()) = [0]
[0]
>= [0]
[0]
= u()
e() = [1]
[0]
>= [1]
[0]
= n__e()
i() = [0]
[1]
>= [0]
[1]
= n__i()
nil() = [1]
[0]
>= [1]
[0]
= n__nil()
o() = [0]
[1]
>= [0]
[1]
= n__o()
u() = [0]
[0]
>= [0]
[0]
= n__u()
***** Step 1.b:7.a:1.a:1.a:2: Assumption WORST_CASE(?,O(1))
+ 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(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(isList#(activate(V2)),activate#(V2))
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(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(isList#(activate(V2)),activate#(V2))
U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),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(isNePal#(activate(V)),activate#(V))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
- Weak DPs:
U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
***** Step 1.b:7.a:1.a:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
+ 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(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(isList#(activate(V2)),activate#(V2))
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(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(isList#(activate(V2)),activate#(V2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
- Weak DPs:
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))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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))
-->_1 U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V)):2
2:S:U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V))
-->_1 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):21
-->_1 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):20
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))
-->_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))
-->_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))
-->_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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):19
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):18
-->_1 U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2)):7
7:S:U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2))
-->_1 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):19
-->_1 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):18
8:S:U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):9
9:S:U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
-->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):10
10:S:U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
-->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2)):11
11: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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):19
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):18
-->_1 U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2)):12
12:S:U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2))
-->_1 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):21
-->_1 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):20
13:S:U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):14
14:S:U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
-->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):15
15:S:U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
-->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2)):16
16: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_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):21
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):20
-->_1 U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2)):17
17:S:U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2))
-->_1 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):19
-->_1 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):18
18:S:isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):1
19:S:isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_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
20:S:isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):8
21:S:isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):13
22:W:U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P))
-->_1 U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P))
,isPal#(activate(P))
,activate#(P)
,activate#(P)):23
23:W:U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P))
,isPal#(activate(P))
,activate#(P)
,activate#(P))
-->_2 isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):27
24:W:U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_1 U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V)):25
25:W:U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
-->_1 isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P)):26
26:W:isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
-->_1 U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P)):22
27:W:isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_1 U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):24
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
22: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P))
26: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
25: U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
24: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
27: isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
23: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P))
***** Step 1.b:7.a:1.a:1.b:2: SimplifyRHS WORST_CASE(?,O(n^1))
+ 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(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(isList#(activate(V2)),activate#(V2))
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(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(isList#(activate(V2)),activate#(V2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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))
-->_1 U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V)):2
2:S:U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V))
-->_1 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):21
-->_1 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):20
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))
-->_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))
-->_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))
-->_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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):19
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):18
-->_1 U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2)):7
7:S:U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2))
-->_1 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):19
-->_1 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):18
8:S:U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):9
9:S:U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
-->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):10
10:S:U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
-->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2)):11
11: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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):19
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):18
-->_1 U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2)):12
12:S:U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2))
-->_1 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):21
-->_1 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):20
13:S:U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):14
14:S:U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
-->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):15
15:S:U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
-->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2)):16
16: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_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):21
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):20
-->_1 U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2)):17
17:S:U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2))
-->_1 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):19
-->_1 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):18
18:S:isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):1
19:S:isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_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
20:S:isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):8
21:S:isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):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)))
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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
***** Step 1.b:7.a:1.a:1.b:3: 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
***** Step 1.b:7.a:1.a:1.b:4: PredecessorEstimationCP 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
20: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Consider the set of all dependency pairs
1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),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)))
4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),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)))
9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),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)))
14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),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: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
19: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
20: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
21: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
SPACE(?,?)on application of the dependency pairs
{20}
These cover all (indirect) predecessors of dependency pairs
{8,9,10,11,12,20}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
****** Step 1.b:7.a:1.a:1.b:4.a:1: NaturalMI 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
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_49) = {1},
uargs(c_50) = {1},
uargs(c_53) = {1},
uargs(c_54) = {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 0] x2 + [1]
[1 0] [1]
p(U12) = [1]
[0]
p(U13) = [1]
[1]
p(U21) = [0 0] x1 + [1 0] x2 + [0 0] x3 + [0]
[0 1] [0 1] [1 1] [1]
p(U22) = [1]
[1]
p(U23) = [1 1] x2 + [0 0] x3 + [1]
[1 0] [1 0] [0]
p(U24) = [0 1] x1 + [0 0] x3 + [0]
[0 0] [1 0] [0]
p(U25) = [0]
[0]
p(U26) = [0]
[0]
p(U31) = [1]
[1]
p(U32) = [1]
[1]
p(U33) = [0]
[1]
p(U41) = [0 1] x1 + [0 1] x2 + [0]
[0 1] [0 0] [0]
p(U42) = [1 0] x3 + [1]
[1 0] [1]
p(U43) = [0 0] x3 + [1]
[1 0] [0]
p(U44) = [0 1] x1 + [1]
[0 0] [1]
p(U45) = [1 0] x2 + [0]
[0 1] [0]
p(U46) = [1]
[0]
p(U51) = [0 0] x1 + [0 0] x2 + [0 1] x3 + [0]
[0 1] [0 1] [0 1] [1]
p(U52) = [0 1] x1 + [1 0] x3 + [0]
[0 0] [0 0] [0]
p(U53) = [0 0] x2 + [0]
[0 1] [0]
p(U54) = [0 1] x1 + [1 1] x2 + [0 0] x3 + [1]
[0 0] [1 0] [1 0] [0]
p(U55) = [1 0] x2 + [0]
[0 0] [0]
p(U56) = [0 0] x1 + [1]
[1 0] [1]
p(U61) = [0]
[0]
p(U62) = [0]
[0]
p(U63) = [0]
[0]
p(U71) = [0]
[0]
p(U72) = [0]
[0]
p(U73) = [0]
[0]
p(U74) = [0]
[0]
p(U81) = [0]
[0]
p(U82) = [0]
[0]
p(U83) = [0]
[0]
p(U91) = [1]
[0]
p(U92) = [0 1] x1 + [0]
[0 1] [0]
p(__) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 1] [1]
p(a) = [0]
[0]
p(activate) = [1 0] x1 + [0]
[0 1] [0]
p(e) = [0]
[0]
p(i) = [0]
[0]
p(isList) = [1 0] x1 + [0]
[0 0] [0]
p(isNeList) = [0]
[0]
p(isNePal) = [0]
[0]
p(isPal) = [0]
[0]
p(isPalListKind) = [0 0] x1 + [0]
[0 1] [1]
p(isQid) = [0]
[0]
p(n____) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 1] [1]
p(n__a) = [0]
[0]
p(n__e) = [0]
[0]
p(n__i) = [0]
[0]
p(n__nil) = [0]
[0]
p(n__o) = [0]
[0]
p(n__u) = [0]
[0]
p(nil) = [0]
[0]
p(o) = [0]
[0]
p(tt) = [0]
[0]
p(u) = [0]
[0]
p(U11#) = [0 1] x2 + [0]
[1 1] [0]
p(U12#) = [0 1] x2 + [0]
[1 0] [0]
p(U13#) = [0]
[0]
p(U21#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [0 0] [0]
p(U22#) = [0 1] x2 + [0 1] x3 + [0]
[1 0] [1 0] [0]
p(U23#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [1 0] [1]
p(U24#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 1] [0]
p(U25#) = [0 1] x2 + [0]
[0 1] [1]
p(U26#) = [0]
[0]
p(U31#) = [0]
[0]
p(U32#) = [0]
[0]
p(U33#) = [0]
[0]
p(U41#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [0 1] [0]
p(U42#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 1] [0]
p(U43#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [1 0] [0]
p(U44#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [1 1] [1]
p(U45#) = [0 1] x2 + [0]
[1 0] [1]
p(U46#) = [0]
[0]
p(U51#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [0 0] [1]
p(U52#) = [0 1] x2 + [0 1] x3 + [0]
[1 1] [1 1] [1]
p(U53#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [1 1] [1]
p(U54#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [1 0] [1]
p(U55#) = [0 1] x2 + [0]
[1 1] [0]
p(U56#) = [0]
[0]
p(U61#) = [0]
[0]
p(U62#) = [0]
[0]
p(U63#) = [0]
[0]
p(U71#) = [0]
[0]
p(U72#) = [0]
[0]
p(U73#) = [0]
[0]
p(U74#) = [0]
[0]
p(U81#) = [0]
[0]
p(U82#) = [0]
[0]
p(U83#) = [0]
[0]
p(U91#) = [0]
[0]
p(U92#) = [0]
[0]
p(__#) = [0]
[0]
p(a#) = [0]
[0]
p(activate#) = [0]
[0]
p(e#) = [0]
[0]
p(i#) = [0]
[0]
p(isList#) = [0 1] x1 + [0]
[0 0] [1]
p(isNeList#) = [0 1] x1 + [0]
[0 0] [1]
p(isNePal#) = [0]
[0]
p(isPal#) = [0]
[0]
p(isPalListKind#) = [0]
[0]
p(isQid#) = [0]
[0]
p(nil#) = [0]
[0]
p(o#) = [0]
[0]
p(u#) = [0]
[0]
p(c_1) = [1 0] x1 + [0]
[0 1] [0]
p(c_2) = [1 0] x1 + [0]
[0 0] [0]
p(c_3) = [0]
[0]
p(c_4) = [1 0] x1 + [0]
[0 0] [0]
p(c_5) = [1 0] x1 + [0]
[0 0] [0]
p(c_6) = [1 0] x1 + [0]
[0 0] [0]
p(c_7) = [1 0] x1 + [1 0] x2 + [0]
[1 0] [0 0] [0]
p(c_8) = [1 0] x1 + [0]
[0 1] [0]
p(c_9) = [0]
[0]
p(c_10) = [0]
[0]
p(c_11) = [0]
[0]
p(c_12) = [0]
[0]
p(c_13) = [1 0] x1 + [0]
[0 1] [0]
p(c_14) = [1 0] x1 + [0]
[0 0] [0]
p(c_15) = [1 0] x1 + [0]
[0 0] [0]
p(c_16) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_17) = [1 0] x1 + [0]
[0 0] [0]
p(c_18) = [0]
[0]
p(c_19) = [1 0] x1 + [0]
[0 0] [0]
p(c_20) = [1 0] x1 + [0]
[0 1] [0]
p(c_21) = [1 0] x1 + [0]
[1 1] [0]
p(c_22) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
p(c_23) = [1 0] x1 + [0]
[0 0] [0]
p(c_24) = [0]
[0]
p(c_25) = [0]
[0]
p(c_26) = [0]
[0]
p(c_27) = [0]
[0]
p(c_28) = [0]
[0]
p(c_29) = [0]
[0]
p(c_30) = [0]
[0]
p(c_31) = [0]
[0]
p(c_32) = [0]
[0]
p(c_33) = [0]
[0]
p(c_34) = [0]
[0]
p(c_35) = [0]
[0]
p(c_36) = [0]
[0]
p(c_37) = [0]
[0]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [0]
[0]
p(c_41) = [0]
[0]
p(c_42) = [0]
[0]
p(c_43) = [0]
[0]
p(c_44) = [0]
[0]
p(c_45) = [0]
[0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [0]
[0]
p(c_49) = [1 0] x1 + [0]
[0 0] [0]
p(c_50) = [1 0] x1 + [1]
[0 0] [0]
p(c_51) = [0]
[0]
p(c_52) = [0]
[0]
p(c_53) = [1 0] x1 + [0]
[0 0] [1]
p(c_54) = [1 0] x1 + [1]
[0 0] [0]
p(c_55) = [0]
[0]
p(c_56) = [0]
[0]
p(c_57) = [0]
[0]
p(c_58) = [0]
[0]
p(c_59) = [0]
[0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [0]
[0]
p(c_64) = [0]
[0]
p(c_65) = [0]
[0]
p(c_66) = [0]
[0]
p(c_67) = [0]
[0]
p(c_68) = [0]
[0]
p(c_69) = [0]
[0]
p(c_70) = [0]
[0]
p(c_71) = [0]
[0]
p(c_72) = [0]
[0]
p(c_73) = [0]
[0]
Following rules are strictly oriented:
isNeList#(n____(V1,V2)) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [1]
> [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [1]
= c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [0 1] V + [0]
[1 1] [0]
>= [0 1] V + [0]
[1 0] [0]
= c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) = [0 1] V + [0]
[1 0] [0]
>= [0 1] V + [0]
[0 0] [0]
= c_2(isNeList#(activate(V)))
U21#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U22#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[1 0] [1 0] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U23#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [1 0] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U24#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 1] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 1] [0]
= c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U25#(tt(),V2) = [0 1] V2 + [0]
[0 1] [1]
>= [0 1] V2 + [0]
[0 0] [1]
= c_8(isList#(activate(V2)))
U41#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [0 1] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 1] [0]
= c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U42#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 1] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U43#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [1 0] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U44#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [1 1] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U45#(tt(),V2) = [0 1] V2 + [0]
[1 0] [1]
>= [0 1] V2 + [0]
[0 0] [0]
= c_17(isNeList#(activate(V2)))
U51#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [0 0] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U52#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[1 1] [1 1] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 1] [1 1] [1]
= c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U53#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [1 1] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 1] [1 1] [1]
= c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U54#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [1 0] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [1]
= c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
U55#(tt(),V2) = [0 1] V2 + [0]
[1 1] [0]
>= [0 1] V2 + [0]
[0 0] [0]
= c_23(isList#(activate(V2)))
isList#(V) = [0 1] V + [0]
[0 0] [1]
>= [0 1] V + [0]
[0 0] [0]
= c_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [1]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [1]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
__(X1,X2) = [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
>= [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
= n____(X1,X2)
a() = [0]
[0]
>= [0]
[0]
= n__a()
activate(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n____(X1,X2)) = [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
>= [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
= __(activate(X1),activate(X2))
activate(n__a()) = [0]
[0]
>= [0]
[0]
= a()
activate(n__e()) = [0]
[0]
>= [0]
[0]
= e()
activate(n__i()) = [0]
[0]
>= [0]
[0]
= i()
activate(n__nil()) = [0]
[0]
>= [0]
[0]
= nil()
activate(n__o()) = [0]
[0]
>= [0]
[0]
= o()
activate(n__u()) = [0]
[0]
>= [0]
[0]
= u()
e() = [0]
[0]
>= [0]
[0]
= n__e()
i() = [0]
[0]
>= [0]
[0]
= n__i()
nil() = [0]
[0]
>= [0]
[0]
= n__nil()
o() = [0]
[0]
>= [0]
[0]
= n__o()
u() = [0]
[0]
>= [0]
[0]
= n__u()
****** Step 1.b:7.a:1.a:1.b:4.a:2: Assumption WORST_CASE(?,O(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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- Weak DPs:
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
****** Step 1.b:7.a:1.a:1.b:4.b:1: PredecessorEstimationCP 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)))
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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- Weak DPs:
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)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Consider the set of all dependency pairs
1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),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)))
4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),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: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
9: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
10: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
11: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
12: U55#(tt(),V2) -> c_23(isList#(activate(V2)))
13: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
14: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
15: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
16: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
17: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
18: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
19: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
20: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)))
21: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
SPACE(?,?)on application of the dependency pairs
{3}
These cover all (indirect) predecessors of dependency pairs
{3,4,5,6,7}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
******* Step 1.b:7.a:1.a:1.b:4.b:1.a:1: NaturalMI 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)))
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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- Weak DPs:
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)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
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_49) = {1},
uargs(c_50) = {1},
uargs(c_53) = {1},
uargs(c_54) = {1}
Following symbols are considered usable:
{U91,U92,__,a,activate,e,i,isPalListKind,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]
[0]
p(U12) = [1 0] x2 + [0]
[0 0] [0]
p(U13) = [0]
[1]
p(U21) = [0 0] x1 + [0 0] x3 + [1]
[1 0] [1 1] [1]
p(U22) = [0 1] x2 + [1 0] x3 + [0]
[1 0] [0 0] [0]
p(U23) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [1 1] [0]
p(U24) = [0 0] x1 + [0 0] x3 + [0]
[1 0] [0 1] [0]
p(U25) = [0 0] x1 + [0]
[0 1] [0]
p(U26) = [1]
[1]
p(U31) = [0 0] x2 + [1]
[0 1] [1]
p(U32) = [1]
[0]
p(U33) = [0 0] x1 + [1]
[1 1] [1]
p(U41) = [0 1] x1 + [1 1] x3 + [0]
[1 0] [1 0] [1]
p(U42) = [1 0] x1 + [1 0] x3 + [0]
[1 1] [1 0] [1]
p(U43) = [1 1] x1 + [0 0] x2 + [0 0] x3 + [1]
[0 0] [1 0] [0 1] [1]
p(U44) = [1 0] x1 + [1 0] x3 + [1]
[0 0] [0 0] [0]
p(U45) = [1 0] x2 + [0]
[1 0] [0]
p(U46) = [1]
[1]
p(U51) = [1 0] x1 + [0 0] x2 + [1 0] x3 + [0]
[0 0] [1 0] [0 1] [1]
p(U52) = [0 1] x1 + [0]
[0 1] [0]
p(U53) = [0 1] x1 + [0 0] x2 + [1 0] x3 + [0]
[0 0] [1 0] [0 0] [0]
p(U54) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
[1 0] [0 1] [0 1] [1]
p(U55) = [1 1] x2 + [0]
[0 0] [0]
p(U56) = [1]
[1]
p(U61) = [0]
[0]
p(U62) = [0]
[0]
p(U63) = [0]
[0]
p(U71) = [0]
[0]
p(U72) = [0]
[0]
p(U73) = [0]
[0]
p(U74) = [0]
[0]
p(U81) = [0]
[0]
p(U82) = [0]
[0]
p(U83) = [0]
[0]
p(U91) = [0]
[1]
p(U92) = [0 0] x1 + [0]
[0 1] [0]
p(__) = [1 1] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
p(a) = [0]
[0]
p(activate) = [1 0] x1 + [0]
[0 1] [0]
p(e) = [0]
[0]
p(i) = [0]
[1]
p(isList) = [0]
[1]
p(isNeList) = [0]
[0]
p(isNePal) = [0]
[0]
p(isPal) = [0]
[0]
p(isPalListKind) = [0 1] x1 + [0]
[0 0] [1]
p(isQid) = [1 1] x1 + [0]
[0 0] [1]
p(n____) = [1 1] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
p(n__a) = [0]
[0]
p(n__e) = [0]
[0]
p(n__i) = [0]
[1]
p(n__nil) = [0]
[1]
p(n__o) = [0]
[0]
p(n__u) = [0]
[0]
p(nil) = [0]
[1]
p(o) = [0]
[0]
p(tt) = [0]
[0]
p(u) = [0]
[0]
p(U11#) = [1 0] x2 + [0]
[1 0] [1]
p(U12#) = [1 0] x2 + [0]
[1 0] [0]
p(U13#) = [0]
[0]
p(U21#) = [1 1] x2 + [1 0] x3 + [1]
[0 0] [0 1] [0]
p(U22#) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [0]
[0 0] [0 0] [0 0] [1]
p(U23#) = [1 0] x2 + [1 0] x3 + [0]
[0 1] [0 1] [0]
p(U24#) = [1 0] x2 + [1 0] x3 + [0]
[1 0] [1 0] [1]
p(U25#) = [1 0] x2 + [0]
[1 0] [0]
p(U26#) = [0]
[0]
p(U31#) = [0]
[0]
p(U32#) = [0]
[0]
p(U33#) = [0]
[0]
p(U41#) = [1 0] x2 + [1 0] x3 + [1]
[0 1] [0 0] [0]
p(U42#) = [1 0] x2 + [1 0] x3 + [1]
[1 1] [1 1] [1]
p(U43#) = [0 0] x1 + [1 0] x2 + [1 0] x3 + [1]
[1 0] [0 1] [1 0] [1]
p(U44#) = [1 0] x2 + [1 0] x3 + [1]
[0 1] [0 0] [0]
p(U45#) = [1 0] x2 + [1]
[1 0] [1]
p(U46#) = [0]
[0]
p(U51#) = [1 0] x2 + [1 0] x3 + [0]
[0 0] [0 1] [1]
p(U52#) = [1 0] x2 + [1 0] x3 + [0]
[0 0] [0 0] [0]
p(U53#) = [1 0] x2 + [1 0] x3 + [0]
[1 0] [0 1] [1]
p(U54#) = [1 0] x2 + [1 0] x3 + [0]
[1 1] [0 0] [1]
p(U55#) = [1 0] x2 + [0]
[1 0] [1]
p(U56#) = [0]
[0]
p(U61#) = [0]
[0]
p(U62#) = [0]
[0]
p(U63#) = [0]
[0]
p(U71#) = [0]
[0]
p(U72#) = [0]
[0]
p(U73#) = [0]
[0]
p(U74#) = [0]
[0]
p(U81#) = [0]
[0]
p(U82#) = [0]
[0]
p(U83#) = [0]
[0]
p(U91#) = [0]
[0]
p(U92#) = [0]
[0]
p(__#) = [0]
[0]
p(a#) = [0]
[0]
p(activate#) = [0]
[0]
p(e#) = [0]
[0]
p(i#) = [0]
[0]
p(isList#) = [1 0] x1 + [0]
[0 0] [1]
p(isNeList#) = [1 0] x1 + [0]
[0 0] [0]
p(isNePal#) = [0]
[0]
p(isPal#) = [0]
[0]
p(isPalListKind#) = [0]
[0]
p(isQid#) = [0]
[0]
p(nil#) = [0]
[0]
p(o#) = [0]
[0]
p(u#) = [0]
[0]
p(c_1) = [1 0] x1 + [0]
[1 0] [0]
p(c_2) = [1 0] x1 + [0]
[0 0] [0]
p(c_3) = [0]
[0]
p(c_4) = [1 0] x1 + [0]
[0 0] [0]
p(c_5) = [1 0] x1 + [0]
[0 0] [0]
p(c_6) = [1 0] x1 + [0]
[0 0] [0]
p(c_7) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [1 0] [0]
p(c_8) = [1 0] x1 + [0]
[0 0] [0]
p(c_9) = [0]
[0]
p(c_10) = [0]
[0]
p(c_11) = [0]
[0]
p(c_12) = [0]
[0]
p(c_13) = [1 0] x1 + [0]
[0 0] [0]
p(c_14) = [1 0] x1 + [0]
[0 0] [1]
p(c_15) = [1 0] x1 + [0]
[0 1] [1]
p(c_16) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_17) = [1 0] x1 + [0]
[1 0] [1]
p(c_18) = [0]
[0]
p(c_19) = [1 0] x1 + [0]
[0 0] [1]
p(c_20) = [1 0] x1 + [0]
[0 0] [0]
p(c_21) = [1 0] x1 + [0]
[0 0] [0]
p(c_22) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [1 0] [1]
p(c_23) = [1 0] x1 + [0]
[0 1] [0]
p(c_24) = [0]
[0]
p(c_25) = [0]
[0]
p(c_26) = [0]
[0]
p(c_27) = [0]
[0]
p(c_28) = [0]
[0]
p(c_29) = [0]
[0]
p(c_30) = [0]
[0]
p(c_31) = [0]
[0]
p(c_32) = [0]
[0]
p(c_33) = [0]
[0]
p(c_34) = [0]
[0]
p(c_35) = [0]
[0]
p(c_36) = [0]
[0]
p(c_37) = [0]
[0]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [0]
[0]
p(c_41) = [0]
[0]
p(c_42) = [0]
[0]
p(c_43) = [0]
[0]
p(c_44) = [0]
[0]
p(c_45) = [0]
[0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [0]
[0]
p(c_49) = [1 0] x1 + [0]
[0 0] [0]
p(c_50) = [1 1] x1 + [0]
[0 0] [0]
p(c_51) = [0]
[0]
p(c_52) = [0]
[0]
p(c_53) = [1 1] x1 + [0]
[0 0] [0]
p(c_54) = [1 1] x1 + [0]
[0 0] [0]
p(c_55) = [0]
[0]
p(c_56) = [0]
[0]
p(c_57) = [0]
[0]
p(c_58) = [0]
[0]
p(c_59) = [0]
[0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [0]
[0]
p(c_64) = [0]
[0]
p(c_65) = [0]
[0]
p(c_66) = [0]
[0]
p(c_67) = [0]
[0]
p(c_68) = [0]
[0]
p(c_69) = [0]
[0]
p(c_70) = [0]
[0]
p(c_71) = [0]
[0]
p(c_72) = [0]
[0]
p(c_73) = [0]
[0]
Following rules are strictly oriented:
U21#(tt(),V1,V2) = [1 1] V1 + [1 0] V2 + [1]
[0 0] [0 1] [0]
> [1 1] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [1 0] V + [0]
[1 0] [1]
>= [1 0] V + [0]
[1 0] [0]
= c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) = [1 0] V + [0]
[1 0] [0]
>= [1 0] V + [0]
[0 0] [0]
= c_2(isNeList#(activate(V)))
U22#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U23#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 1] [0 1] [0]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U24#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[1 0] [1 0] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[1 0] [1 0] [0]
= c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U25#(tt(),V2) = [1 0] V2 + [0]
[1 0] [0]
>= [1 0] V2 + [0]
[0 0] [0]
= c_8(isList#(activate(V2)))
U41#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[0 1] [0 0] [0]
>= [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U42#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[1 1] [1 1] [1]
>= [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 0] [1]
= c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U43#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[0 1] [1 0] [1]
>= [1 0] V1 + [1 0] V2 + [1]
[0 1] [0 0] [1]
= c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U44#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[0 1] [0 0] [0]
>= [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U45#(tt(),V2) = [1 0] V2 + [1]
[1 0] [1]
>= [1 0] V2 + [0]
[1 0] [1]
= c_17(isNeList#(activate(V2)))
U51#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 1] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [1]
= c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U52#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U53#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[1 0] [0 1] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[0 0] [0 0] [0]
= c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U54#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [0]
[1 1] [0 0] [1]
>= [1 0] V1 + [1 0] V2 + [0]
[1 0] [0 0] [1]
= c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
U55#(tt(),V2) = [1 0] V2 + [0]
[1 0] [1]
>= [1 0] V2 + [0]
[0 0] [1]
= c_23(isList#(activate(V2)))
isList#(V) = [1 0] V + [0]
[0 0] [1]
>= [1 0] V + [0]
[0 0] [0]
= c_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [0]
= c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [0]
>= [1 1] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [0]
>= [1 0] V1 + [1 1] V2 + [1]
[0 0] [0 0] [0]
= c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U91(tt(),V2) = [0]
[1]
>= [0]
[1]
= U92(isPalListKind(activate(V2)))
U92(tt()) = [0]
[0]
>= [0]
[0]
= tt()
__(X1,X2) = [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [0]
>= [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [0]
= n____(X1,X2)
a() = [0]
[0]
>= [0]
[0]
= n__a()
activate(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n____(X1,X2)) = [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [0]
>= [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [0]
= __(activate(X1),activate(X2))
activate(n__a()) = [0]
[0]
>= [0]
[0]
= a()
activate(n__e()) = [0]
[0]
>= [0]
[0]
= e()
activate(n__i()) = [0]
[1]
>= [0]
[1]
= i()
activate(n__nil()) = [0]
[1]
>= [0]
[1]
= nil()
activate(n__o()) = [0]
[0]
>= [0]
[0]
= o()
activate(n__u()) = [0]
[0]
>= [0]
[0]
= u()
e() = [0]
[0]
>= [0]
[0]
= n__e()
i() = [0]
[1]
>= [0]
[1]
= n__i()
isPalListKind(n____(V1,V2)) = [0]
[1]
>= [0]
[1]
= U91(isPalListKind(activate(V1)),activate(V2))
isPalListKind(n__a()) = [0]
[1]
>= [0]
[0]
= tt()
isPalListKind(n__e()) = [0]
[1]
>= [0]
[0]
= tt()
isPalListKind(n__i()) = [1]
[1]
>= [0]
[0]
= tt()
isPalListKind(n__nil()) = [1]
[1]
>= [0]
[0]
= tt()
isPalListKind(n__o()) = [0]
[1]
>= [0]
[0]
= tt()
isPalListKind(n__u()) = [0]
[1]
>= [0]
[0]
= tt()
nil() = [0]
[1]
>= [0]
[1]
= n__nil()
o() = [0]
[0]
>= [0]
[0]
= n__o()
u() = [0]
[0]
>= [0]
[0]
= n__u()
******* Step 1.b:7.a:1.a:1.b:4.b:1.a:2: Assumption WORST_CASE(?,O(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)))
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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
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)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
******* Step 1.b:7.a:1.a:1.b:4.b:1.b:1: PredecessorEstimationCP 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)))
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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
9: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Consider the set of all dependency pairs
1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
2: U12#(tt(),V) -> c_2(isNeList#(activate(V)))
3: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
4: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
5: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
6: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
7: U55#(tt(),V2) -> c_23(isList#(activate(V2)))
8: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
9: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
10: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
11: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
12: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
13: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
14: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
15: U25#(tt(),V2) -> c_8(isList#(activate(V2)))
16: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
17: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
18: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
19: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
20: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)))
21: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
SPACE(?,?)on application of the dependency pairs
{9}
These cover all (indirect) predecessors of dependency pairs
{9,11,12,13,14,15}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
******** Step 1.b:7.a:1.a:1.b:4.b:1.b:1.a:1: NaturalMI 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)))
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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
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_49) = {1},
uargs(c_50) = {1},
uargs(c_53) = {1},
uargs(c_54) = {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 0] x2 + [0]
[1 0] [1]
p(U12) = [1]
[0]
p(U13) = [0]
[0]
p(U21) = [0]
[0]
p(U22) = [0 0] x1 + [1 0] x2 + [0]
[0 1] [0 0] [0]
p(U23) = [0 1] x1 + [1 0] x3 + [0]
[0 0] [1 0] [0]
p(U24) = [1 0] x3 + [0]
[0 0] [1]
p(U25) = [0]
[0]
p(U26) = [0 0] x1 + [0]
[1 0] [1]
p(U31) = [0 1] x1 + [1 0] x2 + [1]
[0 0] [0 0] [0]
p(U32) = [0 0] x2 + [0]
[0 1] [0]
p(U33) = [0]
[0]
p(U41) = [0 1] x1 + [1 0] x2 + [0]
[0 1] [0 0] [0]
p(U42) = [0]
[0]
p(U43) = [0 0] x2 + [0 0] x3 + [0]
[1 0] [1 0] [1]
p(U44) = [0 0] x2 + [0 0] x3 + [0]
[1 0] [1 0] [0]
p(U45) = [1]
[0]
p(U46) = [0]
[0]
p(U51) = [0 1] x3 + [1]
[0 0] [0]
p(U52) = [0]
[0]
p(U53) = [1]
[0]
p(U54) = [0 1] x3 + [0]
[0 0] [0]
p(U55) = [1 1] x2 + [0]
[0 0] [0]
p(U56) = [0]
[0]
p(U61) = [0]
[0]
p(U62) = [0]
[0]
p(U63) = [0]
[0]
p(U71) = [0]
[0]
p(U72) = [0]
[0]
p(U73) = [0]
[0]
p(U74) = [0]
[0]
p(U81) = [0]
[0]
p(U82) = [0]
[0]
p(U83) = [0]
[0]
p(U91) = [0 0] x1 + [0]
[0 1] [0]
p(U92) = [0]
[0]
p(__) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 1] [1]
p(a) = [0]
[0]
p(activate) = [1 0] x1 + [0]
[0 1] [0]
p(e) = [0]
[0]
p(i) = [0]
[0]
p(isList) = [1]
[0]
p(isNeList) = [0]
[1]
p(isNePal) = [0]
[0]
p(isPal) = [0]
[0]
p(isPalListKind) = [0 0] x1 + [0]
[0 1] [0]
p(isQid) = [0]
[1]
p(n____) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 1] [1]
p(n__a) = [0]
[0]
p(n__e) = [0]
[0]
p(n__i) = [0]
[0]
p(n__nil) = [0]
[0]
p(n__o) = [0]
[0]
p(n__u) = [0]
[0]
p(nil) = [0]
[0]
p(o) = [0]
[0]
p(tt) = [0]
[0]
p(u) = [0]
[0]
p(U11#) = [0 1] x2 + [0]
[1 1] [0]
p(U12#) = [0 1] x2 + [0]
[0 0] [0]
p(U13#) = [0]
[0]
p(U21#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [0 1] [0]
p(U22#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 0] [1]
p(U23#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 0] [0]
p(U24#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [0 0] [0]
p(U25#) = [0 1] x2 + [0]
[0 0] [0]
p(U26#) = [0]
[0]
p(U31#) = [0]
[0]
p(U32#) = [0]
[0]
p(U33#) = [0]
[0]
p(U41#) = [0 1] x2 + [0 1] x3 + [1]
[0 0] [0 0] [0]
p(U42#) = [0 1] x2 + [0 1] x3 + [1]
[0 0] [1 1] [0]
p(U43#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 1] [0]
p(U44#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [0 1] [0]
p(U45#) = [0 1] x2 + [0]
[0 1] [0]
p(U46#) = [0]
[0]
p(U51#) = [0 1] x2 + [0 1] x3 + [1]
[0 0] [0 0] [0]
p(U52#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 0] [1]
p(U53#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 0] [0]
p(U54#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 0] [1]
p(U55#) = [0 1] x2 + [0]
[0 0] [0]
p(U56#) = [0]
[0]
p(U61#) = [0]
[0]
p(U62#) = [0]
[0]
p(U63#) = [0]
[0]
p(U71#) = [0]
[0]
p(U72#) = [0]
[0]
p(U73#) = [0]
[0]
p(U74#) = [0]
[0]
p(U81#) = [0]
[0]
p(U82#) = [0]
[0]
p(U83#) = [0]
[0]
p(U91#) = [0]
[0]
p(U92#) = [0]
[0]
p(__#) = [0]
[0]
p(a#) = [0]
[0]
p(activate#) = [0]
[0]
p(e#) = [0]
[0]
p(i#) = [0]
[0]
p(isList#) = [0 1] x1 + [0]
[0 0] [1]
p(isNeList#) = [0 1] x1 + [0]
[0 0] [0]
p(isNePal#) = [0]
[0]
p(isPal#) = [0]
[0]
p(isPalListKind#) = [0]
[0]
p(isQid#) = [0]
[0]
p(nil#) = [0]
[0]
p(o#) = [0]
[0]
p(u#) = [0]
[0]
p(c_1) = [1 0] x1 + [0]
[0 0] [0]
p(c_2) = [1 0] x1 + [0]
[0 0] [0]
p(c_3) = [0]
[0]
p(c_4) = [1 0] x1 + [0]
[1 0] [0]
p(c_5) = [1 0] x1 + [0]
[0 0] [1]
p(c_6) = [1 0] x1 + [0]
[0 0] [0]
p(c_7) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_8) = [1 0] x1 + [0]
[0 0] [0]
p(c_9) = [0]
[0]
p(c_10) = [0]
[0]
p(c_11) = [0]
[0]
p(c_12) = [0]
[0]
p(c_13) = [1 0] x1 + [0]
[0 0] [0]
p(c_14) = [1 0] x1 + [0]
[0 1] [0]
p(c_15) = [1 0] x1 + [0]
[0 0] [0]
p(c_16) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_17) = [1 0] x1 + [0]
[1 0] [0]
p(c_18) = [0]
[0]
p(c_19) = [1 1] x1 + [0]
[0 0] [0]
p(c_20) = [1 0] x1 + [0]
[0 0] [0]
p(c_21) = [1 0] x1 + [0]
[0 0] [0]
p(c_22) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_23) = [1 0] x1 + [0]
[0 0] [0]
p(c_24) = [0]
[0]
p(c_25) = [0]
[0]
p(c_26) = [0]
[0]
p(c_27) = [0]
[0]
p(c_28) = [0]
[0]
p(c_29) = [0]
[0]
p(c_30) = [0]
[0]
p(c_31) = [0]
[0]
p(c_32) = [0]
[0]
p(c_33) = [0]
[0]
p(c_34) = [0]
[0]
p(c_35) = [0]
[0]
p(c_36) = [0]
[0]
p(c_37) = [0]
[0]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [0]
[0]
p(c_41) = [0]
[0]
p(c_42) = [0]
[0]
p(c_43) = [0]
[0]
p(c_44) = [0]
[0]
p(c_45) = [0]
[0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [0]
[0]
p(c_49) = [1 0] x1 + [0]
[0 0] [0]
p(c_50) = [1 0] x1 + [0]
[0 0] [0]
p(c_51) = [0]
[0]
p(c_52) = [0]
[0]
p(c_53) = [1 0] x1 + [0]
[0 0] [0]
p(c_54) = [1 0] x1 + [0]
[0 0] [0]
p(c_55) = [0]
[0]
p(c_56) = [0]
[0]
p(c_57) = [0]
[0]
p(c_58) = [0]
[0]
p(c_59) = [0]
[0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [0]
[0]
p(c_64) = [0]
[0]
p(c_65) = [0]
[0]
p(c_66) = [0]
[0]
p(c_67) = [0]
[0]
p(c_68) = [0]
[0]
p(c_69) = [0]
[0]
p(c_70) = [0]
[0]
p(c_71) = [0]
[0]
p(c_72) = [0]
[0]
p(c_73) = [0]
[0]
Following rules are strictly oriented:
isList#(n____(V1,V2)) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [1]
> [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [0 1] V + [0]
[1 1] [0]
>= [0 1] V + [0]
[0 0] [0]
= c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) = [0 1] V + [0]
[0 0] [0]
>= [0 1] V + [0]
[0 0] [0]
= c_2(isNeList#(activate(V)))
U21#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [0 1] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 1] [0 1] [0]
= c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U22#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [1]
= c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U23#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U24#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U25#(tt(),V2) = [0 1] V2 + [0]
[0 0] [0]
>= [0 1] V2 + [0]
[0 0] [0]
= c_8(isList#(activate(V2)))
U41#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U42#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [1 1] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 1] [0]
= c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U43#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 1] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U44#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [0 1] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U45#(tt(),V2) = [0 1] V2 + [0]
[0 1] [0]
>= [0 1] V2 + [0]
[0 1] [0]
= c_17(isNeList#(activate(V2)))
U51#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U52#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U53#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U54#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
U55#(tt(),V2) = [0 1] V2 + [0]
[0 0] [0]
>= [0 1] V2 + [0]
[0 0] [0]
= c_23(isList#(activate(V2)))
isList#(V) = [0 1] V + [0]
[0 0] [1]
>= [0 1] V + [0]
[0 0] [0]
= c_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
__(X1,X2) = [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
>= [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
= n____(X1,X2)
a() = [0]
[0]
>= [0]
[0]
= n__a()
activate(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n____(X1,X2)) = [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
>= [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
= __(activate(X1),activate(X2))
activate(n__a()) = [0]
[0]
>= [0]
[0]
= a()
activate(n__e()) = [0]
[0]
>= [0]
[0]
= e()
activate(n__i()) = [0]
[0]
>= [0]
[0]
= i()
activate(n__nil()) = [0]
[0]
>= [0]
[0]
= nil()
activate(n__o()) = [0]
[0]
>= [0]
[0]
= o()
activate(n__u()) = [0]
[0]
>= [0]
[0]
= u()
e() = [0]
[0]
>= [0]
[0]
= n__e()
i() = [0]
[0]
>= [0]
[0]
= n__i()
nil() = [0]
[0]
>= [0]
[0]
= n__nil()
o() = [0]
[0]
>= [0]
[0]
= n__o()
u() = [0]
[0]
>= [0]
[0]
= n__u()
******** Step 1.b:7.a:1.a:1.b:4.b:1.b:1.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) -> c_2(isNeList#(activate(V)))
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_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
******** Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1: PredecessorEstimationCP 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)))
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_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
7: U55#(tt(),V2) -> c_23(isList#(activate(V2)))
The strictly oriented rules are moved into the weak component.
********* Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.a:1: NaturalMI 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)))
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_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
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_49) = {1},
uargs(c_50) = {1},
uargs(c_53) = {1},
uargs(c_54) = {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]
[1]
p(U12) = [1]
[0]
p(U13) = [0]
[0]
p(U21) = [0]
[0]
p(U22) = [0]
[0]
p(U23) = [1 0] x2 + [0 0] x3 + [0]
[0 0] [1 0] [0]
p(U24) = [0 1] x1 + [0]
[0 0] [0]
p(U25) = [0]
[0]
p(U26) = [0]
[0]
p(U31) = [0 1] x1 + [0]
[0 0] [1]
p(U32) = [0 1] x1 + [1]
[0 0] [1]
p(U33) = [0 0] x1 + [0]
[1 0] [0]
p(U41) = [1 1] x2 + [0 0] x3 + [0]
[0 0] [0 1] [0]
p(U42) = [1 1] x3 + [1]
[0 0] [0]
p(U43) = [0]
[1]
p(U44) = [1]
[0]
p(U45) = [1 1] x2 + [0]
[0 0] [0]
p(U46) = [1]
[1]
p(U51) = [0 0] x1 + [0]
[0 1] [1]
p(U52) = [0 1] x1 + [0]
[0 0] [0]
p(U53) = [0 0] x1 + [1 0] x3 + [1]
[0 1] [0 1] [1]
p(U54) = [0 0] x1 + [0 0] x3 + [0]
[0 1] [1 0] [1]
p(U55) = [0 1] x2 + [0]
[0 0] [1]
p(U56) = [0]
[0]
p(U61) = [0]
[0]
p(U62) = [0]
[0]
p(U63) = [0]
[0]
p(U71) = [0]
[0]
p(U72) = [0]
[0]
p(U73) = [0]
[0]
p(U74) = [0]
[0]
p(U81) = [0]
[0]
p(U82) = [0]
[0]
p(U83) = [0]
[0]
p(U91) = [1]
[0]
p(U92) = [0]
[0]
p(__) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 1] [1]
p(a) = [0]
[1]
p(activate) = [1 0] x1 + [0]
[0 1] [0]
p(e) = [0]
[0]
p(i) = [0]
[1]
p(isList) = [0]
[0]
p(isNeList) = [0]
[0]
p(isNePal) = [0]
[0]
p(isPal) = [0]
[0]
p(isPalListKind) = [0 0] x1 + [0]
[0 1] [1]
p(isQid) = [0 1] x1 + [1]
[0 0] [0]
p(n____) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 1] [1]
p(n__a) = [0]
[1]
p(n__e) = [0]
[0]
p(n__i) = [0]
[1]
p(n__nil) = [0]
[0]
p(n__o) = [0]
[0]
p(n__u) = [0]
[0]
p(nil) = [0]
[0]
p(o) = [0]
[0]
p(tt) = [0]
[0]
p(u) = [0]
[0]
p(U11#) = [0 1] x2 + [0]
[0 1] [0]
p(U12#) = [0 1] x2 + [0]
[1 0] [0]
p(U13#) = [0]
[0]
p(U21#) = [0 1] x2 + [0 1] x3 + [1]
[1 0] [0 1] [0]
p(U22#) = [0 1] x2 + [0 1] x3 + [1]
[0 0] [0 1] [0]
p(U23#) = [0 1] x2 + [0 1] x3 + [1]
[0 0] [0 0] [0]
p(U24#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 0] [0]
p(U25#) = [0 1] x2 + [0]
[0 1] [1]
p(U26#) = [0]
[0]
p(U31#) = [0]
[0]
p(U32#) = [0]
[0]
p(U33#) = [0]
[0]
p(U41#) = [0 1] x2 + [0 1] x3 + [1]
[1 0] [0 0] [0]
p(U42#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 0] [1]
p(U43#) = [0 1] x2 + [0 1] x3 + [0]
[0 1] [0 0] [0]
p(U44#) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [1 0] [1]
p(U45#) = [0 1] x2 + [0]
[0 0] [1]
p(U46#) = [0]
[0]
p(U51#) = [0 1] x2 + [0 1] x3 + [1]
[0 1] [0 1] [1]
p(U52#) = [0 1] x2 + [0 1] x3 + [1]
[0 1] [0 1] [1]
p(U53#) = [0 1] x2 + [0 1] x3 + [1]
[0 0] [0 0] [1]
p(U54#) = [0 1] x2 + [0 1] x3 + [1]
[1 0] [1 1] [0]
p(U55#) = [0 1] x2 + [1]
[0 0] [1]
p(U56#) = [0]
[0]
p(U61#) = [0]
[0]
p(U62#) = [0]
[0]
p(U63#) = [0]
[0]
p(U71#) = [0]
[0]
p(U72#) = [0]
[0]
p(U73#) = [0]
[0]
p(U74#) = [0]
[0]
p(U81#) = [0]
[0]
p(U82#) = [0]
[0]
p(U83#) = [0]
[0]
p(U91#) = [0]
[0]
p(U92#) = [0]
[0]
p(__#) = [0]
[0]
p(a#) = [0]
[0]
p(activate#) = [0]
[0]
p(e#) = [0]
[0]
p(i#) = [0]
[0]
p(isList#) = [0 1] x1 + [0]
[0 0] [0]
p(isNeList#) = [0 1] x1 + [0]
[0 0] [0]
p(isNePal#) = [0]
[0]
p(isPal#) = [0]
[0]
p(isPalListKind#) = [0]
[0]
p(isQid#) = [0]
[0]
p(nil#) = [0]
[0]
p(o#) = [0]
[0]
p(u#) = [0]
[0]
p(c_1) = [1 0] x1 + [0]
[0 0] [0]
p(c_2) = [1 0] x1 + [0]
[0 0] [0]
p(c_3) = [0]
[0]
p(c_4) = [1 0] x1 + [0]
[0 0] [0]
p(c_5) = [1 0] x1 + [0]
[0 0] [0]
p(c_6) = [1 0] x1 + [0]
[0 0] [0]
p(c_7) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_8) = [1 0] x1 + [0]
[0 0] [0]
p(c_9) = [0]
[0]
p(c_10) = [0]
[0]
p(c_11) = [0]
[0]
p(c_12) = [0]
[0]
p(c_13) = [1 1] x1 + [0]
[0 0] [0]
p(c_14) = [1 0] x1 + [0]
[0 0] [0]
p(c_15) = [1 0] x1 + [0]
[0 0] [0]
p(c_16) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [1]
p(c_17) = [1 0] x1 + [0]
[0 0] [0]
p(c_18) = [0]
[0]
p(c_19) = [1 0] x1 + [0]
[0 0] [0]
p(c_20) = [1 0] x1 + [0]
[1 0] [0]
p(c_21) = [1 0] x1 + [0]
[0 0] [0]
p(c_22) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_23) = [1 0] x1 + [0]
[0 0] [1]
p(c_24) = [0]
[0]
p(c_25) = [0]
[0]
p(c_26) = [0]
[0]
p(c_27) = [0]
[0]
p(c_28) = [0]
[0]
p(c_29) = [0]
[0]
p(c_30) = [0]
[0]
p(c_31) = [0]
[0]
p(c_32) = [0]
[0]
p(c_33) = [0]
[0]
p(c_34) = [0]
[0]
p(c_35) = [0]
[0]
p(c_36) = [0]
[0]
p(c_37) = [0]
[0]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [0]
[0]
p(c_41) = [0]
[0]
p(c_42) = [0]
[0]
p(c_43) = [0]
[0]
p(c_44) = [0]
[0]
p(c_45) = [0]
[0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [0]
[0]
p(c_49) = [1 0] x1 + [0]
[0 0] [0]
p(c_50) = [1 0] x1 + [0]
[0 0] [0]
p(c_51) = [0]
[0]
p(c_52) = [0]
[0]
p(c_53) = [1 0] x1 + [0]
[0 0] [0]
p(c_54) = [1 0] x1 + [0]
[0 0] [0]
p(c_55) = [0]
[0]
p(c_56) = [0]
[0]
p(c_57) = [0]
[0]
p(c_58) = [0]
[0]
p(c_59) = [0]
[0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [0]
[0]
p(c_64) = [0]
[0]
p(c_65) = [0]
[0]
p(c_66) = [0]
[0]
p(c_67) = [0]
[0]
p(c_68) = [0]
[0]
p(c_69) = [0]
[0]
p(c_70) = [0]
[0]
p(c_71) = [0]
[0]
p(c_72) = [0]
[0]
p(c_73) = [0]
[0]
Following rules are strictly oriented:
U55#(tt(),V2) = [0 1] V2 + [1]
[0 0] [1]
> [0 1] V2 + [0]
[0 0] [1]
= c_23(isList#(activate(V2)))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [0 1] V + [0]
[0 1] [0]
>= [0 1] V + [0]
[0 0] [0]
= c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) = [0 1] V + [0]
[1 0] [0]
>= [0 1] V + [0]
[0 0] [0]
= c_2(isNeList#(activate(V)))
U21#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[1 0] [0 1] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U22#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 1] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U23#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U24#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U25#(tt(),V2) = [0 1] V2 + [0]
[0 1] [1]
>= [0 1] V2 + [0]
[0 0] [0]
= c_8(isList#(activate(V2)))
U41#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[1 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U42#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U43#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 1] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [0]
= c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U44#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [0]
[0 0] [1 0] [1]
>= [0 1] V1 + [0 1] V2 + [0]
[0 0] [0 0] [1]
= c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U45#(tt(),V2) = [0 1] V2 + [0]
[0 0] [1]
>= [0 1] V2 + [0]
[0 0] [0]
= c_17(isNeList#(activate(V2)))
U51#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[0 1] [0 1] [1]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U52#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[0 1] [0 1] [1]
>= [0 1] V1 + [0 1] V2 + [1]
[0 1] [0 1] [1]
= c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U53#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [1]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U54#(tt(),V1,V2) = [0 1] V1 + [0 1] V2 + [1]
[1 0] [1 1] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
isList#(V) = [0 1] V + [0]
[0 0] [0]
>= [0 1] V + [0]
[0 0] [0]
= c_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
>= [0 1] V1 + [0 1] V2 + [1]
[0 0] [0 0] [0]
= c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
__(X1,X2) = [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
>= [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
= n____(X1,X2)
a() = [0]
[1]
>= [0]
[1]
= n__a()
activate(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n____(X1,X2)) = [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
>= [0 0] X1 + [0 0] X2 + [0]
[0 1] [0 1] [1]
= __(activate(X1),activate(X2))
activate(n__a()) = [0]
[1]
>= [0]
[1]
= a()
activate(n__e()) = [0]
[0]
>= [0]
[0]
= e()
activate(n__i()) = [0]
[1]
>= [0]
[1]
= i()
activate(n__nil()) = [0]
[0]
>= [0]
[0]
= nil()
activate(n__o()) = [0]
[0]
>= [0]
[0]
= o()
activate(n__u()) = [0]
[0]
>= [0]
[0]
= u()
e() = [0]
[0]
>= [0]
[0]
= n__e()
i() = [0]
[1]
>= [0]
[1]
= n__i()
nil() = [0]
[0]
>= [0]
[0]
= n__nil()
o() = [0]
[0]
>= [0]
[0]
= n__o()
u() = [0]
[0]
>= [0]
[0]
= n__u()
********* Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) -> c_2(isNeList#(activate(V)))
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)))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
U55#(tt(),V2) -> c_23(isList#(activate(V2)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
********* Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1: PredecessorEstimationCP 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)))
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)))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
U55#(tt(),V2) -> c_23(isList#(activate(V2)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
3: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Consider the set of all dependency pairs
1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
2: U12#(tt(),V) -> c_2(isNeList#(activate(V)))
3: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
4: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
5: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
6: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
7: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
8: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
9: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
10: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
11: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
12: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
13: U25#(tt(),V2) -> c_8(isList#(activate(V2)))
14: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
15: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
16: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
17: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
18: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)))
19: U55#(tt(),V2) -> c_23(isList#(activate(V2)))
20: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
21: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
SPACE(?,?)on application of the dependency pairs
{3}
These cover all (indirect) predecessors of dependency pairs
{3,4,5,6,19}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
********** Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.a:1: NaturalMI 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)))
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)))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
U55#(tt(),V2) -> c_23(isList#(activate(V2)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
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_49) = {1},
uargs(c_50) = {1},
uargs(c_53) = {1},
uargs(c_54) = {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 1] x1 + [0]
[0 0] [1]
p(U12) = [0 1] x1 + [1 0] x2 + [1]
[0 0] [0 0] [1]
p(U13) = [0]
[1]
p(U21) = [0 0] x1 + [0 0] x3 + [1]
[0 1] [0 1] [1]
p(U22) = [0 1] x2 + [0 1] x3 + [0]
[0 0] [0 0] [0]
p(U23) = [0 1] x1 + [1 1] x2 + [0 1] x3 + [1]
[0 0] [1 0] [0 0] [1]
p(U24) = [0 0] x2 + [0 0] x3 + [0]
[0 1] [1 1] [0]
p(U25) = [0 1] x1 + [0]
[0 1] [1]
p(U26) = [0]
[1]
p(U31) = [0 0] x1 + [0 1] x2 + [1]
[0 1] [1 0] [0]
p(U32) = [1]
[0]
p(U33) = [1]
[0]
p(U41) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 1] [0]
p(U42) = [0 0] x1 + [1 0] x3 + [0]
[0 1] [0 0] [0]
p(U43) = [1 0] x2 + [0 0] x3 + [0]
[1 0] [0 1] [0]
p(U44) = [0 0] x2 + [1]
[1 0] [0]
p(U45) = [1]
[1]
p(U46) = [1 0] x1 + [1]
[0 0] [0]
p(U51) = [1 1] x2 + [0]
[0 1] [0]
p(U52) = [1 0] x3 + [0]
[0 0] [0]
p(U53) = [1 0] x2 + [0]
[0 0] [0]
p(U54) = [0 1] x2 + [0]
[0 0] [0]
p(U55) = [0 0] x1 + [1 0] x2 + [0]
[0 1] [1 0] [0]
p(U56) = [0 1] x1 + [0]
[0 1] [1]
p(U61) = [0]
[0]
p(U62) = [0]
[0]
p(U63) = [0]
[0]
p(U71) = [0]
[0]
p(U72) = [0]
[0]
p(U73) = [0]
[0]
p(U74) = [0]
[0]
p(U81) = [0]
[0]
p(U82) = [0]
[0]
p(U83) = [0]
[0]
p(U91) = [0 0] x1 + [0 0] x2 + [0]
[0 1] [0 1] [1]
p(U92) = [0 1] x1 + [0]
[0 1] [1]
p(__) = [1 1] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
p(a) = [0]
[0]
p(activate) = [1 0] x1 + [0]
[0 1] [0]
p(e) = [0]
[1]
p(i) = [0]
[0]
p(isList) = [0]
[1]
p(isNeList) = [0 0] x1 + [1]
[0 1] [1]
p(isNePal) = [0]
[0]
p(isPal) = [0]
[0]
p(isPalListKind) = [0 0] x1 + [0]
[1 0] [0]
p(isQid) = [1]
[1]
p(n____) = [1 1] x1 + [1 1] x2 + [1]
[0 0] [0 0] [0]
p(n__a) = [0]
[0]
p(n__e) = [0]
[1]
p(n__i) = [0]
[0]
p(n__nil) = [0]
[1]
p(n__o) = [0]
[0]
p(n__u) = [0]
[0]
p(nil) = [0]
[1]
p(o) = [0]
[0]
p(tt) = [0]
[0]
p(u) = [0]
[0]
p(U11#) = [1 1] x2 + [0]
[0 0] [1]
p(U12#) = [1 1] x2 + [0]
[1 1] [1]
p(U13#) = [0]
[0]
p(U21#) = [1 1] x2 + [1 1] x3 + [0]
[0 1] [0 0] [0]
p(U22#) = [1 1] x2 + [1 1] x3 + [0]
[1 1] [0 0] [1]
p(U23#) = [1 1] x2 + [1 1] x3 + [0]
[1 0] [0 0] [1]
p(U24#) = [1 1] x2 + [1 1] x3 + [0]
[1 0] [0 0] [1]
p(U25#) = [1 1] x2 + [0]
[1 0] [1]
p(U26#) = [0]
[0]
p(U31#) = [0]
[0]
p(U32#) = [0]
[0]
p(U33#) = [0]
[0]
p(U41#) = [1 1] x2 + [1 1] x3 + [0]
[1 1] [1 0] [0]
p(U42#) = [1 1] x2 + [1 1] x3 + [0]
[0 0] [0 1] [0]
p(U43#) = [1 1] x2 + [1 1] x3 + [0]
[0 0] [0 0] [1]
p(U44#) = [1 1] x2 + [1 1] x3 + [0]
[0 0] [1 1] [1]
p(U45#) = [1 1] x2 + [0]
[0 0] [0]
p(U46#) = [0]
[0]
p(U51#) = [1 1] x2 + [1 1] x3 + [1]
[1 0] [0 0] [0]
p(U52#) = [1 1] x2 + [1 1] x3 + [0]
[1 1] [1 1] [1]
p(U53#) = [1 1] x2 + [1 1] x3 + [0]
[0 0] [0 0] [1]
p(U54#) = [1 1] x2 + [1 1] x3 + [0]
[0 0] [0 0] [1]
p(U55#) = [1 1] x2 + [0]
[1 0] [0]
p(U56#) = [0]
[0]
p(U61#) = [0]
[0]
p(U62#) = [0]
[0]
p(U63#) = [0]
[0]
p(U71#) = [0]
[0]
p(U72#) = [0]
[0]
p(U73#) = [0]
[0]
p(U74#) = [0]
[0]
p(U81#) = [0]
[0]
p(U82#) = [0]
[0]
p(U83#) = [0]
[0]
p(U91#) = [0]
[0]
p(U92#) = [0]
[0]
p(__#) = [0]
[0]
p(a#) = [0]
[0]
p(activate#) = [0]
[0]
p(e#) = [0]
[0]
p(i#) = [0]
[0]
p(isList#) = [1 1] x1 + [0]
[0 0] [1]
p(isNeList#) = [1 1] x1 + [0]
[0 0] [0]
p(isNePal#) = [0]
[0]
p(isPal#) = [0]
[0]
p(isPalListKind#) = [0]
[0]
p(isQid#) = [0]
[0]
p(nil#) = [0]
[0]
p(o#) = [0]
[0]
p(u#) = [0]
[0]
p(c_1) = [1 0] x1 + [0]
[0 0] [1]
p(c_2) = [1 0] x1 + [0]
[0 0] [1]
p(c_3) = [0]
[0]
p(c_4) = [1 0] x1 + [0]
[0 0] [0]
p(c_5) = [1 0] x1 + [0]
[0 1] [0]
p(c_6) = [1 0] x1 + [0]
[0 1] [0]
p(c_7) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [1]
p(c_8) = [1 0] x1 + [0]
[0 0] [1]
p(c_9) = [0]
[0]
p(c_10) = [0]
[0]
p(c_11) = [0]
[0]
p(c_12) = [0]
[0]
p(c_13) = [1 0] x1 + [0]
[0 0] [0]
p(c_14) = [1 0] x1 + [0]
[0 0] [0]
p(c_15) = [1 0] x1 + [0]
[0 0] [1]
p(c_16) = [1 0] x1 + [1 0] x2 + [0]
[1 0] [0 1] [0]
p(c_17) = [1 0] x1 + [0]
[0 0] [0]
p(c_18) = [0]
[0]
p(c_19) = [1 0] x1 + [0]
[0 0] [0]
p(c_20) = [1 0] x1 + [0]
[1 0] [0]
p(c_21) = [1 0] x1 + [0]
[0 1] [0]
p(c_22) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [1]
p(c_23) = [1 0] x1 + [0]
[0 0] [0]
p(c_24) = [0]
[0]
p(c_25) = [0]
[0]
p(c_26) = [0]
[0]
p(c_27) = [0]
[0]
p(c_28) = [0]
[0]
p(c_29) = [0]
[0]
p(c_30) = [0]
[0]
p(c_31) = [0]
[0]
p(c_32) = [0]
[0]
p(c_33) = [0]
[0]
p(c_34) = [0]
[0]
p(c_35) = [0]
[0]
p(c_36) = [0]
[0]
p(c_37) = [0]
[0]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [0]
[0]
p(c_41) = [0]
[0]
p(c_42) = [0]
[0]
p(c_43) = [0]
[0]
p(c_44) = [0]
[0]
p(c_45) = [0]
[0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [0]
[0]
p(c_49) = [1 0] x1 + [0]
[0 1] [0]
p(c_50) = [1 0] x1 + [0]
[0 0] [1]
p(c_51) = [0]
[0]
p(c_52) = [0]
[0]
p(c_53) = [1 0] x1 + [1]
[0 0] [0]
p(c_54) = [1 0] x1 + [0]
[0 0] [0]
p(c_55) = [0]
[0]
p(c_56) = [0]
[0]
p(c_57) = [0]
[0]
p(c_58) = [0]
[0]
p(c_59) = [0]
[0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [0]
[0]
p(c_64) = [0]
[0]
p(c_65) = [0]
[0]
p(c_66) = [0]
[0]
p(c_67) = [0]
[0]
p(c_68) = [0]
[0]
p(c_69) = [0]
[0]
p(c_70) = [0]
[0]
p(c_71) = [0]
[0]
p(c_72) = [0]
[0]
p(c_73) = [0]
[0]
Following rules are strictly oriented:
U51#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [1]
[1 0] [0 0] [0]
> [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [1 1] V + [0]
[0 0] [1]
>= [1 1] V + [0]
[0 0] [1]
= c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) = [1 1] V + [0]
[1 1] [1]
>= [1 1] V + [0]
[0 0] [1]
= c_2(isNeList#(activate(V)))
U21#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 1] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U22#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[1 1] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[1 0] [0 0] [1]
= c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U23#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[1 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[1 0] [0 0] [1]
= c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U24#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[1 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
= c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U25#(tt(),V2) = [1 1] V2 + [0]
[1 0] [1]
>= [1 1] V2 + [0]
[0 0] [1]
= c_8(isList#(activate(V2)))
U41#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[1 1] [1 0] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U42#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 1] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U43#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
= c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U44#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [1 1] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [1 1] [1]
= c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U45#(tt(),V2) = [1 1] V2 + [0]
[0 0] [0]
>= [1 1] V2 + [0]
[0 0] [0]
= c_17(isNeList#(activate(V2)))
U52#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[1 1] [1 1] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[1 1] [1 1] [0]
= c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U53#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
= c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U54#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
= c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
U55#(tt(),V2) = [1 1] V2 + [0]
[1 0] [0]
>= [1 1] V2 + [0]
[0 0] [0]
= c_23(isList#(activate(V2)))
isList#(V) = [1 1] V + [0]
[0 0] [1]
>= [1 1] V + [0]
[0 0] [1]
= c_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
= c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [0]
= c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [0]
= c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
__(X1,X2) = [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [0]
>= [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [0]
= n____(X1,X2)
a() = [0]
[0]
>= [0]
[0]
= n__a()
activate(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n____(X1,X2)) = [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [0]
>= [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [0]
= __(activate(X1),activate(X2))
activate(n__a()) = [0]
[0]
>= [0]
[0]
= a()
activate(n__e()) = [0]
[1]
>= [0]
[1]
= e()
activate(n__i()) = [0]
[0]
>= [0]
[0]
= i()
activate(n__nil()) = [0]
[1]
>= [0]
[1]
= nil()
activate(n__o()) = [0]
[0]
>= [0]
[0]
= o()
activate(n__u()) = [0]
[0]
>= [0]
[0]
= u()
e() = [0]
[1]
>= [0]
[1]
= n__e()
i() = [0]
[0]
>= [0]
[0]
= n__i()
nil() = [0]
[1]
>= [0]
[1]
= n__nil()
o() = [0]
[0]
>= [0]
[0]
= n__o()
u() = [0]
[0]
>= [0]
[0]
= n__u()
********** Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) -> c_2(isNeList#(activate(V)))
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)))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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)))
U55#(tt(),V2) -> c_23(isList#(activate(V2)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
********** Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.b:1: PredecessorEstimationCP 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
3: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
Consider the set of all dependency pairs
1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
2: U12#(tt(),V) -> c_2(isNeList#(activate(V)))
3: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
4: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
5: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
6: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
7: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
8: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
9: U25#(tt(),V2) -> c_8(isList#(activate(V2)))
10: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
11: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
12: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
13: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
14: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)))
15: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
16: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
17: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
18: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
19: U55#(tt(),V2) -> c_23(isList#(activate(V2)))
20: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
21: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
SPACE(?,?)on application of the dependency pairs
{3}
These cover all (indirect) predecessors of dependency pairs
{1,2,3}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
*********** Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.b:1.a:1: NaturalMI 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
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_49) = {1},
uargs(c_50) = {1},
uargs(c_53) = {1},
uargs(c_54) = {1}
Following symbols are considered usable:
{U91,U92,__,a,activate,e,i,isPalListKind,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 0] x1 + [1 1] x2 + [0]
[1 0] [1 0] [0]
p(U12) = [0 1] x1 + [1 0] x2 + [0]
[1 0] [1 0] [1]
p(U13) = [1]
[0]
p(U21) = [0 0] x1 + [0 0] x3 + [1]
[1 1] [1 1] [0]
p(U22) = [0 1] x1 + [1 0] x2 + [1 0] x3 + [0]
[0 1] [0 0] [0 0] [1]
p(U23) = [1 1] x3 + [0]
[0 0] [1]
p(U24) = [0 1] x2 + [1 0] x3 + [1]
[0 1] [1 1] [1]
p(U25) = [0 0] x1 + [0]
[1 0] [0]
p(U26) = [0 1] x1 + [1]
[1 0] [0]
p(U31) = [0 0] x1 + [0 1] x2 + [0]
[1 0] [1 0] [1]
p(U32) = [1 0] x1 + [0 1] x2 + [0]
[0 1] [0 1] [0]
p(U33) = [1 1] x1 + [1]
[1 0] [1]
p(U41) = [0 1] x1 + [0 0] x2 + [0]
[0 0] [1 0] [1]
p(U42) = [0 0] x1 + [0 0] x2 + [1]
[1 0] [0 1] [1]
p(U43) = [0 0] x1 + [0 1] x3 + [1]
[0 1] [0 0] [1]
p(U44) = [0 0] x1 + [0 0] x3 + [0]
[1 0] [1 0] [1]
p(U45) = [0 0] x1 + [0 0] x2 + [0]
[1 1] [1 1] [0]
p(U46) = [1 0] x1 + [1]
[1 0] [1]
p(U51) = [1 1] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 1] [1 1] [1]
p(U52) = [1 0] x2 + [1 1] x3 + [0]
[0 0] [0 1] [0]
p(U53) = [0 0] x2 + [0 0] x3 + [1]
[1 1] [0 1] [0]
p(U54) = [0 0] x1 + [0 1] x2 + [0 0] x3 + [0]
[1 0] [0 1] [1 1] [1]
p(U55) = [1 0] x1 + [0 1] x2 + [1]
[0 0] [0 1] [0]
p(U56) = [0 0] x1 + [0]
[1 1] [0]
p(U61) = [0]
[0]
p(U62) = [0]
[0]
p(U63) = [0]
[0]
p(U71) = [0]
[0]
p(U72) = [0]
[0]
p(U73) = [0]
[0]
p(U74) = [0]
[0]
p(U81) = [0]
[0]
p(U82) = [0]
[0]
p(U83) = [0]
[0]
p(U91) = [1 0] x1 + [0 1] x2 + [0]
[0 0] [0 0] [1]
p(U92) = [1]
[1]
p(__) = [1 1] x1 + [1 1] x2 + [0]
[0 0] [0 0] [1]
p(a) = [1]
[1]
p(activate) = [1 0] x1 + [0]
[0 1] [0]
p(e) = [1]
[1]
p(i) = [1]
[1]
p(isList) = [0 1] x1 + [0]
[1 0] [0]
p(isNeList) = [0 0] x1 + [0]
[0 1] [0]
p(isNePal) = [0]
[0]
p(isPal) = [0]
[0]
p(isPalListKind) = [1 0] x1 + [0]
[0 1] [0]
p(isQid) = [1 0] x1 + [0]
[1 0] [0]
p(n____) = [1 1] x1 + [1 1] x2 + [0]
[0 0] [0 0] [1]
p(n__a) = [1]
[1]
p(n__e) = [1]
[1]
p(n__i) = [1]
[1]
p(n__nil) = [1]
[1]
p(n__o) = [1]
[1]
p(n__u) = [1]
[1]
p(nil) = [1]
[1]
p(o) = [1]
[1]
p(tt) = [1]
[1]
p(u) = [1]
[1]
p(U11#) = [1 0] x2 + [0]
[0 1] [1]
p(U12#) = [1 0] x2 + [0]
[0 1] [1]
p(U13#) = [0]
[0]
p(U21#) = [1 1] x2 + [1 1] x3 + [1]
[1 1] [0 1] [1]
p(U22#) = [0 1] x1 + [1 0] x2 + [1 1] x3 + [1]
[1 0] [1 0] [1 0] [0]
p(U23#) = [0 0] x1 + [1 0] x2 + [1 1] x3 + [1]
[1 0] [1 0] [0 1] [1]
p(U24#) = [0 1] x1 + [1 0] x2 + [1 0] x3 + [1]
[0 0] [1 0] [0 0] [1]
p(U25#) = [1 0] x2 + [1]
[0 1] [1]
p(U26#) = [0]
[0]
p(U31#) = [0]
[0]
p(U32#) = [0]
[0]
p(U33#) = [0]
[0]
p(U41#) = [1 1] x2 + [1 0] x3 + [0]
[0 0] [0 1] [0]
p(U42#) = [0 1] x1 + [1 0] x2 + [1 0] x3 + [0]
[0 0] [0 0] [0 1] [0]
p(U43#) = [1 0] x2 + [1 0] x3 + [1]
[1 0] [0 0] [0]
p(U44#) = [1 0] x2 + [1 0] x3 + [1]
[1 1] [0 0] [0]
p(U45#) = [1 0] x2 + [0]
[1 0] [0]
p(U46#) = [0]
[0]
p(U51#) = [1 1] x2 + [1 1] x3 + [0]
[0 0] [0 0] [1]
p(U52#) = [0 1] x1 + [1 0] x2 + [1 0] x3 + [0]
[0 0] [0 0] [0 1] [0]
p(U53#) = [1 0] x2 + [1 0] x3 + [1]
[0 0] [0 1] [0]
p(U54#) = [1 0] x2 + [1 0] x3 + [1]
[1 0] [0 0] [1]
p(U55#) = [1 0] x2 + [1]
[0 0] [1]
p(U56#) = [0]
[0]
p(U61#) = [0]
[0]
p(U62#) = [0]
[0]
p(U63#) = [0]
[0]
p(U71#) = [0]
[0]
p(U72#) = [0]
[0]
p(U73#) = [0]
[0]
p(U74#) = [0]
[0]
p(U81#) = [0]
[0]
p(U82#) = [0]
[0]
p(U83#) = [0]
[0]
p(U91#) = [0]
[0]
p(U92#) = [0]
[0]
p(__#) = [0]
[0]
p(a#) = [0]
[0]
p(activate#) = [0]
[0]
p(e#) = [0]
[0]
p(i#) = [0]
[0]
p(isList#) = [1 0] x1 + [1]
[0 1] [0]
p(isNeList#) = [1 0] x1 + [0]
[0 0] [0]
p(isNePal#) = [0]
[0]
p(isPal#) = [0]
[0]
p(isPalListKind#) = [0]
[0]
p(isQid#) = [0]
[0]
p(nil#) = [0]
[0]
p(o#) = [0]
[0]
p(u#) = [0]
[0]
p(c_1) = [1 0] x1 + [0]
[0 0] [0]
p(c_2) = [1 0] x1 + [0]
[0 0] [1]
p(c_3) = [0]
[0]
p(c_4) = [1 0] x1 + [0]
[0 0] [1]
p(c_5) = [1 0] x1 + [0]
[0 0] [1]
p(c_6) = [1 0] x1 + [0]
[0 1] [1]
p(c_7) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [1 0] [0]
p(c_8) = [1 0] x1 + [0]
[0 1] [1]
p(c_9) = [0]
[0]
p(c_10) = [0]
[0]
p(c_11) = [0]
[0]
p(c_12) = [0]
[0]
p(c_13) = [1 0] x1 + [0]
[0 1] [0]
p(c_14) = [1 0] x1 + [0]
[0 0] [0]
p(c_15) = [1 0] x1 + [0]
[0 0] [0]
p(c_16) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_17) = [1 0] x1 + [0]
[0 0] [0]
p(c_18) = [0]
[0]
p(c_19) = [1 1] x1 + [0]
[0 0] [0]
p(c_20) = [1 0] x1 + [0]
[0 0] [0]
p(c_21) = [1 0] x1 + [0]
[0 0] [0]
p(c_22) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 0] [0]
p(c_23) = [1 0] x1 + [0]
[0 0] [1]
p(c_24) = [0]
[0]
p(c_25) = [0]
[0]
p(c_26) = [0]
[0]
p(c_27) = [0]
[0]
p(c_28) = [0]
[0]
p(c_29) = [0]
[0]
p(c_30) = [0]
[0]
p(c_31) = [0]
[0]
p(c_32) = [0]
[0]
p(c_33) = [0]
[0]
p(c_34) = [0]
[0]
p(c_35) = [0]
[0]
p(c_36) = [0]
[0]
p(c_37) = [0]
[0]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [0]
[0]
p(c_41) = [0]
[0]
p(c_42) = [0]
[0]
p(c_43) = [0]
[0]
p(c_44) = [0]
[0]
p(c_45) = [0]
[0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [0]
[0]
p(c_49) = [1 0] x1 + [0]
[0 0] [0]
p(c_50) = [1 0] x1 + [0]
[0 0] [1]
p(c_51) = [0]
[0]
p(c_52) = [0]
[0]
p(c_53) = [1 1] x1 + [0]
[0 0] [0]
p(c_54) = [1 0] x1 + [0]
[0 0] [0]
p(c_55) = [0]
[0]
p(c_56) = [0]
[0]
p(c_57) = [0]
[0]
p(c_58) = [0]
[0]
p(c_59) = [0]
[0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [0]
[0]
p(c_64) = [0]
[0]
p(c_65) = [0]
[0]
p(c_66) = [0]
[0]
p(c_67) = [0]
[0]
p(c_68) = [0]
[0]
p(c_69) = [0]
[0]
p(c_70) = [0]
[0]
p(c_71) = [0]
[0]
p(c_72) = [0]
[0]
p(c_73) = [0]
[0]
Following rules are strictly oriented:
isList#(V) = [1 0] V + [1]
[0 1] [0]
> [1 0] V + [0]
[0 0] [0]
= c_49(U11#(isPalListKind(activate(V)),activate(V)))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [1 0] V + [0]
[0 1] [1]
>= [1 0] V + [0]
[0 0] [0]
= c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) = [1 0] V + [0]
[0 1] [1]
>= [1 0] V + [0]
[0 0] [1]
= c_2(isNeList#(activate(V)))
U21#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [1]
[1 1] [0 1] [1]
>= [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [1]
= c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U22#(tt(),V1,V2) = [1 0] V1 + [1 1] V2 + [2]
[1 0] [1 0] [1]
>= [1 0] V1 + [1 1] V2 + [1]
[0 0] [0 0] [1]
= c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U23#(tt(),V1,V2) = [1 0] V1 + [1 1] V2 + [1]
[1 0] [0 1] [2]
>= [1 0] V1 + [1 1] V2 + [1]
[1 0] [0 0] [2]
= c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U24#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [2]
[1 0] [0 0] [1]
>= [1 0] V1 + [1 0] V2 + [2]
[1 0] [0 0] [1]
= c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U25#(tt(),V2) = [1 0] V2 + [1]
[0 1] [1]
>= [1 0] V2 + [1]
[0 1] [1]
= c_8(isList#(activate(V2)))
U41#(tt(),V1,V2) = [1 1] V1 + [1 0] V2 + [0]
[0 0] [0 1] [0]
>= [1 1] V1 + [1 0] V2 + [0]
[0 0] [0 1] [0]
= c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U42#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 1] [0]
>= [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U43#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[1 0] [0 0] [0]
>= [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U44#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[1 1] [0 0] [0]
>= [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U45#(tt(),V2) = [1 0] V2 + [0]
[1 0] [0]
>= [1 0] V2 + [0]
[0 0] [0]
= c_17(isNeList#(activate(V2)))
U51#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U52#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 1] [0]
>= [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U53#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 1] [0]
>= [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U54#(tt(),V1,V2) = [1 0] V1 + [1 0] V2 + [1]
[1 0] [0 0] [1]
>= [1 0] V1 + [1 0] V2 + [1]
[0 0] [0 0] [1]
= c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
U55#(tt(),V2) = [1 0] V2 + [1]
[0 0] [1]
>= [1 0] V2 + [1]
[0 0] [1]
= c_23(isList#(activate(V2)))
isList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [1]
= c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U91(tt(),V2) = [0 1] V2 + [1]
[0 0] [1]
>= [1]
[1]
= U92(isPalListKind(activate(V2)))
U92(tt()) = [1]
[1]
>= [1]
[1]
= tt()
__(X1,X2) = [1 1] X1 + [1 1] X2 + [0]
[0 0] [0 0] [1]
>= [1 1] X1 + [1 1] X2 + [0]
[0 0] [0 0] [1]
= n____(X1,X2)
a() = [1]
[1]
>= [1]
[1]
= n__a()
activate(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n____(X1,X2)) = [1 1] X1 + [1 1] X2 + [0]
[0 0] [0 0] [1]
>= [1 1] X1 + [1 1] X2 + [0]
[0 0] [0 0] [1]
= __(activate(X1),activate(X2))
activate(n__a()) = [1]
[1]
>= [1]
[1]
= a()
activate(n__e()) = [1]
[1]
>= [1]
[1]
= e()
activate(n__i()) = [1]
[1]
>= [1]
[1]
= i()
activate(n__nil()) = [1]
[1]
>= [1]
[1]
= nil()
activate(n__o()) = [1]
[1]
>= [1]
[1]
= o()
activate(n__u()) = [1]
[1]
>= [1]
[1]
= u()
e() = [1]
[1]
>= [1]
[1]
= n__e()
i() = [1]
[1]
>= [1]
[1]
= n__i()
isPalListKind(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [1]
>= [1 0] V1 + [0 1] V2 + [0]
[0 0] [0 0] [1]
= U91(isPalListKind(activate(V1)),activate(V2))
isPalListKind(n__a()) = [1]
[1]
>= [1]
[1]
= tt()
isPalListKind(n__e()) = [1]
[1]
>= [1]
[1]
= tt()
isPalListKind(n__i()) = [1]
[1]
>= [1]
[1]
= tt()
isPalListKind(n__nil()) = [1]
[1]
>= [1]
[1]
= tt()
isPalListKind(n__o()) = [1]
[1]
>= [1]
[1]
= tt()
isPalListKind(n__u()) = [1]
[1]
>= [1]
[1]
= tt()
nil() = [1]
[1]
>= [1]
[1]
= n__nil()
o() = [1]
[1]
>= [1]
[1]
= n__o()
u() = [1]
[1]
>= [1]
[1]
= n__u()
*********** Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.b:1.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) -> c_2(isNeList#(activate(V)))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
*********** Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.b:1.b:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
1: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Consider the set of all dependency pairs
1: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
2: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
3: U12#(tt(),V) -> c_2(isNeList#(activate(V)))
4: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
5: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
6: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
7: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
8: U25#(tt(),V2) -> c_8(isList#(activate(V2)))
9: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
10: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
11: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
12: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
13: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)))
14: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
15: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
16: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
17: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
18: U55#(tt(),V2) -> c_23(isList#(activate(V2)))
19: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
20: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
21: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
SPACE(?,?)on application of the dependency pairs
{1}
These cover all (indirect) predecessors of dependency pairs
{1,14,15,16,17,18}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
************ Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.b:1.b:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
- 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
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_49) = {1},
uargs(c_50) = {1},
uargs(c_53) = {1},
uargs(c_54) = {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 0] x2 + [0]
[0 1] [0]
p(U12) = [0 1] x2 + [0]
[0 0] [0]
p(U13) = [0 0] x1 + [0]
[0 1] [0]
p(U21) = [0]
[0]
p(U22) = [0]
[0]
p(U23) = [0 0] x1 + [0]
[0 1] [0]
p(U24) = [0]
[0]
p(U25) = [0 0] x2 + [0]
[1 1] [0]
p(U26) = [0]
[0]
p(U31) = [0 0] x1 + [0]
[0 1] [0]
p(U32) = [0 1] x2 + [0]
[0 1] [1]
p(U33) = [1 1] x1 + [1]
[1 1] [1]
p(U41) = [1 1] x2 + [0]
[0 0] [1]
p(U42) = [0]
[0]
p(U43) = [0 0] x2 + [0]
[1 0] [1]
p(U44) = [1 0] x3 + [0]
[1 0] [0]
p(U45) = [1]
[1]
p(U46) = [0 0] x1 + [0]
[1 0] [0]
p(U51) = [0]
[1]
p(U52) = [0]
[0]
p(U53) = [0]
[0]
p(U54) = [0]
[0]
p(U55) = [0 0] x2 + [0]
[0 1] [1]
p(U56) = [0 0] x1 + [0]
[1 0] [0]
p(U61) = [0]
[0]
p(U62) = [0]
[0]
p(U63) = [0]
[0]
p(U71) = [0]
[0]
p(U72) = [0]
[0]
p(U73) = [0]
[0]
p(U74) = [0]
[0]
p(U81) = [0]
[0]
p(U82) = [0]
[0]
p(U83) = [0]
[0]
p(U91) = [0]
[0]
p(U92) = [0]
[1]
p(__) = [1 1] x1 + [1 1] x2 + [1]
[0 0] [0 0] [1]
p(a) = [0]
[0]
p(activate) = [1 0] x1 + [0]
[0 1] [0]
p(e) = [1]
[0]
p(i) = [0]
[0]
p(isList) = [0 1] x1 + [0]
[0 1] [0]
p(isNeList) = [1 0] x1 + [0]
[0 1] [0]
p(isNePal) = [0]
[0]
p(isPal) = [0]
[0]
p(isPalListKind) = [0 0] x1 + [0]
[1 0] [0]
p(isQid) = [1 0] x1 + [1]
[1 0] [0]
p(n____) = [1 1] x1 + [1 1] x2 + [1]
[0 0] [0 0] [1]
p(n__a) = [0]
[0]
p(n__e) = [1]
[0]
p(n__i) = [0]
[0]
p(n__nil) = [0]
[1]
p(n__o) = [0]
[0]
p(n__u) = [0]
[0]
p(nil) = [0]
[1]
p(o) = [0]
[0]
p(tt) = [0]
[0]
p(u) = [0]
[0]
p(U11#) = [1 1] x2 + [0]
[0 0] [0]
p(U12#) = [1 0] x2 + [0]
[0 0] [0]
p(U13#) = [0]
[0]
p(U21#) = [1 1] x2 + [1 1] x3 + [1]
[0 0] [1 0] [1]
p(U22#) = [1 1] x2 + [1 1] x3 + [0]
[0 1] [0 0] [0]
p(U23#) = [1 1] x2 + [1 1] x3 + [0]
[1 1] [0 0] [0]
p(U24#) = [1 1] x2 + [1 1] x3 + [0]
[1 0] [0 0] [0]
p(U25#) = [1 1] x2 + [0]
[0 0] [0]
p(U26#) = [0]
[0]
p(U31#) = [0]
[0]
p(U32#) = [0]
[0]
p(U33#) = [0]
[0]
p(U41#) = [1 1] x2 + [1 1] x3 + [1]
[0 0] [0 1] [0]
p(U42#) = [1 1] x2 + [1 1] x3 + [1]
[0 1] [0 0] [1]
p(U43#) = [1 1] x2 + [1 0] x3 + [1]
[1 1] [1 0] [0]
p(U44#) = [1 1] x2 + [1 0] x3 + [0]
[0 0] [0 0] [1]
p(U45#) = [1 0] x2 + [0]
[0 0] [0]
p(U46#) = [0]
[0]
p(U51#) = [1 1] x2 + [1 1] x3 + [0]
[0 0] [0 0] [0]
p(U52#) = [1 1] x2 + [1 1] x3 + [0]
[1 0] [0 1] [0]
p(U53#) = [1 1] x2 + [1 1] x3 + [0]
[0 0] [0 0] [0]
p(U54#) = [1 1] x2 + [1 1] x3 + [0]
[0 0] [1 1] [0]
p(U55#) = [1 1] x2 + [0]
[0 0] [0]
p(U56#) = [0]
[0]
p(U61#) = [0]
[0]
p(U62#) = [0]
[0]
p(U63#) = [0]
[0]
p(U71#) = [0]
[0]
p(U72#) = [0]
[0]
p(U73#) = [0]
[0]
p(U74#) = [0]
[0]
p(U81#) = [0]
[0]
p(U82#) = [0]
[0]
p(U83#) = [0]
[0]
p(U91#) = [0]
[0]
p(U92#) = [0]
[0]
p(__#) = [0]
[0]
p(a#) = [0]
[0]
p(activate#) = [0]
[0]
p(e#) = [0]
[0]
p(i#) = [0]
[0]
p(isList#) = [1 1] x1 + [0]
[0 0] [0]
p(isNeList#) = [1 0] x1 + [0]
[0 1] [0]
p(isNePal#) = [0]
[0]
p(isPal#) = [0]
[0]
p(isPalListKind#) = [0]
[0]
p(isQid#) = [0]
[0]
p(nil#) = [0]
[0]
p(o#) = [0]
[0]
p(u#) = [0]
[0]
p(c_1) = [1 0] x1 + [0]
[0 0] [0]
p(c_2) = [1 0] x1 + [0]
[0 0] [0]
p(c_3) = [0]
[0]
p(c_4) = [1 0] x1 + [0]
[0 0] [0]
p(c_5) = [1 0] x1 + [0]
[0 0] [0]
p(c_6) = [1 0] x1 + [0]
[0 1] [0]
p(c_7) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_8) = [1 0] x1 + [0]
[0 0] [0]
p(c_9) = [0]
[0]
p(c_10) = [0]
[0]
p(c_11) = [0]
[0]
p(c_12) = [0]
[0]
p(c_13) = [1 0] x1 + [0]
[0 0] [0]
p(c_14) = [1 0] x1 + [0]
[0 0] [0]
p(c_15) = [1 0] x1 + [1]
[0 0] [0]
p(c_16) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [1]
p(c_17) = [1 0] x1 + [0]
[0 0] [0]
p(c_18) = [0]
[0]
p(c_19) = [1 0] x1 + [0]
[0 0] [0]
p(c_20) = [1 0] x1 + [0]
[0 0] [0]
p(c_21) = [1 0] x1 + [0]
[0 0] [0]
p(c_22) = [1 0] x1 + [1 1] x2 + [0]
[0 0] [0 0] [0]
p(c_23) = [1 0] x1 + [0]
[0 0] [0]
p(c_24) = [0]
[0]
p(c_25) = [0]
[0]
p(c_26) = [0]
[0]
p(c_27) = [0]
[0]
p(c_28) = [0]
[0]
p(c_29) = [0]
[0]
p(c_30) = [0]
[0]
p(c_31) = [0]
[0]
p(c_32) = [0]
[0]
p(c_33) = [0]
[0]
p(c_34) = [0]
[0]
p(c_35) = [0]
[0]
p(c_36) = [0]
[0]
p(c_37) = [0]
[0]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [0]
[0]
p(c_41) = [0]
[0]
p(c_42) = [0]
[0]
p(c_43) = [0]
[0]
p(c_44) = [0]
[0]
p(c_45) = [0]
[0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [0]
[0]
p(c_49) = [1 0] x1 + [0]
[0 0] [0]
p(c_50) = [1 0] x1 + [1]
[0 0] [0]
p(c_51) = [0]
[0]
p(c_52) = [0]
[0]
p(c_53) = [1 0] x1 + [0]
[0 0] [1]
p(c_54) = [1 0] x1 + [0]
[0 0] [0]
p(c_55) = [0]
[0]
p(c_56) = [0]
[0]
p(c_57) = [0]
[0]
p(c_58) = [0]
[0]
p(c_59) = [0]
[0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [0]
[0]
p(c_64) = [0]
[0]
p(c_65) = [0]
[0]
p(c_66) = [0]
[0]
p(c_67) = [0]
[0]
p(c_68) = [0]
[0]
p(c_69) = [0]
[0]
p(c_70) = [0]
[0]
p(c_71) = [0]
[0]
p(c_72) = [0]
[0]
p(c_73) = [0]
[0]
Following rules are strictly oriented:
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [1]
> [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [1 1] V + [0]
[0 0] [0]
>= [1 0] V + [0]
[0 0] [0]
= c_1(U12#(isPalListKind(activate(V)),activate(V)))
U12#(tt(),V) = [1 0] V + [0]
[0 0] [0]
>= [1 0] V + [0]
[0 0] [0]
= c_2(isNeList#(activate(V)))
U21#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [1 0] [1]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U22#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 1] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U23#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[1 1] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[1 0] [0 0] [0]
= c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U24#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[1 0] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U25#(tt(),V2) = [1 1] V2 + [0]
[0 0] [0]
>= [1 1] V2 + [0]
[0 0] [0]
= c_8(isList#(activate(V2)))
U41#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 1] [0]
>= [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [0]
= c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U42#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [1]
[0 1] [0 0] [1]
>= [1 1] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U43#(tt(),V1,V2) = [1 1] V1 + [1 0] V2 + [1]
[1 1] [1 0] [0]
>= [1 1] V1 + [1 0] V2 + [1]
[0 0] [0 0] [0]
= c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U44#(tt(),V1,V2) = [1 1] V1 + [1 0] V2 + [0]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 0] V2 + [0]
[0 0] [0 0] [1]
= c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
U45#(tt(),V2) = [1 0] V2 + [0]
[0 0] [0]
>= [1 0] V2 + [0]
[0 0] [0]
= c_17(isNeList#(activate(V2)))
U51#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
U52#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[1 0] [0 1] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U53#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
U54#(tt(),V1,V2) = [1 1] V1 + [1 1] V2 + [0]
[0 0] [1 1] [0]
>= [1 1] V1 + [1 1] V2 + [0]
[0 0] [0 0] [0]
= c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
U55#(tt(),V2) = [1 1] V2 + [0]
[0 0] [0]
>= [1 1] V2 + [0]
[0 0] [0]
= c_23(isList#(activate(V2)))
isList#(V) = [1 1] V + [0]
[0 0] [0]
>= [1 1] V + [0]
[0 0] [0]
= c_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [2]
[0 0] [0 0] [0]
>= [1 1] V1 + [1 1] V2 + [2]
[0 0] [0 0] [0]
= c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) = [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [1]
>= [1 1] V1 + [1 1] V2 + [1]
[0 0] [0 0] [1]
= c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
__(X1,X2) = [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [1]
>= [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [1]
= n____(X1,X2)
a() = [0]
[0]
>= [0]
[0]
= n__a()
activate(X) = [1 0] X + [0]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n____(X1,X2)) = [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [1]
>= [1 1] X1 + [1 1] X2 + [1]
[0 0] [0 0] [1]
= __(activate(X1),activate(X2))
activate(n__a()) = [0]
[0]
>= [0]
[0]
= a()
activate(n__e()) = [1]
[0]
>= [1]
[0]
= e()
activate(n__i()) = [0]
[0]
>= [0]
[0]
= i()
activate(n__nil()) = [0]
[1]
>= [0]
[1]
= nil()
activate(n__o()) = [0]
[0]
>= [0]
[0]
= o()
activate(n__u()) = [0]
[0]
>= [0]
[0]
= u()
e() = [1]
[0]
>= [1]
[0]
= n__e()
i() = [0]
[0]
>= [0]
[0]
= n__i()
nil() = [0]
[1]
>= [0]
[1]
= n__nil()
o() = [0]
[0]
>= [0]
[0]
= n__o()
u() = [0]
[0]
>= [0]
[0]
= n__u()
************ Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.b:1.b:1.a:2: Assumption 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
************ Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.b:1.b:1.b:1: RemoveWeakSuffixes 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_49(U11#(isPalListKind(activate(V)),activate(V)))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
isNeList#(n____(V1,V2)) -> c_54(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:W:U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
-->_1 U12#(tt(),V) -> c_2(isNeList#(activate(V))):2
2:W:U12#(tt(),V) -> c_2(isNeList#(activate(V)))
-->_1 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))):21
-->_1 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))):20
3:W:U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
-->_1 U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))):4
4:W:U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
-->_1 U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))):5
5:W:U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
-->_1 U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1))):6
6:W:U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
-->_2 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))):19
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))):18
-->_1 U25#(tt(),V2) -> c_8(isList#(activate(V2))):7
7:W:U25#(tt(),V2) -> c_8(isList#(activate(V2)))
-->_1 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))):19
-->_1 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))):18
8:W:U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
-->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))):9
9:W:U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
-->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))):10
10:W:U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
-->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1))):11
11:W:U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
-->_2 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))):19
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))):18
-->_1 U45#(tt(),V2) -> c_17(isNeList#(activate(V2))):12
12:W:U45#(tt(),V2) -> c_17(isNeList#(activate(V2)))
-->_1 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))):21
-->_1 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))):20
13:W:U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
-->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))):14
14:W:U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
-->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))):15
15:W:U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
-->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1))):16
16:W:U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
-->_2 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))):21
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))):20
-->_1 U55#(tt(),V2) -> c_23(isList#(activate(V2))):17
17:W:U55#(tt(),V2) -> c_23(isList#(activate(V2)))
-->_1 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))):19
-->_1 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))):18
18:W:isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
-->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))):1
19:W:isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
-->_1 U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))):3
20:W:isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
-->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))):8
21:W:isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
-->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))):13
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
1: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V)))
18: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V)))
17: U55#(tt(),V2) -> c_23(isList#(activate(V2)))
16: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2)),isNeList#(activate(V1)))
15: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
14: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
13: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
21: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
12: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)))
11: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
10: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
9: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
8: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
20: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
2: U12#(tt(),V) -> c_2(isNeList#(activate(V)))
7: U25#(tt(),V2) -> c_8(isList#(activate(V2)))
6: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2)),isList#(activate(V1)))
5: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
4: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)))
3: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
19: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)))
************ Step 1.b:7.a:1.a:1.b:4.b:1.b:1.b:1.b:1.b:1.b:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_10/4,c_11/1,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_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/1,c_50/1,c_51/0,c_52/4,c_53/1,c_54/1,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 1.b:7.a:1.b:1: DecomposeDG WORST_CASE(?,O(n^2))
+ Considered Problem:
- Strict DPs:
U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U32#(tt(),V) -> c_11(activate#(V))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
U25#(tt(),V2) -> isList#(activate(V2))
U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(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(activate#(V))
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> activate#(V)
U82#(tt(),V) -> isNePal#(activate(V))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(V) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> 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)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = Just someStrategy, onLower = Nothing}
+ Details:
We decompose the input problem according to the dependency graph into the upper component
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
U25#(tt(),V2) -> isList#(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(activate#(V))
U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(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(activate#(V))
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> activate#(V)
U82#(tt(),V) -> isNePal#(activate(V))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(V) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,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))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) -> activate#(V)
isPal#(V) -> isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
and a lower component
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
Further, following extension rules are added to the lower component.
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
U25#(tt(),V2) -> isList#(activate(V2))
U31#(tt(),V) -> U32#(isPalListKind(activate(V)),activate(V))
U31#(tt(),V) -> activate#(V)
U31#(tt(),V) -> isPalListKind#(activate(V))
U32#(tt(),V) -> activate#(V)
U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(activate(V2))
U61#(tt(),V) -> U62#(isPalListKind(activate(V)),activate(V))
U61#(tt(),V) -> activate#(V)
U61#(tt(),V) -> isPalListKind#(activate(V))
U62#(tt(),V) -> activate#(V)
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U73#(tt(),P) -> activate#(P)
U73#(tt(),P) -> isPalListKind#(activate(P))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> activate#(V)
U82#(tt(),V) -> isNePal#(activate(V))
U91#(tt(),V2) -> activate#(V2)
U91#(tt(),V2) -> isPalListKind#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(V) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V))
isNeList#(V) -> activate#(V)
isNeList#(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)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V))
isNePal#(V) -> activate#(V)
isNePal#(V) -> isPalListKind#(activate(V))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) -> activate#(V)
isPal#(V) -> isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2))
isPalListKind#(n____(V1,V2)) -> activate#(V1)
isPalListKind#(n____(V1,V2)) -> activate#(V2)
isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1))
***** Step 1.b:7.a:1.b:1.a:1: PredecessorEstimation WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> activate#(V)
U12#(tt(),V) -> activate#(V)
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> activate#(V2)
U22#(tt(),V1,V2) -> activate#(V1)
U22#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U25#(tt(),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(activate#(V))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> activate#(V2)
U42#(tt(),V1,V2) -> activate#(V1)
U42#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U45#(tt(),V2) -> activate#(V2)
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> activate#(V2)
U52#(tt(),V1,V2) -> activate#(V1)
U52#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U55#(tt(),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(activate#(V))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U72#(tt(),P) -> activate#(P)
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U81#(tt(),V) -> activate#(V)
U82#(tt(),V) -> activate#(V)
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> activate#(V)
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,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))
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))
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))
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#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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
{13,33}
by application of
Pre({13,33}) = {12,32}.
Here rules are labelled as follows:
1: U11#(tt(),V) -> activate#(V)
2: U12#(tt(),V) -> activate#(V)
3: U21#(tt(),V1,V2) -> activate#(V1)
4: U21#(tt(),V1,V2) -> activate#(V2)
5: U22#(tt(),V1,V2) -> activate#(V1)
6: U22#(tt(),V1,V2) -> activate#(V2)
7: U23#(tt(),V1,V2) -> activate#(V1)
8: U23#(tt(),V1,V2) -> activate#(V2)
9: U24#(tt(),V1,V2) -> activate#(V1)
10: U24#(tt(),V1,V2) -> activate#(V2)
11: U25#(tt(),V2) -> activate#(V2)
12: U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
13: U32#(tt(),V) -> c_11(activate#(V))
14: U41#(tt(),V1,V2) -> activate#(V1)
15: U41#(tt(),V1,V2) -> activate#(V2)
16: U42#(tt(),V1,V2) -> activate#(V1)
17: U42#(tt(),V1,V2) -> activate#(V2)
18: U43#(tt(),V1,V2) -> activate#(V1)
19: U43#(tt(),V1,V2) -> activate#(V2)
20: U44#(tt(),V1,V2) -> activate#(V1)
21: U44#(tt(),V1,V2) -> activate#(V2)
22: U45#(tt(),V2) -> activate#(V2)
23: U51#(tt(),V1,V2) -> activate#(V1)
24: U51#(tt(),V1,V2) -> activate#(V2)
25: U52#(tt(),V1,V2) -> activate#(V1)
26: U52#(tt(),V1,V2) -> activate#(V2)
27: U53#(tt(),V1,V2) -> activate#(V1)
28: U53#(tt(),V1,V2) -> activate#(V2)
29: U54#(tt(),V1,V2) -> activate#(V1)
30: U54#(tt(),V1,V2) -> activate#(V2)
31: U55#(tt(),V2) -> activate#(V2)
32: U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
33: U62#(tt(),V) -> c_26(activate#(V))
34: U71#(tt(),I,P) -> activate#(I)
35: U71#(tt(),I,P) -> activate#(P)
36: U72#(tt(),P) -> activate#(P)
37: U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
38: U81#(tt(),V) -> activate#(V)
39: U82#(tt(),V) -> activate#(V)
40: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
41: isList#(V) -> activate#(V)
42: isList#(n____(V1,V2)) -> activate#(V1)
43: isList#(n____(V1,V2)) -> activate#(V2)
44: isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
45: isNeList#(n____(V1,V2)) -> activate#(V1)
46: isNeList#(n____(V1,V2)) -> activate#(V2)
47: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
48: isNePal#(n____(I,n____(P,I))) -> activate#(I)
49: isNePal#(n____(I,n____(P,I))) -> activate#(P)
50: isPal#(V) -> activate#(V)
51: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
52: U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
53: U11#(tt(),V) -> isPalListKind#(activate(V))
54: U12#(tt(),V) -> isNeList#(activate(V))
55: U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
56: U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
57: U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
58: U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
59: U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
60: U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
61: U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
62: U24#(tt(),V1,V2) -> isList#(activate(V1))
63: U25#(tt(),V2) -> isList#(activate(V2))
64: U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
65: U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
66: U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
67: U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
68: U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
69: U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
70: U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
71: U44#(tt(),V1,V2) -> isList#(activate(V1))
72: U45#(tt(),V2) -> isNeList#(activate(V2))
73: U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
74: U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
75: U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
76: U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
77: U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
78: U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
79: U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
80: U54#(tt(),V1,V2) -> isNeList#(activate(V1))
81: U55#(tt(),V2) -> isList#(activate(V2))
82: U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
83: U71#(tt(),I,P) -> isPalListKind#(activate(I))
84: U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
85: U72#(tt(),P) -> isPal#(activate(P))
86: U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
87: U81#(tt(),V) -> isPalListKind#(activate(V))
88: U82#(tt(),V) -> isNePal#(activate(V))
89: isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
90: isList#(V) -> isPalListKind#(activate(V))
91: isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
92: isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
93: isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
94: isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
95: isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
96: isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
97: isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
98: isPal#(V) -> isPalListKind#(activate(V))
***** Step 1.b:7.a:1.b:1.a:2: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> activate#(V)
U12#(tt(),V) -> activate#(V)
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> activate#(V2)
U22#(tt(),V1,V2) -> activate#(V1)
U22#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U25#(tt(),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) -> activate#(V1)
U41#(tt(),V1,V2) -> activate#(V2)
U42#(tt(),V1,V2) -> activate#(V1)
U42#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U45#(tt(),V2) -> activate#(V2)
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> activate#(V2)
U52#(tt(),V1,V2) -> activate#(V1)
U52#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U55#(tt(),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) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U72#(tt(),P) -> activate#(P)
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U81#(tt(),V) -> activate#(V)
U82#(tt(),V) -> activate#(V)
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> activate#(V)
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,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))
U32#(tt(),V) -> c_11(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))
U62#(tt(),V) -> c_26(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))
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#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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) -> activate#(V)
2:S:U12#(tt(),V) -> activate#(V)
3:S:U21#(tt(),V1,V2) -> activate#(V1)
4:S:U21#(tt(),V1,V2) -> activate#(V2)
5:S:U22#(tt(),V1,V2) -> activate#(V1)
6:S:U22#(tt(),V1,V2) -> activate#(V2)
7:S:U23#(tt(),V1,V2) -> activate#(V1)
8:S:U23#(tt(),V1,V2) -> activate#(V2)
9:S:U24#(tt(),V1,V2) -> activate#(V1)
10:S:U24#(tt(),V1,V2) -> activate#(V2)
11:S:U25#(tt(),V2) -> activate#(V2)
12: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
-->_1 U32#(tt(),V) -> c_11(activate#(V)):62
13:S:U41#(tt(),V1,V2) -> activate#(V1)
14:S:U41#(tt(),V1,V2) -> activate#(V2)
15:S:U42#(tt(),V1,V2) -> activate#(V1)
16:S:U42#(tt(),V1,V2) -> activate#(V2)
17:S:U43#(tt(),V1,V2) -> activate#(V1)
18:S:U43#(tt(),V1,V2) -> activate#(V2)
19:S:U44#(tt(),V1,V2) -> activate#(V1)
20:S:U44#(tt(),V1,V2) -> activate#(V2)
21:S:U45#(tt(),V2) -> activate#(V2)
22:S:U51#(tt(),V1,V2) -> activate#(V1)
23:S:U51#(tt(),V1,V2) -> activate#(V2)
24:S:U52#(tt(),V1,V2) -> activate#(V1)
25:S:U52#(tt(),V1,V2) -> activate#(V2)
26:S:U53#(tt(),V1,V2) -> activate#(V1)
27:S:U53#(tt(),V1,V2) -> activate#(V2)
28:S:U54#(tt(),V1,V2) -> activate#(V1)
29:S:U54#(tt(),V1,V2) -> activate#(V2)
30:S:U55#(tt(),V2) -> activate#(V2)
31: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
-->_1 U62#(tt(),V) -> c_26(activate#(V)):81
32:S:U71#(tt(),I,P) -> activate#(I)
33:S:U71#(tt(),I,P) -> activate#(P)
34:S:U72#(tt(),P) -> activate#(P)
35:S:U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
36:S:U81#(tt(),V) -> activate#(V)
37:S:U82#(tt(),V) -> activate#(V)
38:S:U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
39:S:isList#(V) -> activate#(V)
40:S:isList#(n____(V1,V2)) -> activate#(V1)
41:S:isList#(n____(V1,V2)) -> activate#(V2)
42:S:isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
-->_1 U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):12
43:S:isNeList#(n____(V1,V2)) -> activate#(V1)
44:S:isNeList#(n____(V1,V2)) -> activate#(V2)
45:S:isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
-->_1 U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
46:S:isNePal#(n____(I,n____(P,I))) -> activate#(I)
47:S:isNePal#(n____(I,n____(P,I))) -> activate#(P)
48:S:isPal#(V) -> activate#(V)
49:S:isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
-->_1 U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2)):38
50:W:U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
-->_1 U12#(tt(),V) -> isNeList#(activate(V)):52
-->_1 U12#(tt(),V) -> activate#(V):2
51:W:U11#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
52:W:U12#(tt(),V) -> isNeList#(activate(V))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):95
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):94
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):93
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):44
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):43
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):42
53:W:U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)):56
-->_1 U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)):55
-->_1 U22#(tt(),V1,V2) -> activate#(V2):6
-->_1 U22#(tt(),V1,V2) -> activate#(V1):5
54:W:U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
55:W:U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)):58
-->_1 U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)):57
-->_1 U23#(tt(),V1,V2) -> activate#(V2):8
-->_1 U23#(tt(),V1,V2) -> activate#(V1):7
56:W:U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
57:W:U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U24#(tt(),V1,V2) -> isList#(activate(V1)):60
-->_1 U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)):59
-->_1 U24#(tt(),V1,V2) -> activate#(V2):10
-->_1 U24#(tt(),V1,V2) -> activate#(V1):9
58:W:U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
59:W:U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
-->_1 U25#(tt(),V2) -> isList#(activate(V2)):61
-->_1 U25#(tt(),V2) -> activate#(V2):11
60:W:U24#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):92
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):91
-->_1 isList#(V) -> isPalListKind#(activate(V)):90
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):89
-->_1 isList#(n____(V1,V2)) -> activate#(V2):41
-->_1 isList#(n____(V1,V2)) -> activate#(V1):40
-->_1 isList#(V) -> activate#(V):39
61:W:U25#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):92
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):91
-->_1 isList#(V) -> isPalListKind#(activate(V)):90
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):89
-->_1 isList#(n____(V1,V2)) -> activate#(V2):41
-->_1 isList#(n____(V1,V2)) -> activate#(V1):40
-->_1 isList#(V) -> activate#(V):39
62:W:U32#(tt(),V) -> c_11(activate#(V))
63:W:U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)):66
-->_1 U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)):65
-->_1 U42#(tt(),V1,V2) -> activate#(V2):16
-->_1 U42#(tt(),V1,V2) -> activate#(V1):15
64:W:U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
65:W:U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)):68
-->_1 U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)):67
-->_1 U43#(tt(),V1,V2) -> activate#(V2):18
-->_1 U43#(tt(),V1,V2) -> activate#(V1):17
66:W:U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
67:W:U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U44#(tt(),V1,V2) -> isList#(activate(V1)):70
-->_1 U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)):69
-->_1 U44#(tt(),V1,V2) -> activate#(V2):20
-->_1 U44#(tt(),V1,V2) -> activate#(V1):19
68:W:U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
69:W:U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
-->_1 U45#(tt(),V2) -> isNeList#(activate(V2)):71
-->_1 U45#(tt(),V2) -> activate#(V2):21
70:W:U44#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):92
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):91
-->_1 isList#(V) -> isPalListKind#(activate(V)):90
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):89
-->_1 isList#(n____(V1,V2)) -> activate#(V2):41
-->_1 isList#(n____(V1,V2)) -> activate#(V1):40
-->_1 isList#(V) -> activate#(V):39
71:W:U45#(tt(),V2) -> isNeList#(activate(V2))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):95
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):94
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):93
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):44
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):43
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):42
72:W:U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)):75
-->_1 U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)):74
-->_1 U52#(tt(),V1,V2) -> activate#(V2):25
-->_1 U52#(tt(),V1,V2) -> activate#(V1):24
73:W:U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
74:W:U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)):77
-->_1 U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)):76
-->_1 U53#(tt(),V1,V2) -> activate#(V2):27
-->_1 U53#(tt(),V1,V2) -> activate#(V1):26
75:W:U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
76:W:U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U54#(tt(),V1,V2) -> isNeList#(activate(V1)):79
-->_1 U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)):78
-->_1 U54#(tt(),V1,V2) -> activate#(V2):29
-->_1 U54#(tt(),V1,V2) -> activate#(V1):28
77:W:U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
78:W:U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
-->_1 U55#(tt(),V2) -> isList#(activate(V2)):80
-->_1 U55#(tt(),V2) -> activate#(V2):30
79:W:U54#(tt(),V1,V2) -> isNeList#(activate(V1))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):95
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):94
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):93
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):44
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):43
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):42
80:W:U55#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):92
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):91
-->_1 isList#(V) -> isPalListKind#(activate(V)):90
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):89
-->_1 isList#(n____(V1,V2)) -> activate#(V2):41
-->_1 isList#(n____(V1,V2)) -> activate#(V1):40
-->_1 isList#(V) -> activate#(V):39
81:W:U62#(tt(),V) -> c_26(activate#(V))
82:W:U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
-->_1 U72#(tt(),P) -> isPal#(activate(P)):85
-->_1 U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)):84
-->_1 U72#(tt(),P) -> activate#(P):34
83:W:U71#(tt(),I,P) -> isPalListKind#(activate(I))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
84:W:U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
-->_1 U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P)):35
85:W:U72#(tt(),P) -> isPal#(activate(P))
-->_1 isPal#(V) -> isPalListKind#(activate(V)):98
-->_1 isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)):97
-->_1 isPal#(V) -> activate#(V):48
86:W:U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
-->_1 U82#(tt(),V) -> isNePal#(activate(V)):88
-->_1 U82#(tt(),V) -> activate#(V):37
87:W:U81#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
88:W:U82#(tt(),V) -> isNePal#(activate(V))
-->_1 isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)):96
-->_1 isNePal#(n____(I,n____(P,I))) -> activate#(P):47
-->_1 isNePal#(n____(I,n____(P,I))) -> activate#(I):46
-->_1 isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):45
89:W:isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
-->_1 U11#(tt(),V) -> isPalListKind#(activate(V)):51
-->_1 U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)):50
-->_1 U11#(tt(),V) -> activate#(V):1
90:W:isList#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
91:W:isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)):54
-->_1 U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)):53
-->_1 U21#(tt(),V1,V2) -> activate#(V2):4
-->_1 U21#(tt(),V1,V2) -> activate#(V1):3
92:W:isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
93:W:isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)):64
-->_1 U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)):63
-->_1 U41#(tt(),V1,V2) -> activate#(V2):14
-->_1 U41#(tt(),V1,V2) -> activate#(V1):13
94:W:isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)):73
-->_1 U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)):72
-->_1 U51#(tt(),V1,V2) -> activate#(V2):23
-->_1 U51#(tt(),V1,V2) -> activate#(V1):22
95:W:isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
96:W:isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
-->_1 U71#(tt(),I,P) -> isPalListKind#(activate(I)):83
-->_1 U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)):82
-->_1 U71#(tt(),I,P) -> activate#(P):33
-->_1 U71#(tt(),I,P) -> activate#(I):32
97:W:isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
-->_1 U81#(tt(),V) -> isPalListKind#(activate(V)):87
-->_1 U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)):86
-->_1 U81#(tt(),V) -> activate#(V):36
98:W:isPal#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
81: U62#(tt(),V) -> c_26(activate#(V))
62: U32#(tt(),V) -> c_11(activate#(V))
***** Step 1.b:7.a:1.b:1.a:3: SimplifyRHS WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> activate#(V)
U12#(tt(),V) -> activate#(V)
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> activate#(V2)
U22#(tt(),V1,V2) -> activate#(V1)
U22#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U25#(tt(),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) -> activate#(V1)
U41#(tt(),V1,V2) -> activate#(V2)
U42#(tt(),V1,V2) -> activate#(V1)
U42#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U45#(tt(),V2) -> activate#(V2)
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> activate#(V2)
U52#(tt(),V1,V2) -> activate#(V1)
U52#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U55#(tt(),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) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U72#(tt(),P) -> activate#(P)
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U81#(tt(),V) -> activate#(V)
U82#(tt(),V) -> activate#(V)
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> activate#(V)
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,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))
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))
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))
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#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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) -> activate#(V)
2:S:U12#(tt(),V) -> activate#(V)
3:S:U21#(tt(),V1,V2) -> activate#(V1)
4:S:U21#(tt(),V1,V2) -> activate#(V2)
5:S:U22#(tt(),V1,V2) -> activate#(V1)
6:S:U22#(tt(),V1,V2) -> activate#(V2)
7:S:U23#(tt(),V1,V2) -> activate#(V1)
8:S:U23#(tt(),V1,V2) -> activate#(V2)
9:S:U24#(tt(),V1,V2) -> activate#(V1)
10:S:U24#(tt(),V1,V2) -> activate#(V2)
11:S:U25#(tt(),V2) -> activate#(V2)
12: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
13:S:U41#(tt(),V1,V2) -> activate#(V1)
14:S:U41#(tt(),V1,V2) -> activate#(V2)
15:S:U42#(tt(),V1,V2) -> activate#(V1)
16:S:U42#(tt(),V1,V2) -> activate#(V2)
17:S:U43#(tt(),V1,V2) -> activate#(V1)
18:S:U43#(tt(),V1,V2) -> activate#(V2)
19:S:U44#(tt(),V1,V2) -> activate#(V1)
20:S:U44#(tt(),V1,V2) -> activate#(V2)
21:S:U45#(tt(),V2) -> activate#(V2)
22:S:U51#(tt(),V1,V2) -> activate#(V1)
23:S:U51#(tt(),V1,V2) -> activate#(V2)
24:S:U52#(tt(),V1,V2) -> activate#(V1)
25:S:U52#(tt(),V1,V2) -> activate#(V2)
26:S:U53#(tt(),V1,V2) -> activate#(V1)
27:S:U53#(tt(),V1,V2) -> activate#(V2)
28:S:U54#(tt(),V1,V2) -> activate#(V1)
29:S:U54#(tt(),V1,V2) -> activate#(V2)
30:S:U55#(tt(),V2) -> activate#(V2)
31: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
32:S:U71#(tt(),I,P) -> activate#(I)
33:S:U71#(tt(),I,P) -> activate#(P)
34:S:U72#(tt(),P) -> activate#(P)
35:S:U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
36:S:U81#(tt(),V) -> activate#(V)
37:S:U82#(tt(),V) -> activate#(V)
38:S:U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
39:S:isList#(V) -> activate#(V)
40:S:isList#(n____(V1,V2)) -> activate#(V1)
41:S:isList#(n____(V1,V2)) -> activate#(V2)
42:S:isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
-->_1 U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):12
43:S:isNeList#(n____(V1,V2)) -> activate#(V1)
44:S:isNeList#(n____(V1,V2)) -> activate#(V2)
45:S:isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
-->_1 U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
46:S:isNePal#(n____(I,n____(P,I))) -> activate#(I)
47:S:isNePal#(n____(I,n____(P,I))) -> activate#(P)
48:S:isPal#(V) -> activate#(V)
49:S:isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
-->_1 U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2)):38
50:W:U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
-->_1 U12#(tt(),V) -> isNeList#(activate(V)):52
-->_1 U12#(tt(),V) -> activate#(V):2
51:W:U11#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
52:W:U12#(tt(),V) -> isNeList#(activate(V))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):95
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):94
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):93
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):44
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):43
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):42
53:W:U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)):56
-->_1 U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)):55
-->_1 U22#(tt(),V1,V2) -> activate#(V2):6
-->_1 U22#(tt(),V1,V2) -> activate#(V1):5
54:W:U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
55:W:U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)):58
-->_1 U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)):57
-->_1 U23#(tt(),V1,V2) -> activate#(V2):8
-->_1 U23#(tt(),V1,V2) -> activate#(V1):7
56:W:U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
57:W:U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U24#(tt(),V1,V2) -> isList#(activate(V1)):60
-->_1 U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)):59
-->_1 U24#(tt(),V1,V2) -> activate#(V2):10
-->_1 U24#(tt(),V1,V2) -> activate#(V1):9
58:W:U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
59:W:U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
-->_1 U25#(tt(),V2) -> isList#(activate(V2)):61
-->_1 U25#(tt(),V2) -> activate#(V2):11
60:W:U24#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):92
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):91
-->_1 isList#(V) -> isPalListKind#(activate(V)):90
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):89
-->_1 isList#(n____(V1,V2)) -> activate#(V2):41
-->_1 isList#(n____(V1,V2)) -> activate#(V1):40
-->_1 isList#(V) -> activate#(V):39
61:W:U25#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):92
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):91
-->_1 isList#(V) -> isPalListKind#(activate(V)):90
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):89
-->_1 isList#(n____(V1,V2)) -> activate#(V2):41
-->_1 isList#(n____(V1,V2)) -> activate#(V1):40
-->_1 isList#(V) -> activate#(V):39
63:W:U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)):66
-->_1 U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)):65
-->_1 U42#(tt(),V1,V2) -> activate#(V2):16
-->_1 U42#(tt(),V1,V2) -> activate#(V1):15
64:W:U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
65:W:U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)):68
-->_1 U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)):67
-->_1 U43#(tt(),V1,V2) -> activate#(V2):18
-->_1 U43#(tt(),V1,V2) -> activate#(V1):17
66:W:U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
67:W:U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U44#(tt(),V1,V2) -> isList#(activate(V1)):70
-->_1 U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)):69
-->_1 U44#(tt(),V1,V2) -> activate#(V2):20
-->_1 U44#(tt(),V1,V2) -> activate#(V1):19
68:W:U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
69:W:U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
-->_1 U45#(tt(),V2) -> isNeList#(activate(V2)):71
-->_1 U45#(tt(),V2) -> activate#(V2):21
70:W:U44#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):92
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):91
-->_1 isList#(V) -> isPalListKind#(activate(V)):90
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):89
-->_1 isList#(n____(V1,V2)) -> activate#(V2):41
-->_1 isList#(n____(V1,V2)) -> activate#(V1):40
-->_1 isList#(V) -> activate#(V):39
71:W:U45#(tt(),V2) -> isNeList#(activate(V2))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):95
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):94
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):93
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):44
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):43
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):42
72:W:U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)):75
-->_1 U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)):74
-->_1 U52#(tt(),V1,V2) -> activate#(V2):25
-->_1 U52#(tt(),V1,V2) -> activate#(V1):24
73:W:U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
74:W:U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)):77
-->_1 U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)):76
-->_1 U53#(tt(),V1,V2) -> activate#(V2):27
-->_1 U53#(tt(),V1,V2) -> activate#(V1):26
75:W:U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
76:W:U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U54#(tt(),V1,V2) -> isNeList#(activate(V1)):79
-->_1 U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)):78
-->_1 U54#(tt(),V1,V2) -> activate#(V2):29
-->_1 U54#(tt(),V1,V2) -> activate#(V1):28
77:W:U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
78:W:U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
-->_1 U55#(tt(),V2) -> isList#(activate(V2)):80
-->_1 U55#(tt(),V2) -> activate#(V2):30
79:W:U54#(tt(),V1,V2) -> isNeList#(activate(V1))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):95
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):94
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):93
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):44
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):43
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):42
80:W:U55#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):92
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):91
-->_1 isList#(V) -> isPalListKind#(activate(V)):90
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):89
-->_1 isList#(n____(V1,V2)) -> activate#(V2):41
-->_1 isList#(n____(V1,V2)) -> activate#(V1):40
-->_1 isList#(V) -> activate#(V):39
82:W:U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
-->_1 U72#(tt(),P) -> isPal#(activate(P)):85
-->_1 U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)):84
-->_1 U72#(tt(),P) -> activate#(P):34
83:W:U71#(tt(),I,P) -> isPalListKind#(activate(I))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
84:W:U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
-->_1 U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P)):35
85:W:U72#(tt(),P) -> isPal#(activate(P))
-->_1 isPal#(V) -> isPalListKind#(activate(V)):98
-->_1 isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)):97
-->_1 isPal#(V) -> activate#(V):48
86:W:U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
-->_1 U82#(tt(),V) -> isNePal#(activate(V)):88
-->_1 U82#(tt(),V) -> activate#(V):37
87:W:U81#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
88:W:U82#(tt(),V) -> isNePal#(activate(V))
-->_1 isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)):96
-->_1 isNePal#(n____(I,n____(P,I))) -> activate#(P):47
-->_1 isNePal#(n____(I,n____(P,I))) -> activate#(I):46
-->_1 isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):45
89:W:isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
-->_1 U11#(tt(),V) -> isPalListKind#(activate(V)):51
-->_1 U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)):50
-->_1 U11#(tt(),V) -> activate#(V):1
90:W:isList#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
91:W:isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)):54
-->_1 U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)):53
-->_1 U21#(tt(),V1,V2) -> activate#(V2):4
-->_1 U21#(tt(),V1,V2) -> activate#(V1):3
92:W:isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
93:W:isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)):64
-->_1 U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)):63
-->_1 U41#(tt(),V1,V2) -> activate#(V2):14
-->_1 U41#(tt(),V1,V2) -> activate#(V1):13
94:W:isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)):73
-->_1 U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)):72
-->_1 U51#(tt(),V1,V2) -> activate#(V2):23
-->_1 U51#(tt(),V1,V2) -> activate#(V1):22
95:W:isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
96:W:isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
-->_1 U71#(tt(),I,P) -> isPalListKind#(activate(I)):83
-->_1 U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)):82
-->_1 U71#(tt(),I,P) -> activate#(P):33
-->_1 U71#(tt(),I,P) -> activate#(I):32
97:W:isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
-->_1 U81#(tt(),V) -> isPalListKind#(activate(V)):87
-->_1 U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)):86
-->_1 U81#(tt(),V) -> activate#(V):36
98:W:isPal#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):49
Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
***** Step 1.b:7.a:1.b:1.a:4: PredecessorEstimationCP WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> activate#(V)
U12#(tt(),V) -> activate#(V)
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> activate#(V2)
U22#(tt(),V1,V2) -> activate#(V1)
U22#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U25#(tt(),V2) -> activate#(V2)
U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> activate#(V2)
U42#(tt(),V1,V2) -> activate#(V1)
U42#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U45#(tt(),V2) -> activate#(V2)
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> activate#(V2)
U52#(tt(),V1,V2) -> activate#(V1)
U52#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U55#(tt(),V2) -> activate#(V2)
U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U72#(tt(),P) -> activate#(P)
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
U81#(tt(),V) -> activate#(V)
U82#(tt(),V) -> activate#(V)
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> activate#(V)
isPalListKind#(n____(V1,V2)) -> c_59(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))
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))
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#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
32: U71#(tt(),I,P) -> activate#(I)
33: U71#(tt(),I,P) -> activate#(P)
34: U72#(tt(),P) -> activate#(P)
35: U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
36: U81#(tt(),V) -> activate#(V)
37: U82#(tt(),V) -> activate#(V)
45: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
46: isNePal#(n____(I,n____(P,I))) -> activate#(I)
47: isNePal#(n____(I,n____(P,I))) -> activate#(P)
48: isPal#(V) -> activate#(V)
Consider the set of all dependency pairs
1: U11#(tt(),V) -> activate#(V)
2: U12#(tt(),V) -> activate#(V)
3: U21#(tt(),V1,V2) -> activate#(V1)
4: U21#(tt(),V1,V2) -> activate#(V2)
5: U22#(tt(),V1,V2) -> activate#(V1)
6: U22#(tt(),V1,V2) -> activate#(V2)
7: U23#(tt(),V1,V2) -> activate#(V1)
8: U23#(tt(),V1,V2) -> activate#(V2)
9: U24#(tt(),V1,V2) -> activate#(V1)
10: U24#(tt(),V1,V2) -> activate#(V2)
11: U25#(tt(),V2) -> activate#(V2)
12: U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
13: U41#(tt(),V1,V2) -> activate#(V1)
14: U41#(tt(),V1,V2) -> activate#(V2)
15: U42#(tt(),V1,V2) -> activate#(V1)
16: U42#(tt(),V1,V2) -> activate#(V2)
17: U43#(tt(),V1,V2) -> activate#(V1)
18: U43#(tt(),V1,V2) -> activate#(V2)
19: U44#(tt(),V1,V2) -> activate#(V1)
20: U44#(tt(),V1,V2) -> activate#(V2)
21: U45#(tt(),V2) -> activate#(V2)
22: U51#(tt(),V1,V2) -> activate#(V1)
23: U51#(tt(),V1,V2) -> activate#(V2)
24: U52#(tt(),V1,V2) -> activate#(V1)
25: U52#(tt(),V1,V2) -> activate#(V2)
26: U53#(tt(),V1,V2) -> activate#(V1)
27: U53#(tt(),V1,V2) -> activate#(V2)
28: U54#(tt(),V1,V2) -> activate#(V1)
29: U54#(tt(),V1,V2) -> activate#(V2)
30: U55#(tt(),V2) -> activate#(V2)
31: U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
32: U71#(tt(),I,P) -> activate#(I)
33: U71#(tt(),I,P) -> activate#(P)
34: U72#(tt(),P) -> activate#(P)
35: U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
36: U81#(tt(),V) -> activate#(V)
37: U82#(tt(),V) -> activate#(V)
38: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
39: isList#(V) -> activate#(V)
40: isList#(n____(V1,V2)) -> activate#(V1)
41: isList#(n____(V1,V2)) -> activate#(V2)
42: isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
43: isNeList#(n____(V1,V2)) -> activate#(V1)
44: isNeList#(n____(V1,V2)) -> activate#(V2)
45: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
46: isNePal#(n____(I,n____(P,I))) -> activate#(I)
47: isNePal#(n____(I,n____(P,I))) -> activate#(P)
48: isPal#(V) -> activate#(V)
49: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
50: U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
51: U11#(tt(),V) -> isPalListKind#(activate(V))
52: U12#(tt(),V) -> isNeList#(activate(V))
53: U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
54: U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
55: U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
56: U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
57: U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
58: U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
59: U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
60: U24#(tt(),V1,V2) -> isList#(activate(V1))
61: U25#(tt(),V2) -> isList#(activate(V2))
62: U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
63: U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
64: U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
65: U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
66: U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
67: U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
68: U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
69: U44#(tt(),V1,V2) -> isList#(activate(V1))
70: U45#(tt(),V2) -> isNeList#(activate(V2))
71: U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
72: U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
73: U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
74: U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
75: U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
76: U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
77: U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
78: U54#(tt(),V1,V2) -> isNeList#(activate(V1))
79: U55#(tt(),V2) -> isList#(activate(V2))
80: U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
81: U71#(tt(),I,P) -> isPalListKind#(activate(I))
82: U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
83: U72#(tt(),P) -> isPal#(activate(P))
84: U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
85: U81#(tt(),V) -> isPalListKind#(activate(V))
86: U82#(tt(),V) -> isNePal#(activate(V))
87: isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
88: isList#(V) -> isPalListKind#(activate(V))
89: isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
90: isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
91: isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
92: isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
93: isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
94: isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
95: isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
96: isPal#(V) -> isPalListKind#(activate(V))
Processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(1))
SPACE(?,?)on application of the dependency pairs
{32,33,34,35,36,37,45,46,47,48}
These cover all (indirect) predecessors of dependency pairs
{31,32,33,34,35,36,37,45,46,47,48}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
****** Step 1.b:7.a:1.b:1.a:4.a:1: NaturalMI WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> activate#(V)
U12#(tt(),V) -> activate#(V)
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> activate#(V2)
U22#(tt(),V1,V2) -> activate#(V1)
U22#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U25#(tt(),V2) -> activate#(V2)
U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> activate#(V2)
U42#(tt(),V1,V2) -> activate#(V1)
U42#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U45#(tt(),V2) -> activate#(V2)
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> activate#(V2)
U52#(tt(),V1,V2) -> activate#(V1)
U52#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U55#(tt(),V2) -> activate#(V2)
U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U72#(tt(),P) -> activate#(P)
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
U81#(tt(),V) -> activate#(V)
U82#(tt(),V) -> activate#(V)
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> activate#(V)
isPalListKind#(n____(V1,V2)) -> c_59(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))
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))
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#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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 first alternative for predecessorEstimation on any intersect of rules of CDG leaf and 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_25) = {1},
uargs(c_30) = {1},
uargs(c_35) = {1},
uargs(c_52) = {1,2},
uargs(c_55) = {1,2},
uargs(c_59) = {1,2}
Following symbols are considered usable:
{U11,U12,U13,U21,U22,U23,U24,U25,U26,isList,isQid,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]
p(U12) = [3]
p(U13) = [3]
p(U21) = [1]
p(U22) = [1]
p(U23) = [1]
p(U24) = [0]
p(U25) = [0]
p(U26) = [0]
p(U31) = [1] x1 + [5]
p(U32) = [1]
p(U33) = [0]
p(U41) = [1] x1 + [4] x2 + [0]
p(U42) = [1] x1 + [0]
p(U43) = [4] x1 + [2] x3 + [2]
p(U44) = [4] x2 + [4]
p(U45) = [3] x1 + [4] x2 + [0]
p(U46) = [4]
p(U51) = [1] x1 + [4] x3 + [2]
p(U52) = [1] x2 + [1] x3 + [0]
p(U53) = [1] x2 + [6]
p(U54) = [2] x1 + [4] x3 + [2]
p(U55) = [4] x1 + [2]
p(U56) = [0]
p(U61) = [6]
p(U62) = [1]
p(U63) = [3]
p(U71) = [1] x1 + [2] x2 + [1] x3 + [2]
p(U72) = [5]
p(U73) = [1] x1 + [4]
p(U74) = [4] x1 + [1]
p(U81) = [1] x1 + [2]
p(U82) = [2] x1 + [4]
p(U83) = [1] x1 + [1]
p(U91) = [4] x1 + [1] x2 + [0]
p(U92) = [0]
p(__) = [1] x1 + [1] x2 + [2]
p(a) = [4]
p(activate) = [0]
p(e) = [0]
p(i) = [0]
p(isList) = [4]
p(isNeList) = [1]
p(isNePal) = [1]
p(isPal) = [4] x1 + [2]
p(isPalListKind) = [0]
p(isQid) = [2]
p(n____) = [0]
p(n__a) = [2]
p(n__e) = [1]
p(n__i) = [0]
p(n__nil) = [0]
p(n__o) = [1]
p(n__u) = [0]
p(nil) = [0]
p(o) = [0]
p(tt) = [0]
p(u) = [1]
p(U11#) = [0]
p(U12#) = [0]
p(U13#) = [2] x1 + [0]
p(U21#) = [0]
p(U22#) = [0]
p(U23#) = [0]
p(U24#) = [0]
p(U25#) = [0]
p(U26#) = [1]
p(U31#) = [0]
p(U32#) = [4] x1 + [2] x2 + [2]
p(U33#) = [1]
p(U41#) = [0]
p(U42#) = [0]
p(U43#) = [0]
p(U44#) = [0]
p(U45#) = [0]
p(U46#) = [4] x1 + [0]
p(U51#) = [0]
p(U52#) = [0]
p(U53#) = [0]
p(U54#) = [0]
p(U55#) = [0]
p(U56#) = [0]
p(U61#) = [0]
p(U62#) = [1] x1 + [1]
p(U63#) = [0]
p(U71#) = [1]
p(U72#) = [1]
p(U73#) = [1]
p(U74#) = [1]
p(U81#) = [1]
p(U82#) = [1]
p(U83#) = [1] x1 + [0]
p(U91#) = [0]
p(U92#) = [1] x1 + [2]
p(__#) = [0]
p(a#) = [0]
p(activate#) = [0]
p(e#) = [2]
p(i#) = [1]
p(isList#) = [0]
p(isNeList#) = [0]
p(isNePal#) = [1]
p(isPal#) = [1]
p(isPalListKind#) = [0]
p(isQid#) = [1]
p(nil#) = [4]
p(o#) = [1]
p(u#) = [4]
p(c_1) = [4] x1 + [2] x2 + [1] x3 + [0]
p(c_2) = [0]
p(c_3) = [0]
p(c_4) = [2] x1 + [2] x2 + [1] x4 + [1]
p(c_5) = [1] x4 + [1] x5 + [0]
p(c_6) = [0]
p(c_7) = [1] x3 + [1]
p(c_8) = [1]
p(c_9) = [0]
p(c_10) = [1] x1 + [0]
p(c_11) = [2]
p(c_12) = [2]
p(c_13) = [2] x3 + [1] x5 + [2]
p(c_14) = [4]
p(c_15) = [1]
p(c_16) = [4] x1 + [2] x4 + [4]
p(c_17) = [1]
p(c_18) = [4]
p(c_19) = [2] x1 + [2] x3 + [0]
p(c_20) = [1]
p(c_21) = [1] x5 + [1]
p(c_22) = [4] x1 + [2]
p(c_23) = [0]
p(c_24) = [0]
p(c_25) = [2] x1 + [0]
p(c_26) = [0]
p(c_27) = [2]
p(c_28) = [2] x2 + [1] x3 + [0]
p(c_29) = [1] x1 + [4]
p(c_30) = [1] x1 + [0]
p(c_31) = [0]
p(c_32) = [1] x3 + [0]
p(c_33) = [1] x2 + [0]
p(c_34) = [0]
p(c_35) = [4] x1 + [0]
p(c_36) = [1]
p(c_37) = [1]
p(c_38) = [4]
p(c_39) = [4]
p(c_40) = [2] x1 + [0]
p(c_41) = [1]
p(c_42) = [2] x1 + [0]
p(c_43) = [0]
p(c_44) = [2] x1 + [4]
p(c_45) = [4] x1 + [0]
p(c_46) = [2] x1 + [1]
p(c_47) = [0]
p(c_48) = [1]
p(c_49) = [2] x1 + [1] x4 + [1]
p(c_50) = [4] x2 + [1] x3 + [1] x4 + [4]
p(c_51) = [1]
p(c_52) = [1] x1 + [1] x2 + [0]
p(c_53) = [4] x3 + [1]
p(c_54) = [2] x1 + [0]
p(c_55) = [4] x1 + [4] x2 + [0]
p(c_56) = [4] x1 + [1]
p(c_57) = [1] x1 + [4]
p(c_58) = [4]
p(c_59) = [4] x1 + [4] x2 + [0]
p(c_60) = [0]
p(c_61) = [0]
p(c_62) = [2]
p(c_63) = [1]
p(c_64) = [0]
p(c_65) = [1]
p(c_66) = [1]
p(c_67) = [2]
p(c_68) = [4]
p(c_69) = [1]
p(c_70) = [1]
p(c_71) = [4]
p(c_72) = [4]
p(c_73) = [0]
Following rules are strictly oriented:
U71#(tt(),I,P) = [1]
> [0]
= activate#(I)
U71#(tt(),I,P) = [1]
> [0]
= activate#(P)
U72#(tt(),P) = [1]
> [0]
= activate#(P)
U73#(tt(),P) = [1]
> [0]
= c_30(isPalListKind#(activate(P)))
U81#(tt(),V) = [1]
> [0]
= activate#(V)
U82#(tt(),V) = [1]
> [0]
= activate#(V)
isNePal#(V) = [1]
> [0]
= c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) = [1]
> [0]
= activate#(I)
isNePal#(n____(I,n____(P,I))) = [1]
> [0]
= activate#(P)
isPal#(V) = [1]
> [0]
= activate#(V)
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [0]
>= [0]
= U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) = [0]
>= [0]
= activate#(V)
U11#(tt(),V) = [0]
>= [0]
= isPalListKind#(activate(V))
U12#(tt(),V) = [0]
>= [0]
= activate#(V)
U12#(tt(),V) = [0]
>= [0]
= isNeList#(activate(V))
U21#(tt(),V1,V2) = [0]
>= [0]
= U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U21#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U21#(tt(),V1,V2) = [0]
>= [0]
= isPalListKind#(activate(V1))
U22#(tt(),V1,V2) = [0]
>= [0]
= U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U22#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U22#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U22#(tt(),V1,V2) = [0]
>= [0]
= isPalListKind#(activate(V2))
U23#(tt(),V1,V2) = [0]
>= [0]
= U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U23#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U23#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U23#(tt(),V1,V2) = [0]
>= [0]
= isPalListKind#(activate(V2))
U24#(tt(),V1,V2) = [0]
>= [0]
= U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U24#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U24#(tt(),V1,V2) = [0]
>= [0]
= isList#(activate(V1))
U25#(tt(),V2) = [0]
>= [0]
= activate#(V2)
U25#(tt(),V2) = [0]
>= [0]
= isList#(activate(V2))
U31#(tt(),V) = [0]
>= [0]
= c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) = [0]
>= [0]
= U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U41#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U41#(tt(),V1,V2) = [0]
>= [0]
= isPalListKind#(activate(V1))
U42#(tt(),V1,V2) = [0]
>= [0]
= U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U42#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U42#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U42#(tt(),V1,V2) = [0]
>= [0]
= isPalListKind#(activate(V2))
U43#(tt(),V1,V2) = [0]
>= [0]
= U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U43#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U43#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U43#(tt(),V1,V2) = [0]
>= [0]
= isPalListKind#(activate(V2))
U44#(tt(),V1,V2) = [0]
>= [0]
= U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U44#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U44#(tt(),V1,V2) = [0]
>= [0]
= isList#(activate(V1))
U45#(tt(),V2) = [0]
>= [0]
= activate#(V2)
U45#(tt(),V2) = [0]
>= [0]
= isNeList#(activate(V2))
U51#(tt(),V1,V2) = [0]
>= [0]
= U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U51#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U51#(tt(),V1,V2) = [0]
>= [0]
= isPalListKind#(activate(V1))
U52#(tt(),V1,V2) = [0]
>= [0]
= U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U52#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U52#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U52#(tt(),V1,V2) = [0]
>= [0]
= isPalListKind#(activate(V2))
U53#(tt(),V1,V2) = [0]
>= [0]
= U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U53#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U53#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U53#(tt(),V1,V2) = [0]
>= [0]
= isPalListKind#(activate(V2))
U54#(tt(),V1,V2) = [0]
>= [0]
= U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) = [0]
>= [0]
= activate#(V1)
U54#(tt(),V1,V2) = [0]
>= [0]
= activate#(V2)
U54#(tt(),V1,V2) = [0]
>= [0]
= isNeList#(activate(V1))
U55#(tt(),V2) = [0]
>= [0]
= activate#(V2)
U55#(tt(),V2) = [0]
>= [0]
= isList#(activate(V2))
U61#(tt(),V) = [0]
>= [0]
= c_25(isPalListKind#(activate(V)))
U71#(tt(),I,P) = [1]
>= [1]
= U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) = [1]
>= [0]
= isPalListKind#(activate(I))
U72#(tt(),P) = [1]
>= [1]
= U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) = [1]
>= [1]
= isPal#(activate(P))
U81#(tt(),V) = [1]
>= [1]
= U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) = [1]
>= [0]
= isPalListKind#(activate(V))
U82#(tt(),V) = [1]
>= [1]
= isNePal#(activate(V))
U91#(tt(),V2) = [0]
>= [0]
= c_35(isPalListKind#(activate(V2)))
isList#(V) = [0]
>= [0]
= U11#(isPalListKind(activate(V)),activate(V))
isList#(V) = [0]
>= [0]
= activate#(V)
isList#(V) = [0]
>= [0]
= isPalListKind#(activate(V))
isList#(n____(V1,V2)) = [0]
>= [0]
= U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) = [0]
>= [0]
= activate#(V1)
isList#(n____(V1,V2)) = [0]
>= [0]
= activate#(V2)
isList#(n____(V1,V2)) = [0]
>= [0]
= isPalListKind#(activate(V1))
isNeList#(V) = [0]
>= [0]
= c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) = [0]
>= [0]
= U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [0]
>= [0]
= U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [0]
>= [0]
= activate#(V1)
isNeList#(n____(V1,V2)) = [0]
>= [0]
= activate#(V2)
isNeList#(n____(V1,V2)) = [0]
>= [0]
= isPalListKind#(activate(V1))
isNePal#(n____(I,n____(P,I))) = [1]
>= [1]
= U71#(isQid(activate(I)),activate(I),activate(P))
isPal#(V) = [1]
>= [1]
= U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) = [1]
>= [0]
= isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) = [0]
>= [0]
= c_59(U91#(isPalListKind(activate(V1)),activate(V2)),isPalListKind#(activate(V1)))
U11(tt(),V) = [3]
>= [3]
= U12(isPalListKind(activate(V)),activate(V))
U12(tt(),V) = [3]
>= [3]
= U13(isNeList(activate(V)))
U13(tt()) = [3]
>= [0]
= tt()
U21(tt(),V1,V2) = [1]
>= [1]
= U22(isPalListKind(activate(V1)),activate(V1),activate(V2))
U22(tt(),V1,V2) = [1]
>= [1]
= U23(isPalListKind(activate(V2)),activate(V1),activate(V2))
U23(tt(),V1,V2) = [1]
>= [0]
= U24(isPalListKind(activate(V2)),activate(V1),activate(V2))
U24(tt(),V1,V2) = [0]
>= [0]
= U25(isList(activate(V1)),activate(V2))
U25(tt(),V2) = [0]
>= [0]
= U26(isList(activate(V2)))
U26(tt()) = [0]
>= [0]
= tt()
isList(V) = [4]
>= [3]
= U11(isPalListKind(activate(V)),activate(V))
isList(n____(V1,V2)) = [4]
>= [1]
= U21(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList(n__nil()) = [4]
>= [0]
= tt()
isQid(n__a()) = [2]
>= [0]
= tt()
isQid(n__e()) = [2]
>= [0]
= tt()
isQid(n__i()) = [2]
>= [0]
= tt()
isQid(n__o()) = [2]
>= [0]
= tt()
isQid(n__u()) = [2]
>= [0]
= tt()
****** Step 1.b:7.a:1.b:1.a:4.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> activate#(V)
U12#(tt(),V) -> activate#(V)
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> activate#(V2)
U22#(tt(),V1,V2) -> activate#(V1)
U22#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U25#(tt(),V2) -> activate#(V2)
U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> activate#(V2)
U42#(tt(),V1,V2) -> activate#(V1)
U42#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U45#(tt(),V2) -> activate#(V2)
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> activate#(V2)
U52#(tt(),V1,V2) -> activate#(V1)
U52#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U55#(tt(),V2) -> activate#(V2)
U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isPalListKind#(n____(V1,V2)) -> c_59(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))
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> 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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
****** Step 1.b:7.a:1.b:1.a:4.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> activate#(V)
U12#(tt(),V) -> activate#(V)
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> activate#(V2)
U22#(tt(),V1,V2) -> activate#(V1)
U22#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U25#(tt(),V2) -> activate#(V2)
U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> activate#(V2)
U42#(tt(),V1,V2) -> activate#(V1)
U42#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U45#(tt(),V2) -> activate#(V2)
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> activate#(V2)
U52#(tt(),V1,V2) -> activate#(V1)
U52#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U55#(tt(),V2) -> activate#(V2)
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isPalListKind#(n____(V1,V2)) -> c_59(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) -> c_25(isPalListKind#(activate(V)))
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> 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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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) -> activate#(V)
2:S:U12#(tt(),V) -> activate#(V)
3:S:U21#(tt(),V1,V2) -> activate#(V1)
4:S:U21#(tt(),V1,V2) -> activate#(V2)
5:S:U22#(tt(),V1,V2) -> activate#(V1)
6:S:U22#(tt(),V1,V2) -> activate#(V2)
7:S:U23#(tt(),V1,V2) -> activate#(V1)
8:S:U23#(tt(),V1,V2) -> activate#(V2)
9:S:U24#(tt(),V1,V2) -> activate#(V1)
10:S:U24#(tt(),V1,V2) -> activate#(V2)
11:S:U25#(tt(),V2) -> activate#(V2)
12:S:U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
13:S:U41#(tt(),V1,V2) -> activate#(V1)
14:S:U41#(tt(),V1,V2) -> activate#(V2)
15:S:U42#(tt(),V1,V2) -> activate#(V1)
16:S:U42#(tt(),V1,V2) -> activate#(V2)
17:S:U43#(tt(),V1,V2) -> activate#(V1)
18:S:U43#(tt(),V1,V2) -> activate#(V2)
19:S:U44#(tt(),V1,V2) -> activate#(V1)
20:S:U44#(tt(),V1,V2) -> activate#(V2)
21:S:U45#(tt(),V2) -> activate#(V2)
22:S:U51#(tt(),V1,V2) -> activate#(V1)
23:S:U51#(tt(),V1,V2) -> activate#(V2)
24:S:U52#(tt(),V1,V2) -> activate#(V1)
25:S:U52#(tt(),V1,V2) -> activate#(V2)
26:S:U53#(tt(),V1,V2) -> activate#(V1)
27:S:U53#(tt(),V1,V2) -> activate#(V2)
28:S:U54#(tt(),V1,V2) -> activate#(V1)
29:S:U54#(tt(),V1,V2) -> activate#(V2)
30:S:U55#(tt(),V2) -> activate#(V2)
31:S:U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
32:S:isList#(V) -> activate#(V)
33:S:isList#(n____(V1,V2)) -> activate#(V1)
34:S:isList#(n____(V1,V2)) -> activate#(V2)
35:S:isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
-->_1 U31#(tt(),V) -> c_10(isPalListKind#(activate(V))):12
36:S:isNeList#(n____(V1,V2)) -> activate#(V1)
37:S:isNeList#(n____(V1,V2)) -> activate#(V2)
38:S:isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
-->_1 U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))):31
39:W:U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
-->_1 U12#(tt(),V) -> isNeList#(activate(V)):41
-->_1 U12#(tt(),V) -> activate#(V):2
40:W:U11#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
41:W:U12#(tt(),V) -> isNeList#(activate(V))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):89
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):88
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):87
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):37
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):36
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):35
42:W:U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)):45
-->_1 U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)):44
-->_1 U22#(tt(),V1,V2) -> activate#(V2):6
-->_1 U22#(tt(),V1,V2) -> activate#(V1):5
43:W:U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
44:W:U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)):47
-->_1 U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)):46
-->_1 U23#(tt(),V1,V2) -> activate#(V2):8
-->_1 U23#(tt(),V1,V2) -> activate#(V1):7
45:W:U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
46:W:U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U24#(tt(),V1,V2) -> isList#(activate(V1)):49
-->_1 U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)):48
-->_1 U24#(tt(),V1,V2) -> activate#(V2):10
-->_1 U24#(tt(),V1,V2) -> activate#(V1):9
47:W:U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
48:W:U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
-->_1 U25#(tt(),V2) -> isList#(activate(V2)):50
-->_1 U25#(tt(),V2) -> activate#(V2):11
49:W:U24#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):86
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):85
-->_1 isList#(V) -> isPalListKind#(activate(V)):84
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):83
-->_1 isList#(n____(V1,V2)) -> activate#(V2):34
-->_1 isList#(n____(V1,V2)) -> activate#(V1):33
-->_1 isList#(V) -> activate#(V):32
50:W:U25#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):86
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):85
-->_1 isList#(V) -> isPalListKind#(activate(V)):84
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):83
-->_1 isList#(n____(V1,V2)) -> activate#(V2):34
-->_1 isList#(n____(V1,V2)) -> activate#(V1):33
-->_1 isList#(V) -> activate#(V):32
51:W:U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)):54
-->_1 U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)):53
-->_1 U42#(tt(),V1,V2) -> activate#(V2):16
-->_1 U42#(tt(),V1,V2) -> activate#(V1):15
52:W:U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
53:W:U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)):56
-->_1 U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)):55
-->_1 U43#(tt(),V1,V2) -> activate#(V2):18
-->_1 U43#(tt(),V1,V2) -> activate#(V1):17
54:W:U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
55:W:U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U44#(tt(),V1,V2) -> isList#(activate(V1)):58
-->_1 U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)):57
-->_1 U44#(tt(),V1,V2) -> activate#(V2):20
-->_1 U44#(tt(),V1,V2) -> activate#(V1):19
56:W:U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
57:W:U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
-->_1 U45#(tt(),V2) -> isNeList#(activate(V2)):59
-->_1 U45#(tt(),V2) -> activate#(V2):21
58:W:U44#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):86
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):85
-->_1 isList#(V) -> isPalListKind#(activate(V)):84
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):83
-->_1 isList#(n____(V1,V2)) -> activate#(V2):34
-->_1 isList#(n____(V1,V2)) -> activate#(V1):33
-->_1 isList#(V) -> activate#(V):32
59:W:U45#(tt(),V2) -> isNeList#(activate(V2))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):89
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):88
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):87
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):37
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):36
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):35
60:W:U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)):63
-->_1 U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)):62
-->_1 U52#(tt(),V1,V2) -> activate#(V2):25
-->_1 U52#(tt(),V1,V2) -> activate#(V1):24
61:W:U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
62:W:U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)):65
-->_1 U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)):64
-->_1 U53#(tt(),V1,V2) -> activate#(V2):27
-->_1 U53#(tt(),V1,V2) -> activate#(V1):26
63:W:U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
64:W:U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U54#(tt(),V1,V2) -> isNeList#(activate(V1)):67
-->_1 U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)):66
-->_1 U54#(tt(),V1,V2) -> activate#(V2):29
-->_1 U54#(tt(),V1,V2) -> activate#(V1):28
65:W:U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
66:W:U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
-->_1 U55#(tt(),V2) -> isList#(activate(V2)):68
-->_1 U55#(tt(),V2) -> activate#(V2):30
67:W:U54#(tt(),V1,V2) -> isNeList#(activate(V1))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):89
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):88
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):87
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):37
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):36
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):35
68:W:U55#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):86
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):85
-->_1 isList#(V) -> isPalListKind#(activate(V)):84
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):83
-->_1 isList#(n____(V1,V2)) -> activate#(V2):34
-->_1 isList#(n____(V1,V2)) -> activate#(V1):33
-->_1 isList#(V) -> activate#(V):32
69:W:U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
70:W:U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
-->_1 U72#(tt(),P) -> isPal#(activate(P)):76
-->_1 U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)):74
-->_1 U72#(tt(),P) -> activate#(P):75
71:W:U71#(tt(),I,P) -> activate#(I)
72:W:U71#(tt(),I,P) -> activate#(P)
73:W:U71#(tt(),I,P) -> isPalListKind#(activate(I))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
74:W:U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
-->_1 U73#(tt(),P) -> c_30(isPalListKind#(activate(P))):77
75:W:U72#(tt(),P) -> activate#(P)
76:W:U72#(tt(),P) -> isPal#(activate(P))
-->_1 isPal#(V) -> isPalListKind#(activate(V)):96
-->_1 isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)):94
-->_1 isPal#(V) -> activate#(V):95
77:W:U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
78:W:U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
-->_1 U82#(tt(),V) -> isNePal#(activate(V)):82
-->_1 U82#(tt(),V) -> activate#(V):81
79:W:U81#(tt(),V) -> activate#(V)
80:W:U81#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
81:W:U82#(tt(),V) -> activate#(V)
82:W:U82#(tt(),V) -> isNePal#(activate(V))
-->_1 isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)):91
-->_1 isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):90
-->_1 isNePal#(n____(I,n____(P,I))) -> activate#(P):93
-->_1 isNePal#(n____(I,n____(P,I))) -> activate#(I):92
83:W:isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
-->_1 U11#(tt(),V) -> isPalListKind#(activate(V)):40
-->_1 U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)):39
-->_1 U11#(tt(),V) -> activate#(V):1
84:W:isList#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
85:W:isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)):43
-->_1 U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)):42
-->_1 U21#(tt(),V1,V2) -> activate#(V2):4
-->_1 U21#(tt(),V1,V2) -> activate#(V1):3
86:W:isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
87:W:isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)):52
-->_1 U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)):51
-->_1 U41#(tt(),V1,V2) -> activate#(V2):14
-->_1 U41#(tt(),V1,V2) -> activate#(V1):13
88:W:isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)):61
-->_1 U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)):60
-->_1 U51#(tt(),V1,V2) -> activate#(V2):23
-->_1 U51#(tt(),V1,V2) -> activate#(V1):22
89:W:isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
90:W:isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
-->_1 U61#(tt(),V) -> c_25(isPalListKind#(activate(V))):69
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
91:W:isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
-->_1 U71#(tt(),I,P) -> isPalListKind#(activate(I)):73
-->_1 U71#(tt(),I,P) -> activate#(P):72
-->_1 U71#(tt(),I,P) -> activate#(I):71
-->_1 U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)):70
92:W:isNePal#(n____(I,n____(P,I))) -> activate#(I)
93:W:isNePal#(n____(I,n____(P,I))) -> activate#(P)
94:W:isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
-->_1 U81#(tt(),V) -> isPalListKind#(activate(V)):80
-->_1 U81#(tt(),V) -> activate#(V):79
-->_1 U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)):78
95:W:isPal#(V) -> activate#(V)
96:W:isPal#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):38
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
75: U72#(tt(),P) -> activate#(P)
95: isPal#(V) -> activate#(V)
81: U82#(tt(),V) -> activate#(V)
92: isNePal#(n____(I,n____(P,I))) -> activate#(I)
93: isNePal#(n____(I,n____(P,I))) -> activate#(P)
71: U71#(tt(),I,P) -> activate#(I)
72: U71#(tt(),I,P) -> activate#(P)
79: U81#(tt(),V) -> activate#(V)
****** Step 1.b:7.a:1.b:1.a:4.b:2: PredecessorEstimationCP WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> activate#(V)
U12#(tt(),V) -> activate#(V)
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> activate#(V2)
U22#(tt(),V1,V2) -> activate#(V1)
U22#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U25#(tt(),V2) -> activate#(V2)
U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> activate#(V2)
U42#(tt(),V1,V2) -> activate#(V1)
U42#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U45#(tt(),V2) -> activate#(V2)
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> activate#(V2)
U52#(tt(),V1,V2) -> activate#(V1)
U52#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U55#(tt(),V2) -> activate#(V2)
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isPalListKind#(n____(V1,V2)) -> c_59(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) -> c_25(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) -> c_30(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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
1: U11#(tt(),V) -> activate#(V)
2: U12#(tt(),V) -> activate#(V)
3: U21#(tt(),V1,V2) -> activate#(V1)
4: U21#(tt(),V1,V2) -> activate#(V2)
5: U22#(tt(),V1,V2) -> activate#(V1)
6: U22#(tt(),V1,V2) -> activate#(V2)
7: U23#(tt(),V1,V2) -> activate#(V1)
8: U23#(tt(),V1,V2) -> activate#(V2)
9: U24#(tt(),V1,V2) -> activate#(V1)
10: U24#(tt(),V1,V2) -> activate#(V2)
11: U25#(tt(),V2) -> activate#(V2)
12: U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
13: U41#(tt(),V1,V2) -> activate#(V1)
14: U41#(tt(),V1,V2) -> activate#(V2)
15: U42#(tt(),V1,V2) -> activate#(V1)
16: U42#(tt(),V1,V2) -> activate#(V2)
17: U43#(tt(),V1,V2) -> activate#(V1)
18: U43#(tt(),V1,V2) -> activate#(V2)
19: U44#(tt(),V1,V2) -> activate#(V1)
20: U44#(tt(),V1,V2) -> activate#(V2)
21: U45#(tt(),V2) -> activate#(V2)
22: U51#(tt(),V1,V2) -> activate#(V1)
23: U51#(tt(),V1,V2) -> activate#(V2)
24: U52#(tt(),V1,V2) -> activate#(V1)
25: U52#(tt(),V1,V2) -> activate#(V2)
26: U53#(tt(),V1,V2) -> activate#(V1)
27: U53#(tt(),V1,V2) -> activate#(V2)
28: U54#(tt(),V1,V2) -> activate#(V1)
29: U54#(tt(),V1,V2) -> activate#(V2)
30: U55#(tt(),V2) -> activate#(V2)
32: isList#(V) -> activate#(V)
33: isList#(n____(V1,V2)) -> activate#(V1)
34: isList#(n____(V1,V2)) -> activate#(V2)
36: isNeList#(n____(V1,V2)) -> activate#(V1)
37: isNeList#(n____(V1,V2)) -> activate#(V2)
The strictly oriented rules are moved into the weak component.
******* Step 1.b:7.a:1.b:1.a:4.b:2.a:1: NaturalMI WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
U11#(tt(),V) -> activate#(V)
U12#(tt(),V) -> activate#(V)
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> activate#(V2)
U22#(tt(),V1,V2) -> activate#(V1)
U22#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U25#(tt(),V2) -> activate#(V2)
U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> activate#(V2)
U42#(tt(),V1,V2) -> activate#(V1)
U42#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U45#(tt(),V2) -> activate#(V2)
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> activate#(V2)
U52#(tt(),V1,V2) -> activate#(V1)
U52#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U55#(tt(),V2) -> activate#(V2)
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isPalListKind#(n____(V1,V2)) -> c_59(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) -> c_25(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) -> c_30(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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
The following argument positions are considered usable:
uargs(c_10) = {1},
uargs(c_25) = {1},
uargs(c_30) = {1},
uargs(c_35) = {1},
uargs(c_52) = {1,2},
uargs(c_55) = {1,2},
uargs(c_59) = {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]
[0]
p(U12) = [0]
[1]
p(U13) = [0]
[0]
p(U21) = [0]
[0]
p(U22) = [0]
[0]
p(U23) = [0]
[0]
p(U24) = [0]
[0]
p(U25) = [0]
[0]
p(U26) = [0]
[0]
p(U31) = [0]
[0]
p(U32) = [0]
[0]
p(U33) = [0]
[0]
p(U41) = [0]
[0]
p(U42) = [0]
[0]
p(U43) = [0 0] x1 + [0]
[0 1] [1]
p(U44) = [0]
[0]
p(U45) = [0]
[0]
p(U46) = [0]
[1]
p(U51) = [1]
[0]
p(U52) = [0]
[0]
p(U53) = [0 0] x2 + [0]
[0 1] [1]
p(U54) = [0]
[0]
p(U55) = [0]
[0]
p(U56) = [0]
[0]
p(U61) = [0]
[0]
p(U62) = [0]
[0]
p(U63) = [0]
[0]
p(U71) = [0]
[0]
p(U72) = [0]
[0]
p(U73) = [0]
[0]
p(U74) = [0]
[0]
p(U81) = [0]
[0]
p(U82) = [0]
[0]
p(U83) = [1]
[0]
p(U91) = [0]
[1]
p(U92) = [1]
[0]
p(__) = [0]
[0]
p(a) = [0]
[0]
p(activate) = [0]
[1]
p(e) = [0]
[0]
p(i) = [0]
[0]
p(isList) = [0]
[0]
p(isNeList) = [0]
[0]
p(isNePal) = [0]
[0]
p(isPal) = [0]
[0]
p(isPalListKind) = [0]
[1]
p(isQid) = [1 0] x1 + [0]
[0 0] [0]
p(n____) = [0]
[0]
p(n__a) = [0]
[0]
p(n__e) = [1]
[0]
p(n__i) = [0]
[0]
p(n__nil) = [0]
[0]
p(n__o) = [0]
[0]
p(n__u) = [0]
[0]
p(nil) = [0]
[0]
p(o) = [0]
[0]
p(tt) = [0]
[1]
p(u) = [0]
[0]
p(U11#) = [1]
[0]
p(U12#) = [1]
[0]
p(U13#) = [0]
[0]
p(U21#) = [1]
[0]
p(U22#) = [1]
[0]
p(U23#) = [1]
[0]
p(U24#) = [1]
[0]
p(U25#) = [1]
[0]
p(U26#) = [0]
[0]
p(U31#) = [1]
[0]
p(U32#) = [0]
[0]
p(U33#) = [0]
[0]
p(U41#) = [1]
[0]
p(U42#) = [1]
[0]
p(U43#) = [1]
[0]
p(U44#) = [1]
[0]
p(U45#) = [1]
[0]
p(U46#) = [0]
[0]
p(U51#) = [1]
[0]
p(U52#) = [1]
[0]
p(U53#) = [1]
[0]
p(U54#) = [1]
[0]
p(U55#) = [1]
[0]
p(U56#) = [0]
[0]
p(U61#) = [0]
[1]
p(U62#) = [0]
[0]
p(U63#) = [0]
[0]
p(U71#) = [0]
[1]
p(U72#) = [0]
[1]
p(U73#) = [0]
[1]
p(U74#) = [0]
[0]
p(U81#) = [0]
[1]
p(U82#) = [0]
[1]
p(U83#) = [0]
[0]
p(U91#) = [0]
[0]
p(U92#) = [0]
[0]
p(__#) = [0]
[0]
p(a#) = [0]
[0]
p(activate#) = [0]
[0]
p(e#) = [0]
[0]
p(i#) = [0]
[0]
p(isList#) = [1]
[0]
p(isNeList#) = [1]
[0]
p(isNePal#) = [0]
[1]
p(isPal#) = [0]
[1]
p(isPalListKind#) = [0]
[0]
p(isQid#) = [0]
[0]
p(nil#) = [0]
[0]
p(o#) = [0]
[0]
p(u#) = [0]
[0]
p(c_1) = [0]
[0]
p(c_2) = [0]
[0]
p(c_3) = [0]
[0]
p(c_4) = [0]
[0]
p(c_5) = [0]
[0]
p(c_6) = [0]
[0]
p(c_7) = [0]
[0]
p(c_8) = [0]
[0]
p(c_9) = [0]
[0]
p(c_10) = [1 0] x1 + [0]
[0 0] [0]
p(c_11) = [0]
[0]
p(c_12) = [0]
[0]
p(c_13) = [0]
[0]
p(c_14) = [0]
[0]
p(c_15) = [0]
[0]
p(c_16) = [0]
[0]
p(c_17) = [0]
[0]
p(c_18) = [0]
[0]
p(c_19) = [0]
[0]
p(c_20) = [0]
[0]
p(c_21) = [0]
[0]
p(c_22) = [0]
[0]
p(c_23) = [0]
[0]
p(c_24) = [0]
[0]
p(c_25) = [1 0] x1 + [0]
[0 0] [1]
p(c_26) = [0]
[0]
p(c_27) = [0]
[0]
p(c_28) = [0]
[0]
p(c_29) = [0]
[0]
p(c_30) = [1 0] x1 + [0]
[0 0] [1]
p(c_31) = [0]
[0]
p(c_32) = [0]
[0]
p(c_33) = [0]
[0]
p(c_34) = [0]
[0]
p(c_35) = [1 0] x1 + [0]
[0 0] [0]
p(c_36) = [0]
[0]
p(c_37) = [0]
[0]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [0]
[0]
p(c_41) = [0]
[0]
p(c_42) = [0]
[0]
p(c_43) = [0]
[0]
p(c_44) = [0]
[0]
p(c_45) = [0]
[0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [0]
[0]
p(c_49) = [0]
[0]
p(c_50) = [0]
[0]
p(c_51) = [0]
[0]
p(c_52) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_53) = [0]
[0]
p(c_54) = [0]
[0]
p(c_55) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 0] [0]
p(c_56) = [0]
[0]
p(c_57) = [0]
[0]
p(c_58) = [0]
[0]
p(c_59) = [1 0] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [0]
[0]
p(c_64) = [0]
[0]
p(c_65) = [0]
[0]
p(c_66) = [0]
[0]
p(c_67) = [0]
[0]
p(c_68) = [0]
[0]
p(c_69) = [0]
[0]
p(c_70) = [0]
[0]
p(c_71) = [0]
[0]
p(c_72) = [0]
[0]
p(c_73) = [0]
[0]
Following rules are strictly oriented:
U11#(tt(),V) = [1]
[0]
> [0]
[0]
= activate#(V)
U12#(tt(),V) = [1]
[0]
> [0]
[0]
= activate#(V)
U21#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U21#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U22#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U22#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U23#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U23#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U24#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U24#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U25#(tt(),V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U31#(tt(),V) = [1]
[0]
> [0]
[0]
= c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U41#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U42#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U42#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U43#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U43#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U44#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U44#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U45#(tt(),V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U51#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U51#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U52#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U52#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U53#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U53#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U54#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V1)
U54#(tt(),V1,V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
U55#(tt(),V2) = [1]
[0]
> [0]
[0]
= activate#(V2)
isList#(V) = [1]
[0]
> [0]
[0]
= activate#(V)
isList#(n____(V1,V2)) = [1]
[0]
> [0]
[0]
= activate#(V1)
isList#(n____(V1,V2)) = [1]
[0]
> [0]
[0]
= activate#(V2)
isNeList#(n____(V1,V2)) = [1]
[0]
> [0]
[0]
= activate#(V1)
isNeList#(n____(V1,V2)) = [1]
[0]
> [0]
[0]
= activate#(V2)
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [1]
[0]
>= [1]
[0]
= U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V))
U12#(tt(),V) = [1]
[0]
>= [1]
[0]
= isNeList#(activate(V))
U21#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V1))
U22#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U22#(tt(),V1,V2) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V2))
U23#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U23#(tt(),V1,V2) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V2))
U24#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= isList#(activate(V1))
U25#(tt(),V2) = [1]
[0]
>= [1]
[0]
= isList#(activate(V2))
U41#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V1))
U42#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U42#(tt(),V1,V2) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V2))
U43#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U43#(tt(),V1,V2) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V2))
U44#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= isList#(activate(V1))
U45#(tt(),V2) = [1]
[0]
>= [1]
[0]
= isNeList#(activate(V2))
U51#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V1))
U52#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U52#(tt(),V1,V2) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V2))
U53#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U53#(tt(),V1,V2) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V2))
U54#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) = [1]
[0]
>= [1]
[0]
= isNeList#(activate(V1))
U55#(tt(),V2) = [1]
[0]
>= [1]
[0]
= isList#(activate(V2))
U61#(tt(),V) = [0]
[1]
>= [0]
[1]
= c_25(isPalListKind#(activate(V)))
U71#(tt(),I,P) = [0]
[1]
>= [0]
[1]
= U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) = [0]
[1]
>= [0]
[0]
= isPalListKind#(activate(I))
U72#(tt(),P) = [0]
[1]
>= [0]
[1]
= U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) = [0]
[1]
>= [0]
[1]
= isPal#(activate(P))
U73#(tt(),P) = [0]
[1]
>= [0]
[1]
= c_30(isPalListKind#(activate(P)))
U81#(tt(),V) = [0]
[1]
>= [0]
[1]
= U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) = [0]
[1]
>= [0]
[0]
= isPalListKind#(activate(V))
U82#(tt(),V) = [0]
[1]
>= [0]
[1]
= isNePal#(activate(V))
U91#(tt(),V2) = [0]
[0]
>= [0]
[0]
= c_35(isPalListKind#(activate(V2)))
isList#(V) = [1]
[0]
>= [1]
[0]
= U11#(isPalListKind(activate(V)),activate(V))
isList#(V) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V))
isList#(n____(V1,V2)) = [1]
[0]
>= [1]
[0]
= U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V1))
isNeList#(V) = [1]
[0]
>= [1]
[0]
= c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) = [1]
[0]
>= [1]
[0]
= U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [1]
[0]
>= [1]
[0]
= U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [1]
[0]
>= [0]
[0]
= isPalListKind#(activate(V1))
isNePal#(V) = [0]
[1]
>= [0]
[1]
= c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) = [0]
[1]
>= [0]
[1]
= U71#(isQid(activate(I)),activate(I),activate(P))
isPal#(V) = [0]
[1]
>= [0]
[1]
= U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) = [0]
[1]
>= [0]
[0]
= isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) = [0]
[0]
>= [0]
[0]
= c_59(U91#(isPalListKind(activate(V1)),activate(V2)),isPalListKind#(activate(V1)))
******* Step 1.b:7.a:1.b:1.a:4.b:2.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
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) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(activate(V2))
U61#(tt(),V) -> c_25(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) -> c_30(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) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> 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)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
******* Step 1.b:7.a:1.b:1.a:4.b:2.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
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) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(activate(V2))
U61#(tt(),V) -> c_25(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) -> c_30(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) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> 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)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
2:S:isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
-->_1 U31#(tt(),V) -> c_10(isPalListKind#(activate(V))):27
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
3:S:isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
-->_1 U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))):1
4:W:U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
-->_1 U12#(tt(),V) -> isNeList#(activate(V)):8
-->_1 U12#(tt(),V) -> activate#(V):7
5:W:U11#(tt(),V) -> activate#(V)
6:W:U11#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
7:W:U12#(tt(),V) -> activate#(V)
8:W:U12#(tt(),V) -> isNeList#(activate(V))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):84
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):81
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):80
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):83
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):82
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):2
9:W:U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)):16
-->_1 U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)):13
-->_1 U22#(tt(),V1,V2) -> activate#(V2):15
-->_1 U22#(tt(),V1,V2) -> activate#(V1):14
10:W:U21#(tt(),V1,V2) -> activate#(V1)
11:W:U21#(tt(),V1,V2) -> activate#(V2)
12:W:U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
13:W:U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)):20
-->_1 U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)):17
-->_1 U23#(tt(),V1,V2) -> activate#(V2):19
-->_1 U23#(tt(),V1,V2) -> activate#(V1):18
14:W:U22#(tt(),V1,V2) -> activate#(V1)
15:W:U22#(tt(),V1,V2) -> activate#(V2)
16:W:U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
17:W:U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U24#(tt(),V1,V2) -> isList#(activate(V1)):24
-->_1 U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)):21
-->_1 U24#(tt(),V1,V2) -> activate#(V2):23
-->_1 U24#(tt(),V1,V2) -> activate#(V1):22
18:W:U23#(tt(),V1,V2) -> activate#(V1)
19:W:U23#(tt(),V1,V2) -> activate#(V2)
20:W:U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
21:W:U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
-->_1 U25#(tt(),V2) -> isList#(activate(V2)):26
-->_1 U25#(tt(),V2) -> activate#(V2):25
22:W:U24#(tt(),V1,V2) -> activate#(V1)
23:W:U24#(tt(),V1,V2) -> activate#(V2)
24:W:U24#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):79
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):76
-->_1 isList#(V) -> isPalListKind#(activate(V)):75
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):73
-->_1 isList#(n____(V1,V2)) -> activate#(V2):78
-->_1 isList#(n____(V1,V2)) -> activate#(V1):77
-->_1 isList#(V) -> activate#(V):74
25:W:U25#(tt(),V2) -> activate#(V2)
26:W:U25#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):79
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):76
-->_1 isList#(V) -> isPalListKind#(activate(V)):75
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):73
-->_1 isList#(n____(V1,V2)) -> activate#(V2):78
-->_1 isList#(n____(V1,V2)) -> activate#(V1):77
-->_1 isList#(V) -> activate#(V):74
27:W:U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
28:W:U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)):35
-->_1 U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)):32
-->_1 U42#(tt(),V1,V2) -> activate#(V2):34
-->_1 U42#(tt(),V1,V2) -> activate#(V1):33
29:W:U41#(tt(),V1,V2) -> activate#(V1)
30:W:U41#(tt(),V1,V2) -> activate#(V2)
31:W:U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
32:W:U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)):39
-->_1 U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)):36
-->_1 U43#(tt(),V1,V2) -> activate#(V2):38
-->_1 U43#(tt(),V1,V2) -> activate#(V1):37
33:W:U42#(tt(),V1,V2) -> activate#(V1)
34:W:U42#(tt(),V1,V2) -> activate#(V2)
35:W:U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
36:W:U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U44#(tt(),V1,V2) -> isList#(activate(V1)):43
-->_1 U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)):40
-->_1 U44#(tt(),V1,V2) -> activate#(V2):42
-->_1 U44#(tt(),V1,V2) -> activate#(V1):41
37:W:U43#(tt(),V1,V2) -> activate#(V1)
38:W:U43#(tt(),V1,V2) -> activate#(V2)
39:W:U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
40:W:U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
-->_1 U45#(tt(),V2) -> isNeList#(activate(V2)):45
-->_1 U45#(tt(),V2) -> activate#(V2):44
41:W:U44#(tt(),V1,V2) -> activate#(V1)
42:W:U44#(tt(),V1,V2) -> activate#(V2)
43:W:U44#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):79
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):76
-->_1 isList#(V) -> isPalListKind#(activate(V)):75
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):73
-->_1 isList#(n____(V1,V2)) -> activate#(V2):78
-->_1 isList#(n____(V1,V2)) -> activate#(V1):77
-->_1 isList#(V) -> activate#(V):74
44:W:U45#(tt(),V2) -> activate#(V2)
45:W:U45#(tt(),V2) -> isNeList#(activate(V2))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):84
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):81
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):80
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):83
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):82
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):2
46:W:U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)):53
-->_1 U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)):50
-->_1 U52#(tt(),V1,V2) -> activate#(V2):52
-->_1 U52#(tt(),V1,V2) -> activate#(V1):51
47:W:U51#(tt(),V1,V2) -> activate#(V1)
48:W:U51#(tt(),V1,V2) -> activate#(V2)
49:W:U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
50:W:U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)):57
-->_1 U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)):54
-->_1 U53#(tt(),V1,V2) -> activate#(V2):56
-->_1 U53#(tt(),V1,V2) -> activate#(V1):55
51:W:U52#(tt(),V1,V2) -> activate#(V1)
52:W:U52#(tt(),V1,V2) -> activate#(V2)
53:W:U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
54:W:U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U54#(tt(),V1,V2) -> isNeList#(activate(V1)):61
-->_1 U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)):58
-->_1 U54#(tt(),V1,V2) -> activate#(V2):60
-->_1 U54#(tt(),V1,V2) -> activate#(V1):59
55:W:U53#(tt(),V1,V2) -> activate#(V1)
56:W:U53#(tt(),V1,V2) -> activate#(V2)
57:W:U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
58:W:U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
-->_1 U55#(tt(),V2) -> isList#(activate(V2)):63
-->_1 U55#(tt(),V2) -> activate#(V2):62
59:W:U54#(tt(),V1,V2) -> activate#(V1)
60:W:U54#(tt(),V1,V2) -> activate#(V2)
61:W:U54#(tt(),V1,V2) -> isNeList#(activate(V1))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):84
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):81
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):80
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):83
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):82
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):2
62:W:U55#(tt(),V2) -> activate#(V2)
63:W:U55#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):79
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):76
-->_1 isList#(V) -> isPalListKind#(activate(V)):75
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):73
-->_1 isList#(n____(V1,V2)) -> activate#(V2):78
-->_1 isList#(n____(V1,V2)) -> activate#(V1):77
-->_1 isList#(V) -> activate#(V):74
64:W:U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
65:W:U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
-->_1 U72#(tt(),P) -> isPal#(activate(P)):68
-->_1 U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)):67
66:W:U71#(tt(),I,P) -> isPalListKind#(activate(I))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
67:W:U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
-->_1 U73#(tt(),P) -> c_30(isPalListKind#(activate(P))):69
68:W:U72#(tt(),P) -> isPal#(activate(P))
-->_1 isPal#(V) -> isPalListKind#(activate(V)):88
-->_1 isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)):87
69:W:U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
70:W:U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
-->_1 U82#(tt(),V) -> isNePal#(activate(V)):72
71:W:U81#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
72:W:U82#(tt(),V) -> isNePal#(activate(V))
-->_1 isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)):86
-->_1 isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):85
73:W:isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
-->_1 U11#(tt(),V) -> isPalListKind#(activate(V)):6
-->_1 U11#(tt(),V) -> activate#(V):5
-->_1 U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)):4
74:W:isList#(V) -> activate#(V)
75:W:isList#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
76:W:isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)):12
-->_1 U21#(tt(),V1,V2) -> activate#(V2):11
-->_1 U21#(tt(),V1,V2) -> activate#(V1):10
-->_1 U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)):9
77:W:isList#(n____(V1,V2)) -> activate#(V1)
78:W:isList#(n____(V1,V2)) -> activate#(V2)
79:W:isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
80:W:isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)):31
-->_1 U41#(tt(),V1,V2) -> activate#(V2):30
-->_1 U41#(tt(),V1,V2) -> activate#(V1):29
-->_1 U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)):28
81:W:isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)):49
-->_1 U51#(tt(),V1,V2) -> activate#(V2):48
-->_1 U51#(tt(),V1,V2) -> activate#(V1):47
-->_1 U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)):46
82:W:isNeList#(n____(V1,V2)) -> activate#(V1)
83:W:isNeList#(n____(V1,V2)) -> activate#(V2)
84:W:isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
85:W:isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
-->_1 U61#(tt(),V) -> c_25(isPalListKind#(activate(V))):64
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
86:W:isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
-->_1 U71#(tt(),I,P) -> isPalListKind#(activate(I)):66
-->_1 U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)):65
87:W:isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
-->_1 U81#(tt(),V) -> isPalListKind#(activate(V)):71
-->_1 U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)):70
88:W:isPal#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):3
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
7: U12#(tt(),V) -> activate#(V)
51: U52#(tt(),V1,V2) -> activate#(V1)
52: U52#(tt(),V1,V2) -> activate#(V2)
55: U53#(tt(),V1,V2) -> activate#(V1)
56: U53#(tt(),V1,V2) -> activate#(V2)
59: U54#(tt(),V1,V2) -> activate#(V1)
60: U54#(tt(),V1,V2) -> activate#(V2)
62: U55#(tt(),V2) -> activate#(V2)
33: U42#(tt(),V1,V2) -> activate#(V1)
34: U42#(tt(),V1,V2) -> activate#(V2)
37: U43#(tt(),V1,V2) -> activate#(V1)
38: U43#(tt(),V1,V2) -> activate#(V2)
41: U44#(tt(),V1,V2) -> activate#(V1)
42: U44#(tt(),V1,V2) -> activate#(V2)
44: U45#(tt(),V2) -> activate#(V2)
82: isNeList#(n____(V1,V2)) -> activate#(V1)
83: isNeList#(n____(V1,V2)) -> activate#(V2)
14: U22#(tt(),V1,V2) -> activate#(V1)
15: U22#(tt(),V1,V2) -> activate#(V2)
18: U23#(tt(),V1,V2) -> activate#(V1)
19: U23#(tt(),V1,V2) -> activate#(V2)
22: U24#(tt(),V1,V2) -> activate#(V1)
23: U24#(tt(),V1,V2) -> activate#(V2)
25: U25#(tt(),V2) -> activate#(V2)
74: isList#(V) -> activate#(V)
77: isList#(n____(V1,V2)) -> activate#(V1)
78: isList#(n____(V1,V2)) -> activate#(V2)
5: U11#(tt(),V) -> activate#(V)
10: U21#(tt(),V1,V2) -> activate#(V1)
11: U21#(tt(),V1,V2) -> activate#(V2)
29: U41#(tt(),V1,V2) -> activate#(V1)
30: U41#(tt(),V1,V2) -> activate#(V2)
47: U51#(tt(),V1,V2) -> activate#(V1)
48: U51#(tt(),V1,V2) -> activate#(V2)
******* Step 1.b:7.a:1.b:1.a:4.b:2.b:2: PredecessorEstimationCP WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isPalListKind#(n____(V1,V2)) -> c_59(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) -> c_25(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) -> c_30(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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
1: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
The strictly oriented rules are moved into the weak component.
******** Step 1.b:7.a:1.b:1.a:4.b:2.b:2.a:1: NaturalMI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isPalListKind#(n____(V1,V2)) -> c_59(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) -> c_25(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) -> c_30(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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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 first alternative for predecessorEstimation on any intersect of rules of CDG leaf and 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_25) = {1},
uargs(c_30) = {1},
uargs(c_35) = {1},
uargs(c_52) = {1,2},
uargs(c_55) = {1,2},
uargs(c_59) = {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) = [2] x1 + [5] x2 + [0]
p(U12) = [4] x2 + [0]
p(U13) = [2] x1 + [4]
p(U21) = [3] x1 + [1] x2 + [0]
p(U22) = [4] x2 + [0]
p(U23) = [1] x1 + [4] x2 + [6]
p(U24) = [4] x2 + [1]
p(U25) = [1] x1 + [3]
p(U26) = [1] x1 + [7]
p(U31) = [0]
p(U32) = [0]
p(U33) = [1] x1 + [0]
p(U41) = [2] x1 + [5]
p(U42) = [3] x3 + [1]
p(U43) = [1] x1 + [4] x2 + [2] x3 + [4]
p(U44) = [2]
p(U45) = [7]
p(U46) = [1] x1 + [2]
p(U51) = [2] x1 + [4] x2 + [0]
p(U52) = [1] x1 + [0]
p(U53) = [5] x3 + [0]
p(U54) = [2] x1 + [2] x2 + [1] x3 + [0]
p(U55) = [2] x1 + [2] x2 + [0]
p(U56) = [2] x1 + [0]
p(U61) = [3] x2 + [2]
p(U62) = [1] x1 + [5] x2 + [0]
p(U63) = [2]
p(U71) = [1] x1 + [4] x2 + [0]
p(U72) = [5] x2 + [0]
p(U73) = [0]
p(U74) = [0]
p(U81) = [2] x1 + [1]
p(U82) = [5] x2 + [2]
p(U83) = [1] x1 + [1]
p(U91) = [4] x2 + [1]
p(U92) = [7]
p(__) = [1] x1 + [1] x2 + [1]
p(a) = [0]
p(activate) = [1] x1 + [0]
p(e) = [0]
p(i) = [0]
p(isList) = [1]
p(isNeList) = [4] x1 + [2]
p(isNePal) = [1] x1 + [1]
p(isPal) = [3] x1 + [0]
p(isPalListKind) = [2] x1 + [0]
p(isQid) = [7]
p(n____) = [1] x1 + [1] x2 + [1]
p(n__a) = [0]
p(n__e) = [0]
p(n__i) = [0]
p(n__nil) = [1]
p(n__o) = [0]
p(n__u) = [0]
p(nil) = [1]
p(o) = [0]
p(tt) = [4]
p(u) = [0]
p(U11#) = [4] x2 + [1]
p(U12#) = [4] x2 + [1]
p(U13#) = [2] x1 + [0]
p(U21#) = [4] x2 + [4] x3 + [5]
p(U22#) = [4] x2 + [4] x3 + [5]
p(U23#) = [4] x2 + [4] x3 + [5]
p(U24#) = [4] x2 + [4] x3 + [3]
p(U25#) = [4] x2 + [3]
p(U26#) = [1] x1 + [0]
p(U31#) = [2] x2 + [0]
p(U32#) = [1] x2 + [0]
p(U33#) = [1] x1 + [1]
p(U41#) = [4] x2 + [4] x3 + [1]
p(U42#) = [4] x2 + [4] x3 + [1]
p(U43#) = [4] x2 + [4] x3 + [1]
p(U44#) = [4] x2 + [4] x3 + [1]
p(U45#) = [4] x2 + [1]
p(U46#) = [0]
p(U51#) = [4] x2 + [4] x3 + [1]
p(U52#) = [4] x2 + [4] x3 + [1]
p(U53#) = [4] x2 + [4] x3 + [1]
p(U54#) = [4] x2 + [4] x3 + [1]
p(U55#) = [4] x2 + [1]
p(U56#) = [4] x1 + [1]
p(U61#) = [2] x2 + [1]
p(U62#) = [1] x1 + [1]
p(U63#) = [2] x1 + [0]
p(U71#) = [4] x2 + [4] x3 + [5]
p(U72#) = [4] x2 + [5]
p(U73#) = [4] x2 + [0]
p(U74#) = [1] x1 + [0]
p(U81#) = [4] x2 + [5]
p(U82#) = [4] x2 + [5]
p(U83#) = [2] x1 + [1]
p(U91#) = [2] x2 + [2]
p(U92#) = [1] x1 + [4]
p(__#) = [1] x2 + [4]
p(a#) = [0]
p(activate#) = [0]
p(e#) = [0]
p(i#) = [1]
p(isList#) = [4] x1 + [1]
p(isNeList#) = [4] x1 + [1]
p(isNePal#) = [4] x1 + [4]
p(isPal#) = [4] x1 + [5]
p(isPalListKind#) = [2] x1 + [0]
p(isQid#) = [0]
p(nil#) = [1]
p(o#) = [0]
p(u#) = [2]
p(c_1) = [1] x1 + [4] x3 + [2] x4 + [0]
p(c_2) = [1] x1 + [1] x2 + [2]
p(c_3) = [1]
p(c_4) = [2]
p(c_5) = [4] x1 + [1] x4 + [1]
p(c_6) = [2] x4 + [1] x5 + [4]
p(c_7) = [4] x2 + [1] x3 + [2] x4 + [0]
p(c_8) = [1] x1 + [1] x2 + [1]
p(c_9) = [0]
p(c_10) = [1] x1 + [0]
p(c_11) = [1]
p(c_12) = [0]
p(c_13) = [1] x1 + [4] x2 + [1] x4 + [0]
p(c_14) = [4] x5 + [4]
p(c_15) = [1] x5 + [4]
p(c_16) = [4] x3 + [1] x4 + [4]
p(c_17) = [2] x2 + [2]
p(c_18) = [1]
p(c_19) = [1] x1 + [1] x2 + [1] x4 + [1] x5 + [1]
p(c_20) = [1] x1 + [4] x4 + [1]
p(c_21) = [1] x1 + [1] x2 + [2] x4 + [4] x5 + [0]
p(c_22) = [2] x4 + [4]
p(c_23) = [1] x1 + [1] x2 + [0]
p(c_24) = [2]
p(c_25) = [1] x1 + [1]
p(c_26) = [0]
p(c_27) = [1]
p(c_28) = [4] x1 + [1] x4 + [1]
p(c_29) = [4] x4 + [4]
p(c_30) = [2] x1 + [0]
p(c_31) = [2]
p(c_32) = [2] x3 + [4] x4 + [4]
p(c_33) = [4] x1 + [1]
p(c_34) = [2]
p(c_35) = [1] x1 + [0]
p(c_36) = [0]
p(c_37) = [0]
p(c_38) = [1]
p(c_39) = [0]
p(c_40) = [4] x1 + [4]
p(c_41) = [1]
p(c_42) = [1]
p(c_43) = [2]
p(c_44) = [0]
p(c_45) = [4]
p(c_46) = [2] x1 + [1]
p(c_47) = [0]
p(c_48) = [0]
p(c_49) = [1] x1 + [4]
p(c_50) = [1] x2 + [1] x3 + [1]
p(c_51) = [1]
p(c_52) = [1] x1 + [1] x2 + [1]
p(c_53) = [2] x1 + [1] x2 + [1] x3 + [1] x4 + [1] x5 + [0]
p(c_54) = [2]
p(c_55) = [1] x1 + [1] x2 + [3]
p(c_56) = [1] x2 + [1] x3 + [2]
p(c_57) = [1] x1 + [2] x3 + [1]
p(c_58) = [4]
p(c_59) = [1] x1 + [1] x2 + [0]
p(c_60) = [0]
p(c_61) = [1]
p(c_62) = [0]
p(c_63) = [1]
p(c_64) = [1]
p(c_65) = [1]
p(c_66) = [1]
p(c_67) = [0]
p(c_68) = [1]
p(c_69) = [0]
p(c_70) = [1]
p(c_71) = [1]
p(c_72) = [4]
p(c_73) = [1]
Following rules are strictly oriented:
U91#(tt(),V2) = [2] V2 + [2]
> [2] V2 + [0]
= c_35(isPalListKind#(activate(V2)))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [4] V + [1]
>= [4] V + [1]
= U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) = [4] V + [1]
>= [2] V + [0]
= isPalListKind#(activate(V))
U12#(tt(),V) = [4] V + [1]
>= [4] V + [1]
= isNeList#(activate(V))
U21#(tt(),V1,V2) = [4] V1 + [4] V2 + [5]
>= [4] V1 + [4] V2 + [5]
= U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) = [4] V1 + [4] V2 + [5]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
U22#(tt(),V1,V2) = [4] V1 + [4] V2 + [5]
>= [4] V1 + [4] V2 + [5]
= U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U22#(tt(),V1,V2) = [4] V1 + [4] V2 + [5]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U23#(tt(),V1,V2) = [4] V1 + [4] V2 + [5]
>= [4] V1 + [4] V2 + [3]
= U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U23#(tt(),V1,V2) = [4] V1 + [4] V2 + [5]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U24#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [4] V2 + [3]
= U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [4] V1 + [1]
= isList#(activate(V1))
U25#(tt(),V2) = [4] V2 + [3]
>= [4] V2 + [1]
= isList#(activate(V2))
U31#(tt(),V) = [2] V + [0]
>= [2] V + [0]
= c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V1 + [4] V2 + [1]
= U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
U42#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V1 + [4] V2 + [1]
= U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U42#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U43#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V1 + [4] V2 + [1]
= U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U43#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U44#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V2 + [1]
= U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V1 + [1]
= isList#(activate(V1))
U45#(tt(),V2) = [4] V2 + [1]
>= [4] V2 + [1]
= isNeList#(activate(V2))
U51#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V1 + [4] V2 + [1]
= U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
U52#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V1 + [4] V2 + [1]
= U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U52#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U53#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V1 + [4] V2 + [1]
= U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U53#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U54#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V2 + [1]
= U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V1 + [1]
= isNeList#(activate(V1))
U55#(tt(),V2) = [4] V2 + [1]
>= [4] V2 + [1]
= isList#(activate(V2))
U61#(tt(),V) = [2] V + [1]
>= [2] V + [1]
= c_25(isPalListKind#(activate(V)))
U71#(tt(),I,P) = [4] I + [4] P + [5]
>= [4] P + [5]
= U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) = [4] I + [4] P + [5]
>= [2] I + [0]
= isPalListKind#(activate(I))
U72#(tt(),P) = [4] P + [5]
>= [4] P + [0]
= U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) = [4] P + [5]
>= [4] P + [5]
= isPal#(activate(P))
U73#(tt(),P) = [4] P + [0]
>= [4] P + [0]
= c_30(isPalListKind#(activate(P)))
U81#(tt(),V) = [4] V + [5]
>= [4] V + [5]
= U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) = [4] V + [5]
>= [2] V + [0]
= isPalListKind#(activate(V))
U82#(tt(),V) = [4] V + [5]
>= [4] V + [4]
= isNePal#(activate(V))
isList#(V) = [4] V + [1]
>= [4] V + [1]
= U11#(isPalListKind(activate(V)),activate(V))
isList#(V) = [4] V + [1]
>= [2] V + [0]
= isPalListKind#(activate(V))
isList#(n____(V1,V2)) = [4] V1 + [4] V2 + [5]
>= [4] V1 + [4] V2 + [5]
= U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) = [4] V1 + [4] V2 + [5]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
isNeList#(V) = [4] V + [1]
>= [4] V + [1]
= c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) = [4] V1 + [4] V2 + [5]
>= [4] V1 + [4] V2 + [1]
= U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [4] V1 + [4] V2 + [5]
>= [4] V1 + [4] V2 + [1]
= U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [4] V1 + [4] V2 + [5]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
isNePal#(V) = [4] V + [4]
>= [4] V + [4]
= c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) = [8] I + [4] P + [12]
>= [4] I + [4] P + [5]
= U71#(isQid(activate(I)),activate(I),activate(P))
isPal#(V) = [4] V + [5]
>= [4] V + [5]
= U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) = [4] V + [5]
>= [2] V + [0]
= isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) = [2] V1 + [2] V2 + [2]
>= [2] V1 + [2] V2 + [2]
= c_59(U91#(isPalListKind(activate(V1)),activate(V2)),isPalListKind#(activate(V1)))
__(X1,X2) = [1] X1 + [1] X2 + [1]
>= [1] X1 + [1] X2 + [1]
= n____(X1,X2)
a() = [0]
>= [0]
= n__a()
activate(X) = [1] X + [0]
>= [1] X + [0]
= X
activate(n____(X1,X2)) = [1] X1 + [1] X2 + [1]
>= [1] X1 + [1] X2 + [1]
= __(activate(X1),activate(X2))
activate(n__a()) = [0]
>= [0]
= a()
activate(n__e()) = [0]
>= [0]
= e()
activate(n__i()) = [0]
>= [0]
= i()
activate(n__nil()) = [1]
>= [1]
= nil()
activate(n__o()) = [0]
>= [0]
= o()
activate(n__u()) = [0]
>= [0]
= u()
e() = [0]
>= [0]
= n__e()
i() = [0]
>= [0]
= n__i()
nil() = [1]
>= [1]
= n__nil()
o() = [0]
>= [0]
= n__o()
u() = [0]
>= [0]
= n__u()
******** Step 1.b:7.a:1.b:1.a:4.b:2.b:2.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isPalListKind#(n____(V1,V2)) -> c_59(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) -> c_25(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) -> c_30(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#(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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
******** Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isPalListKind#(n____(V1,V2)) -> c_59(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) -> c_25(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) -> c_30(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#(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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
2: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
Consider the set of all dependency pairs
1: isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
2: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
3: U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
4: U11#(tt(),V) -> isPalListKind#(activate(V))
5: U12#(tt(),V) -> isNeList#(activate(V))
6: U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
7: U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
8: U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
9: U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
10: U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
11: U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
12: U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
13: U24#(tt(),V1,V2) -> isList#(activate(V1))
14: U25#(tt(),V2) -> isList#(activate(V2))
15: U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
16: U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
17: U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
18: U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
19: U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
20: U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
21: U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
22: U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
23: U44#(tt(),V1,V2) -> isList#(activate(V1))
24: U45#(tt(),V2) -> isNeList#(activate(V2))
25: U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
26: U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
27: U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
28: U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
29: U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
30: U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
31: U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
32: U54#(tt(),V1,V2) -> isNeList#(activate(V1))
33: U55#(tt(),V2) -> isList#(activate(V2))
34: U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
35: U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
36: U71#(tt(),I,P) -> isPalListKind#(activate(I))
37: U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
38: U72#(tt(),P) -> isPal#(activate(P))
39: U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
40: U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
41: U81#(tt(),V) -> isPalListKind#(activate(V))
42: U82#(tt(),V) -> isNePal#(activate(V))
43: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
44: isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
45: isList#(V) -> isPalListKind#(activate(V))
46: isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
47: isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
48: isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
49: isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
50: isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
51: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
52: isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
53: isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
54: isPal#(V) -> isPalListKind#(activate(V))
Processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
SPACE(?,?)on application of the dependency pairs
{2}
These cover all (indirect) predecessors of dependency pairs
{2,43}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
********* Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isPalListKind#(n____(V1,V2)) -> c_59(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) -> c_25(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) -> c_30(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#(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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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 first alternative for predecessorEstimation on any intersect of rules of CDG leaf and 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_25) = {1},
uargs(c_30) = {1},
uargs(c_35) = {1},
uargs(c_52) = {1,2},
uargs(c_55) = {1,2},
uargs(c_59) = {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) = [1] x1 + [0]
p(U12) = [2] x2 + [2]
p(U13) = [3]
p(U21) = [4] x1 + [5]
p(U22) = [4] x3 + [0]
p(U23) = [0]
p(U24) = [1] x1 + [6] x2 + [6]
p(U25) = [0]
p(U26) = [0]
p(U31) = [4] x1 + [0]
p(U32) = [0]
p(U33) = [0]
p(U41) = [4] x1 + [2] x2 + [1] x3 + [4]
p(U42) = [1] x1 + [1]
p(U43) = [2] x3 + [3]
p(U44) = [1] x1 + [6] x2 + [1]
p(U45) = [1] x1 + [1] x2 + [5]
p(U46) = [1]
p(U51) = [2] x1 + [1] x2 + [1] x3 + [6]
p(U52) = [1] x1 + [4]
p(U53) = [1] x2 + [1]
p(U54) = [5] x1 + [4] x3 + [5]
p(U55) = [0]
p(U56) = [1]
p(U61) = [3]
p(U62) = [1] x2 + [3]
p(U63) = [0]
p(U71) = [2] x2 + [3] x3 + [3]
p(U72) = [4] x2 + [0]
p(U73) = [2] x1 + [1] x2 + [1]
p(U74) = [0]
p(U81) = [2] x1 + [0]
p(U82) = [2] x2 + [0]
p(U83) = [2] x1 + [0]
p(U91) = [5] x2 + [0]
p(U92) = [0]
p(__) = [1] x1 + [1] x2 + [1]
p(a) = [0]
p(activate) = [1] x1 + [0]
p(e) = [0]
p(i) = [0]
p(isList) = [0]
p(isNeList) = [0]
p(isNePal) = [4] x1 + [2]
p(isPal) = [1]
p(isPalListKind) = [1]
p(isQid) = [4]
p(n____) = [1] x1 + [1] x2 + [1]
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#) = [4] x2 + [0]
p(U12#) = [4] x2 + [0]
p(U13#) = [0]
p(U21#) = [4] x2 + [4] x3 + [1]
p(U22#) = [4] x2 + [4] x3 + [0]
p(U23#) = [4] x2 + [4] x3 + [0]
p(U24#) = [4] x2 + [4] x3 + [0]
p(U25#) = [4] x2 + [0]
p(U26#) = [0]
p(U31#) = [2] x2 + [0]
p(U32#) = [0]
p(U33#) = [0]
p(U41#) = [4] x2 + [4] x3 + [0]
p(U42#) = [4] x2 + [4] x3 + [0]
p(U43#) = [4] x2 + [4] x3 + [0]
p(U44#) = [4] x2 + [4] x3 + [0]
p(U45#) = [4] x2 + [0]
p(U46#) = [0]
p(U51#) = [4] x2 + [4] x3 + [3]
p(U52#) = [4] x2 + [4] x3 + [3]
p(U53#) = [4] x2 + [4] x3 + [3]
p(U54#) = [4] x2 + [4] x3 + [3]
p(U55#) = [4] x2 + [3]
p(U56#) = [0]
p(U61#) = [2] x2 + [0]
p(U62#) = [0]
p(U63#) = [0]
p(U71#) = [3] x2 + [7] x3 + [4]
p(U72#) = [7] x2 + [4]
p(U73#) = [7] x2 + [4]
p(U74#) = [0]
p(U81#) = [7] x2 + [0]
p(U82#) = [7] x2 + [0]
p(U83#) = [0]
p(U91#) = [2] x2 + [0]
p(U92#) = [0]
p(__#) = [0]
p(a#) = [0]
p(activate#) = [0]
p(e#) = [0]
p(i#) = [0]
p(isList#) = [4] x1 + [0]
p(isNeList#) = [4] x1 + [0]
p(isNePal#) = [7] x1 + [0]
p(isPal#) = [7] x1 + [0]
p(isPalListKind#) = [2] x1 + [0]
p(isQid#) = [0]
p(nil#) = [0]
p(o#) = [0]
p(u#) = [0]
p(c_1) = [0]
p(c_2) = [1] x2 + [0]
p(c_3) = [4]
p(c_4) = [1] x1 + [1] x4 + [1]
p(c_5) = [0]
p(c_6) = [1] x1 + [1] x3 + [4] x5 + [1]
p(c_7) = [2] x1 + [2] x2 + [2] x3 + [1] x4 + [0]
p(c_8) = [1] x1 + [1]
p(c_9) = [0]
p(c_10) = [1] x1 + [0]
p(c_11) = [1]
p(c_12) = [2]
p(c_13) = [1] x1 + [4] x4 + [1]
p(c_14) = [1] x3 + [1] x4 + [1] x5 + [1]
p(c_15) = [1] x4 + [1]
p(c_16) = [2] x1 + [4] x3 + [1] x4 + [1]
p(c_17) = [1] x1 + [0]
p(c_18) = [0]
p(c_19) = [2] x3 + [1] x5 + [0]
p(c_20) = [1] x1 + [1] x2 + [4] x4 + [4]
p(c_21) = [4] x1 + [2] x2 + [0]
p(c_22) = [4]
p(c_23) = [1]
p(c_24) = [0]
p(c_25) = [1] x1 + [0]
p(c_26) = [0]
p(c_27) = [0]
p(c_28) = [2] x1 + [1] x3 + [1]
p(c_29) = [1] x1 + [2] x2 + [2] x3 + [4]
p(c_30) = [1] x1 + [4]
p(c_31) = [1]
p(c_32) = [1] x3 + [1] x4 + [1]
p(c_33) = [2] x2 + [1]
p(c_34) = [1]
p(c_35) = [1] x1 + [0]
p(c_36) = [0]
p(c_37) = [2]
p(c_38) = [0]
p(c_39) = [1]
p(c_40) = [2] x2 + [2]
p(c_41) = [0]
p(c_42) = [0]
p(c_43) = [4]
p(c_44) = [0]
p(c_45) = [1]
p(c_46) = [1] x1 + [0]
p(c_47) = [4]
p(c_48) = [1]
p(c_49) = [2] x1 + [1] x2 + [1] x3 + [1]
p(c_50) = [1] x1 + [1] x2 + [4] x4 + [0]
p(c_51) = [1]
p(c_52) = [1] x1 + [1] x2 + [0]
p(c_53) = [1] x1 + [1] x2 + [1] x5 + [1]
p(c_54) = [1] x2 + [1] x4 + [1] x5 + [0]
p(c_55) = [2] x1 + [1] x2 + [0]
p(c_56) = [1] x3 + [1]
p(c_57) = [1] x2 + [1] x3 + [2] x4 + [0]
p(c_58) = [2]
p(c_59) = [1] x1 + [1] x2 + [0]
p(c_60) = [1]
p(c_61) = [4]
p(c_62) = [2]
p(c_63) = [1]
p(c_64) = [0]
p(c_65) = [0]
p(c_66) = [0]
p(c_67) = [2]
p(c_68) = [0]
p(c_69) = [1]
p(c_70) = [0]
p(c_71) = [0]
p(c_72) = [0]
p(c_73) = [4]
Following rules are strictly oriented:
isPalListKind#(n____(V1,V2)) = [2] V1 + [2] V2 + [2]
> [2] V1 + [2] V2 + [0]
= c_59(U91#(isPalListKind(activate(V1)),activate(V2)),isPalListKind#(activate(V1)))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [4] V + [0]
>= [4] V + [0]
= U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) = [4] V + [0]
>= [2] V + [0]
= isPalListKind#(activate(V))
U12#(tt(),V) = [4] V + [0]
>= [4] V + [0]
= isNeList#(activate(V))
U21#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [4] V1 + [4] V2 + [0]
= U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) = [4] V1 + [4] V2 + [1]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
U22#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [4] V1 + [4] V2 + [0]
= U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U22#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U23#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [4] V1 + [4] V2 + [0]
= U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U23#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U24#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [4] V2 + [0]
= U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [4] V1 + [0]
= isList#(activate(V1))
U25#(tt(),V2) = [4] V2 + [0]
>= [4] V2 + [0]
= isList#(activate(V2))
U31#(tt(),V) = [2] V + [0]
>= [2] V + [0]
= c_10(isPalListKind#(activate(V)))
U41#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [4] V1 + [4] V2 + [0]
= U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
U42#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [4] V1 + [4] V2 + [0]
= U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U42#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U43#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [4] V1 + [4] V2 + [0]
= U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U43#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U44#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [4] V2 + [0]
= U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) = [4] V1 + [4] V2 + [0]
>= [4] V1 + [0]
= isList#(activate(V1))
U45#(tt(),V2) = [4] V2 + [0]
>= [4] V2 + [0]
= isNeList#(activate(V2))
U51#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [4] V1 + [4] V2 + [3]
= U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
U52#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [4] V1 + [4] V2 + [3]
= U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U52#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U53#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [4] V1 + [4] V2 + [3]
= U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U53#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U54#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [4] V2 + [3]
= U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) = [4] V1 + [4] V2 + [3]
>= [4] V1 + [0]
= isNeList#(activate(V1))
U55#(tt(),V2) = [4] V2 + [3]
>= [4] V2 + [0]
= isList#(activate(V2))
U61#(tt(),V) = [2] V + [0]
>= [2] V + [0]
= c_25(isPalListKind#(activate(V)))
U71#(tt(),I,P) = [3] I + [7] P + [4]
>= [7] P + [4]
= U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) = [3] I + [7] P + [4]
>= [2] I + [0]
= isPalListKind#(activate(I))
U72#(tt(),P) = [7] P + [4]
>= [7] P + [4]
= U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) = [7] P + [4]
>= [7] P + [0]
= isPal#(activate(P))
U73#(tt(),P) = [7] P + [4]
>= [2] P + [4]
= c_30(isPalListKind#(activate(P)))
U81#(tt(),V) = [7] V + [0]
>= [7] V + [0]
= U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) = [7] V + [0]
>= [2] V + [0]
= isPalListKind#(activate(V))
U82#(tt(),V) = [7] V + [0]
>= [7] V + [0]
= isNePal#(activate(V))
U91#(tt(),V2) = [2] V2 + [0]
>= [2] V2 + [0]
= c_35(isPalListKind#(activate(V2)))
isList#(V) = [4] V + [0]
>= [4] V + [0]
= U11#(isPalListKind(activate(V)),activate(V))
isList#(V) = [4] V + [0]
>= [2] V + [0]
= isPalListKind#(activate(V))
isList#(n____(V1,V2)) = [4] V1 + [4] V2 + [4]
>= [4] V1 + [4] V2 + [1]
= U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) = [4] V1 + [4] V2 + [4]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
isNeList#(V) = [4] V + [0]
>= [4] V + [0]
= c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNeList#(n____(V1,V2)) = [4] V1 + [4] V2 + [4]
>= [4] V1 + [4] V2 + [0]
= U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [4] V1 + [4] V2 + [4]
>= [4] V1 + [4] V2 + [3]
= U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [4] V1 + [4] V2 + [4]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
isNePal#(V) = [7] V + [0]
>= [6] V + [0]
= c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) = [14] I + [7] P + [14]
>= [3] I + [7] P + [4]
= U71#(isQid(activate(I)),activate(I),activate(P))
isPal#(V) = [7] V + [0]
>= [7] V + [0]
= U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) = [7] V + [0]
>= [2] V + [0]
= isPalListKind#(activate(V))
__(X1,X2) = [1] X1 + [1] X2 + [1]
>= [1] X1 + [1] X2 + [1]
= n____(X1,X2)
a() = [0]
>= [0]
= n__a()
activate(X) = [1] X + [0]
>= [1] X + [0]
= X
activate(n____(X1,X2)) = [1] X1 + [1] X2 + [1]
>= [1] X1 + [1] X2 + [1]
= __(activate(X1),activate(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 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
- 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) -> c_25(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) -> c_30(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#(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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) -> isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
********* Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
- 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) -> c_25(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) -> c_30(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#(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) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) -> isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
-->_1 U31#(tt(),V) -> c_10(isPalListKind#(activate(V))):14
2:W:U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
-->_1 U12#(tt(),V) -> isNeList#(activate(V)):4
3:W:U11#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
4:W:U12#(tt(),V) -> isNeList#(activate(V))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):49
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):48
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):47
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):1
5:W:U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)):8
-->_1 U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)):7
6:W:U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
7:W:U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)):10
-->_1 U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)):9
8:W:U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
9:W:U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U24#(tt(),V1,V2) -> isList#(activate(V1)):12
-->_1 U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)):11
10:W:U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
11:W:U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
-->_1 U25#(tt(),V2) -> isList#(activate(V2)):13
12:W:U24#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):46
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):45
-->_1 isList#(V) -> isPalListKind#(activate(V)):44
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):43
13:W:U25#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):46
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):45
-->_1 isList#(V) -> isPalListKind#(activate(V)):44
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):43
14:W:U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
15:W:U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)):18
-->_1 U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)):17
16:W:U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
17:W:U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)):20
-->_1 U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)):19
18:W:U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
19:W:U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U44#(tt(),V1,V2) -> isList#(activate(V1)):22
-->_1 U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)):21
20:W:U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
21:W:U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
-->_1 U45#(tt(),V2) -> isNeList#(activate(V2)):23
22:W:U44#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):46
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):45
-->_1 isList#(V) -> isPalListKind#(activate(V)):44
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):43
23:W:U45#(tt(),V2) -> isNeList#(activate(V2))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):49
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):48
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):47
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):1
24:W:U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)):27
-->_1 U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)):26
25:W:U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
26:W:U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)):29
-->_1 U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)):28
27:W:U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
28:W:U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U54#(tt(),V1,V2) -> isNeList#(activate(V1)):31
-->_1 U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)):30
29:W:U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
30:W:U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
-->_1 U55#(tt(),V2) -> isList#(activate(V2)):32
31:W:U54#(tt(),V1,V2) -> isNeList#(activate(V1))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):49
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):48
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):47
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):1
32:W:U55#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):46
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):45
-->_1 isList#(V) -> isPalListKind#(activate(V)):44
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):43
33:W:U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
34:W:U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
-->_1 U72#(tt(),P) -> isPal#(activate(P)):37
-->_1 U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)):36
35:W:U71#(tt(),I,P) -> isPalListKind#(activate(I))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
36:W:U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
-->_1 U73#(tt(),P) -> c_30(isPalListKind#(activate(P))):38
37:W:U72#(tt(),P) -> isPal#(activate(P))
-->_1 isPal#(V) -> isPalListKind#(activate(V)):53
-->_1 isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)):52
38:W:U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
39:W:U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
-->_1 U82#(tt(),V) -> isNePal#(activate(V)):41
40:W:U81#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
41:W:U82#(tt(),V) -> isNePal#(activate(V))
-->_1 isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)):51
-->_1 isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):50
42:W:U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
43:W:isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
-->_1 U11#(tt(),V) -> isPalListKind#(activate(V)):3
-->_1 U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)):2
44:W:isList#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
45:W:isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)):6
-->_1 U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)):5
46:W:isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
47:W:isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)):16
-->_1 U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)):15
48:W:isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)):25
-->_1 U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)):24
49:W:isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
50:W:isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
-->_1 U61#(tt(),V) -> c_25(isPalListKind#(activate(V))):33
51:W:isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
-->_1 U71#(tt(),I,P) -> isPalListKind#(activate(I)):35
-->_1 U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)):34
52:W:isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
-->_1 U81#(tt(),V) -> isPalListKind#(activate(V)):40
-->_1 U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)):39
53:W:isPal#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
54:W:isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))):54
-->_1 U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2))):42
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
34: U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
51: isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
41: U82#(tt(),V) -> isNePal#(activate(V))
39: U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
52: isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
37: U72#(tt(),P) -> isPal#(activate(P))
36: U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
38: U73#(tt(),P) -> c_30(isPalListKind#(activate(P)))
50: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
35: U71#(tt(),I,P) -> isPalListKind#(activate(I))
40: U81#(tt(),V) -> isPalListKind#(activate(V))
53: isPal#(V) -> isPalListKind#(activate(V))
33: U61#(tt(),V) -> c_25(isPalListKind#(activate(V)))
3: U11#(tt(),V) -> isPalListKind#(activate(V))
44: isList#(V) -> isPalListKind#(activate(V))
10: U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
8: U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
6: U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
46: isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
20: U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
18: U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
16: U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
29: U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
27: U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
25: U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
49: isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
14: U31#(tt(),V) -> c_10(isPalListKind#(activate(V)))
54: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1)))
42: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)))
********* Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.b:2: SimplifyRHS WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U12#(tt(),V) -> isNeList#(activate(V))
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))
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))
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))
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))
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))
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> isList#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/2,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V)))
2:W:U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
-->_1 U12#(tt(),V) -> isNeList#(activate(V)):4
4:W:U12#(tt(),V) -> isNeList#(activate(V))
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):48
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):47
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):1
5:W:U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)):7
7:W:U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)):9
9:W:U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U24#(tt(),V1,V2) -> isList#(activate(V1)):12
-->_1 U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)):11
11:W:U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
-->_1 U25#(tt(),V2) -> isList#(activate(V2)):13
12:W:U24#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):45
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):43
13:W:U25#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):45
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):43
15:W:U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)):17
17:W:U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)):19
19:W:U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U44#(tt(),V1,V2) -> isList#(activate(V1)):22
-->_1 U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)):21
21:W:U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
-->_1 U45#(tt(),V2) -> isNeList#(activate(V2)):23
22:W:U44#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):45
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):43
23:W:U45#(tt(),V2) -> isNeList#(activate(V2))
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):48
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):47
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):1
24:W:U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)):26
26:W:U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)):28
28:W:U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U54#(tt(),V1,V2) -> isNeList#(activate(V1)):31
-->_1 U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)):30
30:W:U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
-->_1 U55#(tt(),V2) -> isList#(activate(V2)):32
31:W:U54#(tt(),V1,V2) -> isNeList#(activate(V1))
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):48
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):47
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V)),isPalListKind#(activate(V))):1
32:W:U55#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):45
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):43
43:W:isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
-->_1 U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)):2
45:W:isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)):5
47:W:isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)):15
48:W:isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)):24
Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
isNeList#(V) -> c_52()
********* Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.b:3: UsableRules WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
isNeList#(V) -> c_52()
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U12#(tt(),V) -> isNeList#(activate(V))
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))
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))
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))
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))
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))
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> isList#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/0,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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) -> U12#(isPalListKind(activate(V)),activate(V))
U12#(tt(),V) -> isNeList#(activate(V))
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))
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))
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))
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))
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))
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> isList#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(V) -> c_52()
isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
********* Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.b:4: PredecessorEstimationCP WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
isNeList#(V) -> c_52()
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U12#(tt(),V) -> isNeList#(activate(V))
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))
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))
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))
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))
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))
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> isList#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_1/4,c_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/0,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
1: isNeList#(V) -> c_52()
The strictly oriented rules are moved into the weak component.
********** Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.b:4.a:1: NaturalMI WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
isNeList#(V) -> c_52()
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U12#(tt(),V) -> isNeList#(activate(V))
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))
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))
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))
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))
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))
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> isList#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_1/4,c_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/0,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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 = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
The following argument positions are considered usable:
none
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) = [3] x2 + [0]
p(U12) = [0]
p(U13) = [0]
p(U21) = [0]
p(U22) = [0]
p(U23) = [0]
p(U24) = [6] x2 + [0]
p(U25) = [0]
p(U26) = [0]
p(U31) = [7]
p(U32) = [0]
p(U33) = [1] x1 + [0]
p(U41) = [0]
p(U42) = [1] x2 + [0]
p(U43) = [0]
p(U44) = [7]
p(U45) = [0]
p(U46) = [2] x1 + [0]
p(U51) = [5] x2 + [0]
p(U52) = [0]
p(U53) = [1] x3 + [3]
p(U54) = [0]
p(U55) = [5] x1 + [0]
p(U56) = [0]
p(U61) = [4] x2 + [0]
p(U62) = [1] x2 + [0]
p(U63) = [1] x1 + [0]
p(U71) = [1] x1 + [1] x3 + [0]
p(U72) = [2] x2 + [0]
p(U73) = [1] x1 + [0]
p(U74) = [1] x1 + [0]
p(U81) = [1] x1 + [1] x2 + [0]
p(U82) = [2] x1 + [1] x2 + [0]
p(U83) = [0]
p(U91) = [0]
p(U92) = [0]
p(__) = [1] x2 + [0]
p(a) = [0]
p(activate) = [2] x1 + [0]
p(e) = [0]
p(i) = [0]
p(isList) = [0]
p(isNeList) = [1]
p(isNePal) = [0]
p(isPal) = [0]
p(isPalListKind) = [0]
p(isQid) = [5] x1 + [1]
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) = [1]
p(nil) = [0]
p(o) = [0]
p(tt) = [0]
p(u) = [0]
p(U11#) = [1]
p(U12#) = [1]
p(U13#) = [1] x1 + [0]
p(U21#) = [1]
p(U22#) = [1]
p(U23#) = [1]
p(U24#) = [1]
p(U25#) = [1]
p(U26#) = [1] x1 + [0]
p(U31#) = [4] x1 + [4] x2 + [0]
p(U32#) = [1] x1 + [0]
p(U33#) = [2] x1 + [0]
p(U41#) = [1]
p(U42#) = [1]
p(U43#) = [1]
p(U44#) = [1]
p(U45#) = [1]
p(U46#) = [1] x1 + [0]
p(U51#) = [1]
p(U52#) = [1]
p(U53#) = [1]
p(U54#) = [1]
p(U55#) = [1]
p(U56#) = [4] x1 + [0]
p(U61#) = [2] x2 + [0]
p(U62#) = [1] x1 + [0]
p(U63#) = [1] x1 + [0]
p(U71#) = [2] x1 + [4] x2 + [4] x3 + [0]
p(U72#) = [0]
p(U73#) = [4] x1 + [0]
p(U74#) = [1] x1 + [0]
p(U81#) = [2] x1 + [1] x2 + [0]
p(U82#) = [4] x1 + [1] x2 + [0]
p(U83#) = [1] x1 + [0]
p(U91#) = [0]
p(U92#) = [0]
p(__#) = [1] x1 + [0]
p(a#) = [0]
p(activate#) = [0]
p(e#) = [0]
p(i#) = [0]
p(isList#) = [1]
p(isNeList#) = [1]
p(isNePal#) = [4] x1 + [0]
p(isPal#) = [0]
p(isPalListKind#) = [2] x1 + [0]
p(isQid#) = [4] x1 + [0]
p(nil#) = [0]
p(o#) = [0]
p(u#) = [0]
p(c_1) = [2] x1 + [1] x2 + [1] x3 + [1] x4 + [0]
p(c_2) = [0]
p(c_3) = [0]
p(c_4) = [4] x1 + [1] x3 + [4] x4 + [0]
p(c_5) = [2] x2 + [2] x3 + [1] x5 + [0]
p(c_6) = [1] x3 + [1] x4 + [0]
p(c_7) = [1] x1 + [0]
p(c_8) = [1] x1 + [0]
p(c_9) = [0]
p(c_10) = [0]
p(c_11) = [1] x1 + [0]
p(c_12) = [0]
p(c_13) = [4] x2 + [2] x4 + [1] x5 + [0]
p(c_14) = [1] x1 + [1] x3 + [1] x4 + [0]
p(c_15) = [1] x3 + [1] x4 + [0]
p(c_16) = [0]
p(c_17) = [1] x1 + [2] x2 + [0]
p(c_18) = [0]
p(c_19) = [4] x1 + [0]
p(c_20) = [4] x1 + [1] x3 + [2] x4 + [2] x5 + [0]
p(c_21) = [1] x4 + [2] x5 + [0]
p(c_22) = [1] x1 + [4] x3 + [2] x4 + [0]
p(c_23) = [1] x1 + [0]
p(c_24) = [0]
p(c_25) = [0]
p(c_26) = [0]
p(c_27) = [0]
p(c_28) = [2] x1 + [1] x3 + [0]
p(c_29) = [2] x1 + [1] x2 + [4] x4 + [0]
p(c_30) = [0]
p(c_31) = [0]
p(c_32) = [1] x1 + [4] x4 + [0]
p(c_33) = [1] x1 + [0]
p(c_34) = [0]
p(c_35) = [0]
p(c_36) = [0]
p(c_37) = [0]
p(c_38) = [0]
p(c_39) = [0]
p(c_40) = [2] x2 + [0]
p(c_41) = [0]
p(c_42) = [1] x1 + [0]
p(c_43) = [1] x1 + [0]
p(c_44) = [0]
p(c_45) = [0]
p(c_46) = [0]
p(c_47) = [0]
p(c_48) = [0]
p(c_49) = [1] x3 + [0]
p(c_50) = [2] x1 + [1] x3 + [2] x4 + [1] x5 + [0]
p(c_51) = [0]
p(c_52) = [0]
p(c_53) = [0]
p(c_54) = [2] x1 + [1] x2 + [4] x5 + [0]
p(c_55) = [1] x2 + [0]
p(c_56) = [0]
p(c_57) = [1] x1 + [4] x4 + [0]
p(c_58) = [0]
p(c_59) = [4] x1 + [4] x2 + [0]
p(c_60) = [0]
p(c_61) = [0]
p(c_62) = [0]
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]
Following rules are strictly oriented:
isNeList#(V) = [1]
> [0]
= c_52()
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [1]
>= [1]
= U12#(isPalListKind(activate(V)),activate(V))
U12#(tt(),V) = [1]
>= [1]
= isNeList#(activate(V))
U21#(tt(),V1,V2) = [1]
>= [1]
= U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U22#(tt(),V1,V2) = [1]
>= [1]
= U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U23#(tt(),V1,V2) = [1]
>= [1]
= U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U24#(tt(),V1,V2) = [1]
>= [1]
= U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) = [1]
>= [1]
= isList#(activate(V1))
U25#(tt(),V2) = [1]
>= [1]
= isList#(activate(V2))
U41#(tt(),V1,V2) = [1]
>= [1]
= U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U42#(tt(),V1,V2) = [1]
>= [1]
= U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U43#(tt(),V1,V2) = [1]
>= [1]
= U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U44#(tt(),V1,V2) = [1]
>= [1]
= U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) = [1]
>= [1]
= isList#(activate(V1))
U45#(tt(),V2) = [1]
>= [1]
= isNeList#(activate(V2))
U51#(tt(),V1,V2) = [1]
>= [1]
= U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U52#(tt(),V1,V2) = [1]
>= [1]
= U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U53#(tt(),V1,V2) = [1]
>= [1]
= U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U54#(tt(),V1,V2) = [1]
>= [1]
= U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) = [1]
>= [1]
= isNeList#(activate(V1))
U55#(tt(),V2) = [1]
>= [1]
= isList#(activate(V2))
isList#(V) = [1]
>= [1]
= U11#(isPalListKind(activate(V)),activate(V))
isList#(n____(V1,V2)) = [1]
>= [1]
= U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [1]
>= [1]
= U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [1]
>= [1]
= U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
********** Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.b:4.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U12#(tt(),V) -> isNeList#(activate(V))
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))
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))
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))
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))
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))
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> isList#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(V) -> c_52()
isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_1/4,c_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/0,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
********** Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.b:4.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
+ Considered Problem:
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U12#(tt(),V) -> isNeList#(activate(V))
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))
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))
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))
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))
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))
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> isList#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(V) -> c_52()
isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) -> 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_1/4,c_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/0,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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:W:U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
-->_1 U12#(tt(),V) -> isNeList#(activate(V)):2
2:W:U12#(tt(),V) -> isNeList#(activate(V))
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):25
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):24
-->_1 isNeList#(V) -> c_52():23
3:W:U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)):4
4:W:U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)):5
5:W:U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U24#(tt(),V1,V2) -> isList#(activate(V1)):7
-->_1 U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)):6
6:W:U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
-->_1 U25#(tt(),V2) -> isList#(activate(V2)):8
7:W:U24#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):22
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):21
8:W:U25#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):22
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):21
9:W:U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)):10
10:W:U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)):11
11:W:U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U44#(tt(),V1,V2) -> isList#(activate(V1)):13
-->_1 U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)):12
12:W:U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
-->_1 U45#(tt(),V2) -> isNeList#(activate(V2)):14
13:W:U44#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):22
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):21
14:W:U45#(tt(),V2) -> isNeList#(activate(V2))
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):25
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):24
-->_1 isNeList#(V) -> c_52():23
15:W:U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)):16
16:W:U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)):17
17:W:U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U54#(tt(),V1,V2) -> isNeList#(activate(V1)):19
-->_1 U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)):18
18:W:U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
-->_1 U55#(tt(),V2) -> isList#(activate(V2)):20
19:W:U54#(tt(),V1,V2) -> isNeList#(activate(V1))
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):25
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):24
-->_1 isNeList#(V) -> c_52():23
20:W:U55#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):22
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):21
21:W:isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
-->_1 U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)):1
22:W:isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)):3
23:W:isNeList#(V) -> c_52()
24:W:isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)):9
25:W:isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)):15
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
1: U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
21: isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
20: U55#(tt(),V2) -> isList#(activate(V2))
18: U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
17: U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
16: U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
15: U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
25: isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
19: U54#(tt(),V1,V2) -> isNeList#(activate(V1))
14: U45#(tt(),V2) -> isNeList#(activate(V2))
12: U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
11: U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
10: U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
9: U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
24: isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
2: U12#(tt(),V) -> isNeList#(activate(V))
13: U44#(tt(),V1,V2) -> isList#(activate(V1))
8: U25#(tt(),V2) -> isList#(activate(V2))
6: U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
5: U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
4: U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
3: U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
22: isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
7: U24#(tt(),V1,V2) -> isList#(activate(V1))
23: isNeList#(V) -> c_52()
********** Step 1.b:7.a:1.b:1.a:4.b:2.b:2.b:1.b:4.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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_1/4,c_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/1,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/1,c_26/1,c_27/0,c_28/4,c_29/4,c_30/1,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/1,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/0,c_53/5,c_54/5,c_55/2,c_56/4,c_57/4,c_58/0,c_59/2,c_60/0,c_61/0
,c_62/0,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}
- 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 1.b:7.a:1.b:1.b:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
U25#(tt(),V2) -> isList#(activate(V2))
U31#(tt(),V) -> U32#(isPalListKind(activate(V)),activate(V))
U31#(tt(),V) -> activate#(V)
U31#(tt(),V) -> isPalListKind#(activate(V))
U32#(tt(),V) -> activate#(V)
U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(activate(V2))
U61#(tt(),V) -> U62#(isPalListKind(activate(V)),activate(V))
U61#(tt(),V) -> activate#(V)
U61#(tt(),V) -> isPalListKind#(activate(V))
U62#(tt(),V) -> activate#(V)
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U73#(tt(),P) -> activate#(P)
U73#(tt(),P) -> isPalListKind#(activate(P))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> activate#(V)
U82#(tt(),V) -> isNePal#(activate(V))
U91#(tt(),V2) -> activate#(V2)
U91#(tt(),V2) -> isPalListKind#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(V) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V))
isNeList#(V) -> activate#(V)
isNeList#(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)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V))
isNePal#(V) -> activate#(V)
isNePal#(V) -> isPalListKind#(activate(V))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) -> activate#(V)
isPal#(V) -> isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2))
isPalListKind#(n____(V1,V2)) -> activate#(V1)
isPalListKind#(n____(V1,V2)) -> activate#(V2)
isPalListKind#(n____(V1,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
1: activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
The strictly oriented rules are moved into the weak component.
****** Step 1.b:7.a:1.b:1.b:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
U25#(tt(),V2) -> isList#(activate(V2))
U31#(tt(),V) -> U32#(isPalListKind(activate(V)),activate(V))
U31#(tt(),V) -> activate#(V)
U31#(tt(),V) -> isPalListKind#(activate(V))
U32#(tt(),V) -> activate#(V)
U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(activate(V2))
U61#(tt(),V) -> U62#(isPalListKind(activate(V)),activate(V))
U61#(tt(),V) -> activate#(V)
U61#(tt(),V) -> isPalListKind#(activate(V))
U62#(tt(),V) -> activate#(V)
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U73#(tt(),P) -> activate#(P)
U73#(tt(),P) -> isPalListKind#(activate(P))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> activate#(V)
U82#(tt(),V) -> isNePal#(activate(V))
U91#(tt(),V2) -> activate#(V2)
U91#(tt(),V2) -> isPalListKind#(activate(V2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(V) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V))
isNeList#(V) -> activate#(V)
isNeList#(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)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V))
isNePal#(V) -> activate#(V)
isNePal#(V) -> isPalListKind#(activate(V))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) -> activate#(V)
isPal#(V) -> isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2))
isPalListKind#(n____(V1,V2)) -> activate#(V1)
isPalListKind#(n____(V1,V2)) -> activate#(V2)
isPalListKind#(n____(V1,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(c_40) = {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) = [3] x2 + [0]
p(U12) = [1] x1 + [0]
p(U13) = [3]
p(U21) = [7] x2 + [2] x3 + [0]
p(U22) = [4] x1 + [5] x2 + [0]
p(U23) = [1]
p(U24) = [6] x1 + [7]
p(U25) = [0]
p(U26) = [1]
p(U31) = [2] x1 + [4] x2 + [0]
p(U32) = [0]
p(U33) = [7] x1 + [0]
p(U41) = [3] x1 + [1] x2 + [4] x3 + [2]
p(U42) = [5] x2 + [0]
p(U43) = [2] x1 + [5] x2 + [5]
p(U44) = [2] x1 + [0]
p(U45) = [1] x1 + [5] x2 + [6]
p(U46) = [0]
p(U51) = [2] x1 + [5] x2 + [2]
p(U52) = [2] x1 + [4] x2 + [0]
p(U53) = [4] x1 + [4]
p(U54) = [1] x2 + [2]
p(U55) = [2] x2 + [0]
p(U56) = [1] x1 + [6]
p(U61) = [5] x1 + [3] x2 + [0]
p(U62) = [0]
p(U63) = [4] x1 + [5]
p(U71) = [3] x1 + [1] x3 + [5]
p(U72) = [1] x2 + [2]
p(U73) = [2] x1 + [1] x2 + [1]
p(U74) = [0]
p(U81) = [3]
p(U82) = [0]
p(U83) = [1] x1 + [1]
p(U91) = [6] x1 + [0]
p(U92) = [3]
p(__) = [1] x1 + [1] x2 + [3]
p(a) = [0]
p(activate) = [1] x1 + [0]
p(e) = [2]
p(i) = [0]
p(isList) = [0]
p(isNeList) = [0]
p(isNePal) = [1]
p(isPal) = [2] x1 + [0]
p(isPalListKind) = [1] x1 + [0]
p(isQid) = [1]
p(n____) = [1] x1 + [1] x2 + [3]
p(n__a) = [0]
p(n__e) = [2]
p(n__i) = [0]
p(n__nil) = [4]
p(n__o) = [0]
p(n__u) = [0]
p(nil) = [4]
p(o) = [0]
p(tt) = [0]
p(u) = [0]
p(U11#) = [2] x2 + [2]
p(U12#) = [2] x2 + [2]
p(U13#) = [4]
p(U21#) = [2] x2 + [2] x3 + [5]
p(U22#) = [2] x2 + [2] x3 + [3]
p(U23#) = [2] x2 + [2] x3 + [3]
p(U24#) = [2] x2 + [2] x3 + [2]
p(U25#) = [2] x2 + [2]
p(U26#) = [0]
p(U31#) = [2] x2 + [2]
p(U32#) = [2] x2 + [0]
p(U33#) = [0]
p(U41#) = [2] x2 + [2] x3 + [3]
p(U42#) = [2] x2 + [2] x3 + [2]
p(U43#) = [2] x2 + [2] x3 + [2]
p(U44#) = [2] x2 + [2] x3 + [2]
p(U45#) = [2] x2 + [2]
p(U46#) = [4] x1 + [1]
p(U51#) = [2] x2 + [2] x3 + [4]
p(U52#) = [2] x2 + [2] x3 + [4]
p(U53#) = [2] x2 + [2] x3 + [4]
p(U54#) = [2] x2 + [2] x3 + [4]
p(U55#) = [2] x2 + [4]
p(U56#) = [1] x1 + [1]
p(U61#) = [2] x2 + [1]
p(U62#) = [2] x2 + [1]
p(U63#) = [0]
p(U71#) = [4] x2 + [2] x3 + [5]
p(U72#) = [2] x2 + [5]
p(U73#) = [2] x2 + [5]
p(U74#) = [0]
p(U81#) = [2] x2 + [4]
p(U82#) = [2] x2 + [4]
p(U83#) = [1] x1 + [0]
p(U91#) = [2] x2 + [6]
p(U92#) = [0]
p(__#) = [1] x1 + [4] x2 + [0]
p(a#) = [0]
p(activate#) = [2] x1 + [0]
p(e#) = [0]
p(i#) = [0]
p(isList#) = [2] x1 + [2]
p(isNeList#) = [2] x1 + [2]
p(isNePal#) = [2] x1 + [1]
p(isPal#) = [2] x1 + [4]
p(isPalListKind#) = [2] x1 + [0]
p(isQid#) = [1] x1 + [0]
p(nil#) = [1]
p(o#) = [0]
p(u#) = [0]
p(c_1) = [1] x1 + [1] x2 + [0]
p(c_2) = [1]
p(c_3) = [1]
p(c_4) = [1] x2 + [2]
p(c_5) = [2] x1 + [1] x3 + [2]
p(c_6) = [1] x2 + [1] x5 + [1]
p(c_7) = [4] x3 + [2] x4 + [1]
p(c_8) = [1]
p(c_9) = [4]
p(c_10) = [4] x2 + [0]
p(c_11) = [2]
p(c_12) = [4]
p(c_13) = [1] x2 + [1] x3 + [1] x5 + [4]
p(c_14) = [4] x2 + [1] x4 + [0]
p(c_15) = [1] x1 + [4] x3 + [1]
p(c_16) = [2] x4 + [1]
p(c_17) = [1] x1 + [1] x2 + [0]
p(c_18) = [0]
p(c_19) = [1] x1 + [1] x2 + [1] x4 + [2] x5 + [2]
p(c_20) = [1] x5 + [2]
p(c_21) = [1] x5 + [1]
p(c_22) = [1] x4 + [2]
p(c_23) = [1] x1 + [1] x2 + [0]
p(c_24) = [4]
p(c_25) = [1] x1 + [4] x3 + [0]
p(c_26) = [1] x1 + [1]
p(c_27) = [2]
p(c_28) = [1] x3 + [1]
p(c_29) = [1] x3 + [1] x4 + [0]
p(c_30) = [1] x1 + [4] x2 + [1]
p(c_31) = [0]
p(c_32) = [1] x3 + [4] x4 + [0]
p(c_33) = [1]
p(c_34) = [2]
p(c_35) = [1] x2 + [0]
p(c_36) = [1]
p(c_37) = [0]
p(c_38) = [0]
p(c_39) = [1]
p(c_40) = [1] x1 + [1] x2 + [2]
p(c_41) = [1] x1 + [1]
p(c_42) = [0]
p(c_43) = [1]
p(c_44) = [2] x1 + [4]
p(c_45) = [4]
p(c_46) = [1] x1 + [0]
p(c_47) = [0]
p(c_48) = [2]
p(c_49) = [1] x1 + [1] x3 + [0]
p(c_50) = [1] x1 + [4] x2 + [4] x4 + [4]
p(c_51) = [4]
p(c_52) = [1] x3 + [2] x4 + [0]
p(c_53) = [1]
p(c_54) = [1] x1 + [1] x2 + [1] x4 + [1] x5 + [0]
p(c_55) = [1] x4 + [2]
p(c_56) = [1] x1 + [4] x3 + [4]
p(c_57) = [1]
p(c_58) = [0]
p(c_59) = [1] x1 + [1] x2 + [1]
p(c_60) = [0]
p(c_61) = [0]
p(c_62) = [1]
p(c_63) = [1]
p(c_64) = [1]
p(c_65) = [4]
p(c_66) = [1]
p(c_67) = [4]
p(c_68) = [1]
p(c_69) = [1]
p(c_70) = [4]
p(c_71) = [0]
p(c_72) = [0]
p(c_73) = [1]
Following rules are strictly oriented:
activate#(n____(X1,X2)) = [2] X1 + [2] X2 + [6]
> [2] X1 + [2] X2 + [2]
= c_40(activate#(X1),activate#(X2))
Following rules are (at-least) weakly oriented:
U11#(tt(),V) = [2] V + [2]
>= [2] V + [2]
= U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) = [2] V + [2]
>= [2] V + [0]
= activate#(V)
U11#(tt(),V) = [2] V + [2]
>= [2] V + [0]
= isPalListKind#(activate(V))
U12#(tt(),V) = [2] V + [2]
>= [2] V + [0]
= activate#(V)
U12#(tt(),V) = [2] V + [2]
>= [2] V + [2]
= isNeList#(activate(V))
U21#(tt(),V1,V2) = [2] V1 + [2] V2 + [5]
>= [2] V1 + [2] V2 + [3]
= U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) = [2] V1 + [2] V2 + [5]
>= [2] V1 + [0]
= activate#(V1)
U21#(tt(),V1,V2) = [2] V1 + [2] V2 + [5]
>= [2] V2 + [0]
= activate#(V2)
U21#(tt(),V1,V2) = [2] V1 + [2] V2 + [5]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
U22#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V1 + [2] V2 + [3]
= U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U22#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V1 + [0]
= activate#(V1)
U22#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V2 + [0]
= activate#(V2)
U22#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U23#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V1 + [2] V2 + [2]
= U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U23#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V1 + [0]
= activate#(V1)
U23#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V2 + [0]
= activate#(V2)
U23#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U24#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V2 + [2]
= U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V1 + [0]
= activate#(V1)
U24#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V2 + [0]
= activate#(V2)
U24#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V1 + [2]
= isList#(activate(V1))
U25#(tt(),V2) = [2] V2 + [2]
>= [2] V2 + [0]
= activate#(V2)
U25#(tt(),V2) = [2] V2 + [2]
>= [2] V2 + [2]
= isList#(activate(V2))
U31#(tt(),V) = [2] V + [2]
>= [2] V + [0]
= U32#(isPalListKind(activate(V)),activate(V))
U31#(tt(),V) = [2] V + [2]
>= [2] V + [0]
= activate#(V)
U31#(tt(),V) = [2] V + [2]
>= [2] V + [0]
= isPalListKind#(activate(V))
U32#(tt(),V) = [2] V + [0]
>= [2] V + [0]
= activate#(V)
U41#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V1 + [2] V2 + [2]
= U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V1 + [0]
= activate#(V1)
U41#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V2 + [0]
= activate#(V2)
U41#(tt(),V1,V2) = [2] V1 + [2] V2 + [3]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
U42#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V1 + [2] V2 + [2]
= U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U42#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V1 + [0]
= activate#(V1)
U42#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V2 + [0]
= activate#(V2)
U42#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U43#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V1 + [2] V2 + [2]
= U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U43#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V1 + [0]
= activate#(V1)
U43#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V2 + [0]
= activate#(V2)
U43#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U44#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V2 + [2]
= U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V1 + [0]
= activate#(V1)
U44#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V2 + [0]
= activate#(V2)
U44#(tt(),V1,V2) = [2] V1 + [2] V2 + [2]
>= [2] V1 + [2]
= isList#(activate(V1))
U45#(tt(),V2) = [2] V2 + [2]
>= [2] V2 + [0]
= activate#(V2)
U45#(tt(),V2) = [2] V2 + [2]
>= [2] V2 + [2]
= isNeList#(activate(V2))
U51#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V1 + [2] V2 + [4]
= U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V1 + [0]
= activate#(V1)
U51#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V2 + [0]
= activate#(V2)
U51#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
U52#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V1 + [2] V2 + [4]
= U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U52#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V1 + [0]
= activate#(V1)
U52#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V2 + [0]
= activate#(V2)
U52#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U53#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V1 + [2] V2 + [4]
= U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
U53#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V1 + [0]
= activate#(V1)
U53#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V2 + [0]
= activate#(V2)
U53#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
U54#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V2 + [4]
= U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V1 + [0]
= activate#(V1)
U54#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V2 + [0]
= activate#(V2)
U54#(tt(),V1,V2) = [2] V1 + [2] V2 + [4]
>= [2] V1 + [2]
= isNeList#(activate(V1))
U55#(tt(),V2) = [2] V2 + [4]
>= [2] V2 + [0]
= activate#(V2)
U55#(tt(),V2) = [2] V2 + [4]
>= [2] V2 + [2]
= isList#(activate(V2))
U61#(tt(),V) = [2] V + [1]
>= [2] V + [1]
= U62#(isPalListKind(activate(V)),activate(V))
U61#(tt(),V) = [2] V + [1]
>= [2] V + [0]
= activate#(V)
U61#(tt(),V) = [2] V + [1]
>= [2] V + [0]
= isPalListKind#(activate(V))
U62#(tt(),V) = [2] V + [1]
>= [2] V + [0]
= activate#(V)
U71#(tt(),I,P) = [4] I + [2] P + [5]
>= [2] P + [5]
= U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) = [4] I + [2] P + [5]
>= [2] I + [0]
= activate#(I)
U71#(tt(),I,P) = [4] I + [2] P + [5]
>= [2] P + [0]
= activate#(P)
U71#(tt(),I,P) = [4] I + [2] P + [5]
>= [2] I + [0]
= isPalListKind#(activate(I))
U72#(tt(),P) = [2] P + [5]
>= [2] P + [5]
= U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) = [2] P + [5]
>= [2] P + [0]
= activate#(P)
U72#(tt(),P) = [2] P + [5]
>= [2] P + [4]
= isPal#(activate(P))
U73#(tt(),P) = [2] P + [5]
>= [2] P + [0]
= activate#(P)
U73#(tt(),P) = [2] P + [5]
>= [2] P + [0]
= isPalListKind#(activate(P))
U81#(tt(),V) = [2] V + [4]
>= [2] V + [4]
= U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) = [2] V + [4]
>= [2] V + [0]
= activate#(V)
U81#(tt(),V) = [2] V + [4]
>= [2] V + [0]
= isPalListKind#(activate(V))
U82#(tt(),V) = [2] V + [4]
>= [2] V + [0]
= activate#(V)
U82#(tt(),V) = [2] V + [4]
>= [2] V + [1]
= isNePal#(activate(V))
U91#(tt(),V2) = [2] V2 + [6]
>= [2] V2 + [0]
= activate#(V2)
U91#(tt(),V2) = [2] V2 + [6]
>= [2] V2 + [0]
= isPalListKind#(activate(V2))
isList#(V) = [2] V + [2]
>= [2] V + [2]
= U11#(isPalListKind(activate(V)),activate(V))
isList#(V) = [2] V + [2]
>= [2] V + [0]
= activate#(V)
isList#(V) = [2] V + [2]
>= [2] V + [0]
= isPalListKind#(activate(V))
isList#(n____(V1,V2)) = [2] V1 + [2] V2 + [8]
>= [2] V1 + [2] V2 + [5]
= U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) = [2] V1 + [2] V2 + [8]
>= [2] V1 + [0]
= activate#(V1)
isList#(n____(V1,V2)) = [2] V1 + [2] V2 + [8]
>= [2] V2 + [0]
= activate#(V2)
isList#(n____(V1,V2)) = [2] V1 + [2] V2 + [8]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
isNeList#(V) = [2] V + [2]
>= [2] V + [2]
= U31#(isPalListKind(activate(V)),activate(V))
isNeList#(V) = [2] V + [2]
>= [2] V + [0]
= activate#(V)
isNeList#(V) = [2] V + [2]
>= [2] V + [0]
= isPalListKind#(activate(V))
isNeList#(n____(V1,V2)) = [2] V1 + [2] V2 + [8]
>= [2] V1 + [2] V2 + [3]
= U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [2] V1 + [2] V2 + [8]
>= [2] V1 + [2] V2 + [4]
= U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isNeList#(n____(V1,V2)) = [2] V1 + [2] V2 + [8]
>= [2] V1 + [0]
= activate#(V1)
isNeList#(n____(V1,V2)) = [2] V1 + [2] V2 + [8]
>= [2] V2 + [0]
= activate#(V2)
isNeList#(n____(V1,V2)) = [2] V1 + [2] V2 + [8]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
isNePal#(V) = [2] V + [1]
>= [2] V + [1]
= U61#(isPalListKind(activate(V)),activate(V))
isNePal#(V) = [2] V + [1]
>= [2] V + [0]
= activate#(V)
isNePal#(V) = [2] V + [1]
>= [2] V + [0]
= isPalListKind#(activate(V))
isNePal#(n____(I,n____(P,I))) = [4] I + [2] P + [13]
>= [4] I + [2] P + [5]
= U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) = [4] I + [2] P + [13]
>= [2] I + [0]
= activate#(I)
isNePal#(n____(I,n____(P,I))) = [4] I + [2] P + [13]
>= [2] P + [0]
= activate#(P)
isPal#(V) = [2] V + [4]
>= [2] V + [4]
= U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) = [2] V + [4]
>= [2] V + [0]
= activate#(V)
isPal#(V) = [2] V + [4]
>= [2] V + [0]
= isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) = [2] V1 + [2] V2 + [6]
>= [2] V2 + [6]
= U91#(isPalListKind(activate(V1)),activate(V2))
isPalListKind#(n____(V1,V2)) = [2] V1 + [2] V2 + [6]
>= [2] V1 + [0]
= activate#(V1)
isPalListKind#(n____(V1,V2)) = [2] V1 + [2] V2 + [6]
>= [2] V2 + [0]
= activate#(V2)
isPalListKind#(n____(V1,V2)) = [2] V1 + [2] V2 + [6]
>= [2] V1 + [0]
= isPalListKind#(activate(V1))
__(X1,X2) = [1] X1 + [1] X2 + [3]
>= [1] X1 + [1] X2 + [3]
= n____(X1,X2)
a() = [0]
>= [0]
= n__a()
activate(X) = [1] X + [0]
>= [1] X + [0]
= X
activate(n____(X1,X2)) = [1] X1 + [1] X2 + [3]
>= [1] X1 + [1] X2 + [3]
= __(activate(X1),activate(X2))
activate(n__a()) = [0]
>= [0]
= a()
activate(n__e()) = [2]
>= [2]
= e()
activate(n__i()) = [0]
>= [0]
= i()
activate(n__nil()) = [4]
>= [4]
= nil()
activate(n__o()) = [0]
>= [0]
= o()
activate(n__u()) = [0]
>= [0]
= u()
e() = [2]
>= [2]
= n__e()
i() = [0]
>= [0]
= n__i()
nil() = [4]
>= [4]
= n__nil()
o() = [0]
>= [0]
= n__o()
u() = [0]
>= [0]
= n__u()
****** Step 1.b:7.a:1.b:1.b:1.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
U25#(tt(),V2) -> isList#(activate(V2))
U31#(tt(),V) -> U32#(isPalListKind(activate(V)),activate(V))
U31#(tt(),V) -> activate#(V)
U31#(tt(),V) -> isPalListKind#(activate(V))
U32#(tt(),V) -> activate#(V)
U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(activate(V2))
U61#(tt(),V) -> U62#(isPalListKind(activate(V)),activate(V))
U61#(tt(),V) -> activate#(V)
U61#(tt(),V) -> isPalListKind#(activate(V))
U62#(tt(),V) -> activate#(V)
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U73#(tt(),P) -> activate#(P)
U73#(tt(),P) -> isPalListKind#(activate(P))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> activate#(V)
U82#(tt(),V) -> isNePal#(activate(V))
U91#(tt(),V2) -> activate#(V2)
U91#(tt(),V2) -> isPalListKind#(activate(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(V) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V))
isNeList#(V) -> activate#(V)
isNeList#(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)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V))
isNePal#(V) -> activate#(V)
isNePal#(V) -> isPalListKind#(activate(V))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) -> activate#(V)
isPal#(V) -> isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2))
isPalListKind#(n____(V1,V2)) -> activate#(V1)
isPalListKind#(n____(V1,V2)) -> activate#(V2)
isPalListKind#(n____(V1,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
****** Step 1.b:7.a:1.b:1.b:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
+ Considered Problem:
- Weak DPs:
U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
U11#(tt(),V) -> activate#(V)
U11#(tt(),V) -> isPalListKind#(activate(V))
U12#(tt(),V) -> activate#(V)
U12#(tt(),V) -> isNeList#(activate(V))
U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U21#(tt(),V1,V2) -> activate#(V1)
U21#(tt(),V1,V2) -> 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) -> activate#(V1)
U22#(tt(),V1,V2) -> 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) -> activate#(V1)
U23#(tt(),V1,V2) -> activate#(V2)
U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
U24#(tt(),V1,V2) -> activate#(V1)
U24#(tt(),V1,V2) -> activate#(V2)
U24#(tt(),V1,V2) -> isList#(activate(V1))
U25#(tt(),V2) -> activate#(V2)
U25#(tt(),V2) -> isList#(activate(V2))
U31#(tt(),V) -> U32#(isPalListKind(activate(V)),activate(V))
U31#(tt(),V) -> activate#(V)
U31#(tt(),V) -> isPalListKind#(activate(V))
U32#(tt(),V) -> activate#(V)
U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U41#(tt(),V1,V2) -> activate#(V1)
U41#(tt(),V1,V2) -> 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) -> activate#(V1)
U42#(tt(),V1,V2) -> 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) -> activate#(V1)
U43#(tt(),V1,V2) -> activate#(V2)
U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
U44#(tt(),V1,V2) -> activate#(V1)
U44#(tt(),V1,V2) -> activate#(V2)
U44#(tt(),V1,V2) -> isList#(activate(V1))
U45#(tt(),V2) -> activate#(V2)
U45#(tt(),V2) -> isNeList#(activate(V2))
U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
U51#(tt(),V1,V2) -> activate#(V1)
U51#(tt(),V1,V2) -> 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) -> activate#(V1)
U52#(tt(),V1,V2) -> 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) -> activate#(V1)
U53#(tt(),V1,V2) -> activate#(V2)
U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
U54#(tt(),V1,V2) -> activate#(V1)
U54#(tt(),V1,V2) -> activate#(V2)
U54#(tt(),V1,V2) -> isNeList#(activate(V1))
U55#(tt(),V2) -> activate#(V2)
U55#(tt(),V2) -> isList#(activate(V2))
U61#(tt(),V) -> U62#(isPalListKind(activate(V)),activate(V))
U61#(tt(),V) -> activate#(V)
U61#(tt(),V) -> isPalListKind#(activate(V))
U62#(tt(),V) -> activate#(V)
U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
U71#(tt(),I,P) -> activate#(I)
U71#(tt(),I,P) -> activate#(P)
U71#(tt(),I,P) -> isPalListKind#(activate(I))
U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
U72#(tt(),P) -> activate#(P)
U72#(tt(),P) -> isPal#(activate(P))
U73#(tt(),P) -> activate#(P)
U73#(tt(),P) -> isPalListKind#(activate(P))
U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
U81#(tt(),V) -> activate#(V)
U81#(tt(),V) -> isPalListKind#(activate(V))
U82#(tt(),V) -> activate#(V)
U82#(tt(),V) -> isNePal#(activate(V))
U91#(tt(),V2) -> activate#(V2)
U91#(tt(),V2) -> isPalListKind#(activate(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
isList#(V) -> activate#(V)
isList#(V) -> isPalListKind#(activate(V))
isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V))
isNeList#(V) -> activate#(V)
isNeList#(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)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V))
isNePal#(V) -> activate#(V)
isNePal#(V) -> isPalListKind#(activate(V))
isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
isPal#(V) -> activate#(V)
isPal#(V) -> isPalListKind#(activate(V))
isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2))
isPalListKind#(n____(V1,V2)) -> activate#(V1)
isPalListKind#(n____(V1,V2)) -> activate#(V2)
isPalListKind#(n____(V1,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:W:U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
-->_1 U12#(tt(),V) -> isNeList#(activate(V)):5
-->_1 U12#(tt(),V) -> activate#(V):4
2:W:U11#(tt(),V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
3:W:U11#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
4:W:U12#(tt(),V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
5:W:U12#(tt(),V) -> isNeList#(activate(V))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):99
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):98
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):97
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):96
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):95
-->_1 isNeList#(V) -> isPalListKind#(activate(V)):94
-->_1 isNeList#(V) -> activate#(V):93
-->_1 isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)):92
6:W:U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U22#(tt(),V1,V2) -> isPalListKind#(activate(V2)):13
-->_1 U22#(tt(),V1,V2) -> activate#(V2):12
-->_1 U22#(tt(),V1,V2) -> activate#(V1):11
-->_1 U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2)):10
7:W:U21#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
8:W:U21#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
9:W:U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
10:W:U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U23#(tt(),V1,V2) -> isPalListKind#(activate(V2)):17
-->_1 U23#(tt(),V1,V2) -> activate#(V2):16
-->_1 U23#(tt(),V1,V2) -> activate#(V1):15
-->_1 U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2)):14
11:W:U22#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
12:W:U22#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
13:W:U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
14:W:U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U24#(tt(),V1,V2) -> isList#(activate(V1)):21
-->_1 U24#(tt(),V1,V2) -> activate#(V2):20
-->_1 U24#(tt(),V1,V2) -> activate#(V1):19
-->_1 U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2)):18
15:W:U23#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
16:W:U23#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
17:W:U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
18:W:U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
-->_1 U25#(tt(),V2) -> isList#(activate(V2)):23
-->_1 U25#(tt(),V2) -> activate#(V2):22
19:W:U24#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
20:W:U24#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
21:W:U24#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):91
-->_1 isList#(n____(V1,V2)) -> activate#(V2):90
-->_1 isList#(n____(V1,V2)) -> activate#(V1):89
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):88
-->_1 isList#(V) -> isPalListKind#(activate(V)):87
-->_1 isList#(V) -> activate#(V):86
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):85
22:W:U25#(tt(),V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
23:W:U25#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):91
-->_1 isList#(n____(V1,V2)) -> activate#(V2):90
-->_1 isList#(n____(V1,V2)) -> activate#(V1):89
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):88
-->_1 isList#(V) -> isPalListKind#(activate(V)):87
-->_1 isList#(V) -> activate#(V):86
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):85
24:W:U31#(tt(),V) -> U32#(isPalListKind(activate(V)),activate(V))
-->_1 U32#(tt(),V) -> activate#(V):27
25:W:U31#(tt(),V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
26:W:U31#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
27:W:U32#(tt(),V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
28:W:U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U42#(tt(),V1,V2) -> isPalListKind#(activate(V2)):35
-->_1 U42#(tt(),V1,V2) -> activate#(V2):34
-->_1 U42#(tt(),V1,V2) -> activate#(V1):33
-->_1 U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2)):32
29:W:U41#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
30:W:U41#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
31:W:U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
32:W:U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U43#(tt(),V1,V2) -> isPalListKind#(activate(V2)):39
-->_1 U43#(tt(),V1,V2) -> activate#(V2):38
-->_1 U43#(tt(),V1,V2) -> activate#(V1):37
-->_1 U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2)):36
33:W:U42#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
34:W:U42#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
35:W:U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
36:W:U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U44#(tt(),V1,V2) -> isList#(activate(V1)):43
-->_1 U44#(tt(),V1,V2) -> activate#(V2):42
-->_1 U44#(tt(),V1,V2) -> activate#(V1):41
-->_1 U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2)):40
37:W:U43#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
38:W:U43#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
39:W:U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
40:W:U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
-->_1 U45#(tt(),V2) -> isNeList#(activate(V2)):45
-->_1 U45#(tt(),V2) -> activate#(V2):44
41:W:U44#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
42:W:U44#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
43:W:U44#(tt(),V1,V2) -> isList#(activate(V1))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):91
-->_1 isList#(n____(V1,V2)) -> activate#(V2):90
-->_1 isList#(n____(V1,V2)) -> activate#(V1):89
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):88
-->_1 isList#(V) -> isPalListKind#(activate(V)):87
-->_1 isList#(V) -> activate#(V):86
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):85
44:W:U45#(tt(),V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
45:W:U45#(tt(),V2) -> isNeList#(activate(V2))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):99
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):98
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):97
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):96
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):95
-->_1 isNeList#(V) -> isPalListKind#(activate(V)):94
-->_1 isNeList#(V) -> activate#(V):93
-->_1 isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)):92
46:W:U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U52#(tt(),V1,V2) -> isPalListKind#(activate(V2)):53
-->_1 U52#(tt(),V1,V2) -> activate#(V2):52
-->_1 U52#(tt(),V1,V2) -> activate#(V1):51
-->_1 U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2)):50
47:W:U51#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
48:W:U51#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
49:W:U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
50:W:U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U53#(tt(),V1,V2) -> isPalListKind#(activate(V2)):57
-->_1 U53#(tt(),V1,V2) -> activate#(V2):56
-->_1 U53#(tt(),V1,V2) -> activate#(V1):55
-->_1 U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2)):54
51:W:U52#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
52:W:U52#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
53:W:U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
54:W:U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
-->_1 U54#(tt(),V1,V2) -> isNeList#(activate(V1)):61
-->_1 U54#(tt(),V1,V2) -> activate#(V2):60
-->_1 U54#(tt(),V1,V2) -> activate#(V1):59
-->_1 U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2)):58
55:W:U53#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
56:W:U53#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
57:W:U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
58:W:U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
-->_1 U55#(tt(),V2) -> isList#(activate(V2)):63
-->_1 U55#(tt(),V2) -> activate#(V2):62
59:W:U54#(tt(),V1,V2) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
60:W:U54#(tt(),V1,V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
61:W:U54#(tt(),V1,V2) -> isNeList#(activate(V1))
-->_1 isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):99
-->_1 isNeList#(n____(V1,V2)) -> activate#(V2):98
-->_1 isNeList#(n____(V1,V2)) -> activate#(V1):97
-->_1 isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2)):96
-->_1 isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2)):95
-->_1 isNeList#(V) -> isPalListKind#(activate(V)):94
-->_1 isNeList#(V) -> activate#(V):93
-->_1 isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)):92
62:W:U55#(tt(),V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
63:W:U55#(tt(),V2) -> isList#(activate(V2))
-->_1 isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)):91
-->_1 isList#(n____(V1,V2)) -> activate#(V2):90
-->_1 isList#(n____(V1,V2)) -> activate#(V1):89
-->_1 isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2)):88
-->_1 isList#(V) -> isPalListKind#(activate(V)):87
-->_1 isList#(V) -> activate#(V):86
-->_1 isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)):85
64:W:U61#(tt(),V) -> U62#(isPalListKind(activate(V)),activate(V))
-->_1 U62#(tt(),V) -> activate#(V):67
65:W:U61#(tt(),V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
66:W:U61#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
67:W:U62#(tt(),V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
68:W:U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
-->_1 U72#(tt(),P) -> isPal#(activate(P)):74
-->_1 U72#(tt(),P) -> activate#(P):73
-->_1 U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P)):72
69:W:U71#(tt(),I,P) -> activate#(I)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
70:W:U71#(tt(),I,P) -> activate#(P)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
71:W:U71#(tt(),I,P) -> isPalListKind#(activate(I))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
72:W:U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
-->_1 U73#(tt(),P) -> isPalListKind#(activate(P)):76
-->_1 U73#(tt(),P) -> activate#(P):75
73:W:U72#(tt(),P) -> activate#(P)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
74:W:U72#(tt(),P) -> isPal#(activate(P))
-->_1 isPal#(V) -> isPalListKind#(activate(V)):108
-->_1 isPal#(V) -> activate#(V):107
-->_1 isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V)):106
75:W:U73#(tt(),P) -> activate#(P)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
76:W:U73#(tt(),P) -> isPalListKind#(activate(P))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
77:W:U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
-->_1 U82#(tt(),V) -> isNePal#(activate(V)):81
-->_1 U82#(tt(),V) -> activate#(V):80
78:W:U81#(tt(),V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
79:W:U81#(tt(),V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
80:W:U82#(tt(),V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
81:W:U82#(tt(),V) -> isNePal#(activate(V))
-->_1 isNePal#(n____(I,n____(P,I))) -> activate#(P):105
-->_1 isNePal#(n____(I,n____(P,I))) -> activate#(I):104
-->_1 isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P)):103
-->_1 isNePal#(V) -> isPalListKind#(activate(V)):102
-->_1 isNePal#(V) -> activate#(V):101
-->_1 isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)):100
82:W:U91#(tt(),V2) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
83:W:U91#(tt(),V2) -> isPalListKind#(activate(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
84:W:activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
85:W:isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
-->_1 U11#(tt(),V) -> isPalListKind#(activate(V)):3
-->_1 U11#(tt(),V) -> activate#(V):2
-->_1 U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V)):1
86:W:isList#(V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
87:W:isList#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
88:W:isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U21#(tt(),V1,V2) -> isPalListKind#(activate(V1)):9
-->_1 U21#(tt(),V1,V2) -> activate#(V2):8
-->_1 U21#(tt(),V1,V2) -> activate#(V1):7
-->_1 U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2)):6
89:W:isList#(n____(V1,V2)) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
90:W:isList#(n____(V1,V2)) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
91:W:isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
92:W:isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V))
-->_1 U31#(tt(),V) -> isPalListKind#(activate(V)):26
-->_1 U31#(tt(),V) -> activate#(V):25
-->_1 U31#(tt(),V) -> U32#(isPalListKind(activate(V)),activate(V)):24
93:W:isNeList#(V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
94:W:isNeList#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
95:W:isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U41#(tt(),V1,V2) -> isPalListKind#(activate(V1)):31
-->_1 U41#(tt(),V1,V2) -> activate#(V2):30
-->_1 U41#(tt(),V1,V2) -> activate#(V1):29
-->_1 U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2)):28
96:W:isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
-->_1 U51#(tt(),V1,V2) -> isPalListKind#(activate(V1)):49
-->_1 U51#(tt(),V1,V2) -> activate#(V2):48
-->_1 U51#(tt(),V1,V2) -> activate#(V1):47
-->_1 U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2)):46
97:W:isNeList#(n____(V1,V2)) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
98:W:isNeList#(n____(V1,V2)) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
99:W:isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
100:W:isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V))
-->_1 U61#(tt(),V) -> isPalListKind#(activate(V)):66
-->_1 U61#(tt(),V) -> activate#(V):65
-->_1 U61#(tt(),V) -> U62#(isPalListKind(activate(V)),activate(V)):64
101:W:isNePal#(V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
102:W:isNePal#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
103:W:isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
-->_1 U71#(tt(),I,P) -> isPalListKind#(activate(I)):71
-->_1 U71#(tt(),I,P) -> activate#(P):70
-->_1 U71#(tt(),I,P) -> activate#(I):69
-->_1 U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P)):68
104:W:isNePal#(n____(I,n____(P,I))) -> activate#(I)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
105:W:isNePal#(n____(I,n____(P,I))) -> activate#(P)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
106:W:isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
-->_1 U81#(tt(),V) -> isPalListKind#(activate(V)):79
-->_1 U81#(tt(),V) -> activate#(V):78
-->_1 U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V)):77
107:W:isPal#(V) -> activate#(V)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
108:W:isPal#(V) -> isPalListKind#(activate(V))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
109:W:isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2))
-->_1 U91#(tt(),V2) -> isPalListKind#(activate(V2)):83
-->_1 U91#(tt(),V2) -> activate#(V2):82
110:W:isPalListKind#(n____(V1,V2)) -> activate#(V1)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
111:W:isPalListKind#(n____(V1,V2)) -> activate#(V2)
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):84
112:W:isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1))
-->_1 isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)):112
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V2):111
-->_1 isPalListKind#(n____(V1,V2)) -> activate#(V1):110
-->_1 isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2)):109
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
68: U71#(tt(),I,P) -> U72#(isPalListKind(activate(I)),activate(P))
103: isNePal#(n____(I,n____(P,I))) -> U71#(isQid(activate(I)),activate(I),activate(P))
81: U82#(tt(),V) -> isNePal#(activate(V))
77: U81#(tt(),V) -> U82#(isPalListKind(activate(V)),activate(V))
106: isPal#(V) -> U81#(isPalListKind(activate(V)),activate(V))
74: U72#(tt(),P) -> isPal#(activate(P))
72: U72#(tt(),P) -> U73#(isPal(activate(P)),activate(P))
75: U73#(tt(),P) -> activate#(P)
76: U73#(tt(),P) -> isPalListKind#(activate(P))
73: U72#(tt(),P) -> activate#(P)
80: U82#(tt(),V) -> activate#(V)
100: isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V))
101: isNePal#(V) -> activate#(V)
102: isNePal#(V) -> isPalListKind#(activate(V))
69: U71#(tt(),I,P) -> activate#(I)
70: U71#(tt(),I,P) -> activate#(P)
71: U71#(tt(),I,P) -> isPalListKind#(activate(I))
104: isNePal#(n____(I,n____(P,I))) -> activate#(I)
105: isNePal#(n____(I,n____(P,I))) -> activate#(P)
78: U81#(tt(),V) -> activate#(V)
79: U81#(tt(),V) -> isPalListKind#(activate(V))
107: isPal#(V) -> activate#(V)
108: isPal#(V) -> isPalListKind#(activate(V))
66: U61#(tt(),V) -> isPalListKind#(activate(V))
65: U61#(tt(),V) -> activate#(V)
64: U61#(tt(),V) -> U62#(isPalListKind(activate(V)),activate(V))
67: U62#(tt(),V) -> activate#(V)
1: U11#(tt(),V) -> U12#(isPalListKind(activate(V)),activate(V))
85: isList#(V) -> U11#(isPalListKind(activate(V)),activate(V))
63: U55#(tt(),V2) -> isList#(activate(V2))
58: U54#(tt(),V1,V2) -> U55#(isNeList(activate(V1)),activate(V2))
54: U53#(tt(),V1,V2) -> U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
50: U52#(tt(),V1,V2) -> U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
46: U51#(tt(),V1,V2) -> U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
96: isNeList#(n____(V1,V2)) -> U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
61: U54#(tt(),V1,V2) -> isNeList#(activate(V1))
45: U45#(tt(),V2) -> isNeList#(activate(V2))
40: U44#(tt(),V1,V2) -> U45#(isList(activate(V1)),activate(V2))
36: U43#(tt(),V1,V2) -> U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
32: U42#(tt(),V1,V2) -> U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
28: U41#(tt(),V1,V2) -> U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
95: isNeList#(n____(V1,V2)) -> U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
5: U12#(tt(),V) -> isNeList#(activate(V))
43: U44#(tt(),V1,V2) -> isList#(activate(V1))
23: U25#(tt(),V2) -> isList#(activate(V2))
18: U24#(tt(),V1,V2) -> U25#(isList(activate(V1)),activate(V2))
14: U23#(tt(),V1,V2) -> U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
10: U22#(tt(),V1,V2) -> U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
6: U21#(tt(),V1,V2) -> U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
88: isList#(n____(V1,V2)) -> U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
21: U24#(tt(),V1,V2) -> isList#(activate(V1))
4: U12#(tt(),V) -> activate#(V)
62: U55#(tt(),V2) -> activate#(V2)
59: U54#(tt(),V1,V2) -> activate#(V1)
60: U54#(tt(),V1,V2) -> activate#(V2)
44: U45#(tt(),V2) -> activate#(V2)
92: isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V))
24: U31#(tt(),V) -> U32#(isPalListKind(activate(V)),activate(V))
27: U32#(tt(),V) -> activate#(V)
25: U31#(tt(),V) -> activate#(V)
26: U31#(tt(),V) -> isPalListKind#(activate(V))
93: isNeList#(V) -> activate#(V)
94: isNeList#(V) -> isPalListKind#(activate(V))
41: U44#(tt(),V1,V2) -> activate#(V1)
42: U44#(tt(),V1,V2) -> activate#(V2)
22: U25#(tt(),V2) -> activate#(V2)
19: U24#(tt(),V1,V2) -> activate#(V1)
20: U24#(tt(),V1,V2) -> activate#(V2)
2: U11#(tt(),V) -> activate#(V)
3: U11#(tt(),V) -> isPalListKind#(activate(V))
86: isList#(V) -> activate#(V)
87: isList#(V) -> isPalListKind#(activate(V))
15: U23#(tt(),V1,V2) -> activate#(V1)
16: U23#(tt(),V1,V2) -> activate#(V2)
17: U23#(tt(),V1,V2) -> isPalListKind#(activate(V2))
11: U22#(tt(),V1,V2) -> activate#(V1)
12: U22#(tt(),V1,V2) -> activate#(V2)
13: U22#(tt(),V1,V2) -> isPalListKind#(activate(V2))
7: U21#(tt(),V1,V2) -> activate#(V1)
8: U21#(tt(),V1,V2) -> activate#(V2)
9: U21#(tt(),V1,V2) -> isPalListKind#(activate(V1))
89: isList#(n____(V1,V2)) -> activate#(V1)
90: isList#(n____(V1,V2)) -> activate#(V2)
91: isList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
37: U43#(tt(),V1,V2) -> activate#(V1)
38: U43#(tt(),V1,V2) -> activate#(V2)
39: U43#(tt(),V1,V2) -> isPalListKind#(activate(V2))
33: U42#(tt(),V1,V2) -> activate#(V1)
34: U42#(tt(),V1,V2) -> activate#(V2)
35: U42#(tt(),V1,V2) -> isPalListKind#(activate(V2))
29: U41#(tt(),V1,V2) -> activate#(V1)
30: U41#(tt(),V1,V2) -> activate#(V2)
31: U41#(tt(),V1,V2) -> isPalListKind#(activate(V1))
55: U53#(tt(),V1,V2) -> activate#(V1)
56: U53#(tt(),V1,V2) -> activate#(V2)
57: U53#(tt(),V1,V2) -> isPalListKind#(activate(V2))
51: U52#(tt(),V1,V2) -> activate#(V1)
52: U52#(tt(),V1,V2) -> activate#(V2)
53: U52#(tt(),V1,V2) -> isPalListKind#(activate(V2))
47: U51#(tt(),V1,V2) -> activate#(V1)
48: U51#(tt(),V1,V2) -> activate#(V2)
49: U51#(tt(),V1,V2) -> isPalListKind#(activate(V1))
97: isNeList#(n____(V1,V2)) -> activate#(V1)
98: isNeList#(n____(V1,V2)) -> activate#(V2)
99: isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1))
112: isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1))
83: U91#(tt(),V2) -> isPalListKind#(activate(V2))
109: isPalListKind#(n____(V1,V2)) -> U91#(isPalListKind(activate(V1)),activate(V2))
82: U91#(tt(),V2) -> activate#(V2)
110: isPalListKind#(n____(V1,V2)) -> activate#(V1)
111: isPalListKind#(n____(V1,V2)) -> activate#(V2)
84: activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
****** Step 1.b:7.a:1.b:1.b:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- 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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 1.b:7.b:1: PredecessorEstimation WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U62#(tt(),V) -> c_26(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(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(isNePal#(activate(V)),activate#(V))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
- Weak DPs:
U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U12#(tt(),V) -> c_2(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(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(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(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(isList#(activate(V2)),activate#(V2))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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
{2,5}
by application of
Pre({2,5}) = {1,4}.
Here rules are labelled as follows:
1: U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
2: U62#(tt(),V) -> c_26(activate#(V))
3: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P))
4: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P))
5: U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
6: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
7: U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
8: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
9: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
10: isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
11: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
12: U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V))
13: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
14: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
15: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
16: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2))
17: U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2))
18: U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
19: U32#(tt(),V) -> c_11(activate#(V))
20: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
21: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
22: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
23: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2))
24: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2))
25: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
26: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
27: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
28: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2))
29: U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2))
30: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
31: activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
32: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
33: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
34: isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
35: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
36: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
37: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
*** Step 1.b:7.b:2: PredecessorEstimation WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
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))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
- Weak DPs:
U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U12#(tt(),V) -> c_2(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(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(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(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(isList#(activate(V2)),activate#(V2))
U62#(tt(),V) -> c_26(activate#(V))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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
{1}
by application of
Pre({1}) = {6}.
Here rules are labelled as follows:
1: U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
2: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P))
3: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P))
4: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
5: U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
6: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
7: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
8: isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
9: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
10: U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V))
11: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
12: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
13: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
14: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2))
15: U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2))
16: U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
17: U32#(tt(),V) -> c_11(activate#(V))
18: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
19: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
20: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
21: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2))
22: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2))
23: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
24: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
25: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
26: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2))
27: U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2))
28: U62#(tt(),V) -> c_26(activate#(V))
29: U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
30: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
31: activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
32: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
33: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
34: isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
35: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
36: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
37: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
*** Step 1.b:7.b:3: PredecessorEstimation WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
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))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
- Weak DPs:
U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U12#(tt(),V) -> c_2(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(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(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(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(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(activate#(V))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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
{5}
by application of
Pre({5}) = {4}.
Here rules are labelled as follows:
1: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P))
2: U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P))
3: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
4: U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
5: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
6: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
7: isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
8: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
9: U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V))
10: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
11: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
12: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
13: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2))
14: U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2))
15: U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
16: U32#(tt(),V) -> c_11(activate#(V))
17: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
18: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
19: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
20: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2))
21: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2))
22: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
23: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
24: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
25: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2))
26: U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2))
27: U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
28: U62#(tt(),V) -> c_26(activate#(V))
29: U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
30: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
31: activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
32: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
33: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
34: isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
35: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
36: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
37: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
*** Step 1.b:7.b:4: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
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))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
- Weak DPs:
U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U12#(tt(),V) -> c_2(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(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(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(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(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(activate#(V))
U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
isPalListKind#(n____(V1,V2)) -> c_59(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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P))
,isPal#(activate(P))
,activate#(P)
,activate#(P)):2
2:S:U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P))
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P)):28
-->_2 isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):6
3: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V)):4
4:S:U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
-->_1 isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):36
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P)):5
5:S:isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P)):1
6:S:isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):3
7:W:U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V)):8
8:W:U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V))
-->_1 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):35
-->_1 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):34
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):33
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
9:W: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):10
10:W: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):11
11:W: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2)):12
12:W: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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2)):13
13:W:U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2))
-->_1 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_1 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
14:W:U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U32#(tt(),V) -> c_11(activate#(V)):15
15:W:U32#(tt(),V) -> c_11(activate#(V))
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
16:W: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):17
17:W: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):18
18:W: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2)):19
19:W: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_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_2 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2)):20
20:W:U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2))
-->_1 isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):35
-->_1 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):34
-->_1 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):33
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
21:W: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):22
22:W: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2)):23
23:W: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_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2)):24
24:W: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_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):35
-->_2 isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):34
-->_2 isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):33
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2)):25
25:W:U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2))
-->_1 isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):32
-->_1 isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):31
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
26:W:U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U62#(tt(),V) -> c_26(activate#(V)):27
27:W:U62#(tt(),V) -> c_26(activate#(V))
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
28:W:U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
29:W:U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
-->_1 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
30:W:activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
-->_2 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
31:W:isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):7
32:W:isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):9
33:W:isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):14
34:W:isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):16
35:W:isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_5 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2)):21
36:W:isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):26
37:W:isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
-->_2 isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2)):37
-->_4 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_3 activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2)):30
-->_1 U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2)):29
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
7: U11#(tt(),V) -> c_1(U12#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
31: isList#(V) -> c_49(U11#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
25: U55#(tt(),V2) -> c_23(isList#(activate(V2)),activate#(V2))
24: U54#(tt(),V1,V2) -> c_22(U55#(isNeList(activate(V1)),activate(V2))
,isNeList#(activate(V1))
,activate#(V1)
,activate#(V2))
23: U53#(tt(),V1,V2) -> c_21(U54#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
22: U52#(tt(),V1,V2) -> c_20(U53#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
21: U51#(tt(),V1,V2) -> c_19(U52#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
35: isNeList#(n____(V1,V2)) -> c_54(U51#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
20: U45#(tt(),V2) -> c_17(isNeList#(activate(V2)),activate#(V2))
19: U44#(tt(),V1,V2) -> c_16(U45#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2))
18: U43#(tt(),V1,V2) -> c_15(U44#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
17: U42#(tt(),V1,V2) -> c_14(U43#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
16: U41#(tt(),V1,V2) -> c_13(U42#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
34: isNeList#(n____(V1,V2)) -> c_53(U41#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
8: U12#(tt(),V) -> c_2(isNeList#(activate(V)),activate#(V))
13: U25#(tt(),V2) -> c_8(isList#(activate(V2)),activate#(V2))
12: U24#(tt(),V1,V2) -> c_7(U25#(isList(activate(V1)),activate(V2))
,isList#(activate(V1))
,activate#(V1)
,activate#(V2))
11: U23#(tt(),V1,V2) -> c_6(U24#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
10: U22#(tt(),V1,V2) -> c_5(U23#(isPalListKind(activate(V2)),activate(V1),activate(V2))
,isPalListKind#(activate(V2))
,activate#(V2)
,activate#(V1)
,activate#(V2))
9: U21#(tt(),V1,V2) -> c_4(U22#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
32: isList#(n____(V1,V2)) -> c_50(U21#(isPalListKind(activate(V1)),activate(V1),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V1)
,activate#(V2))
33: isNeList#(V) -> c_52(U31#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
14: U31#(tt(),V) -> c_10(U32#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
15: U32#(tt(),V) -> c_11(activate#(V))
36: isNePal#(V) -> c_55(U61#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
26: U61#(tt(),V) -> c_25(U62#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
27: U62#(tt(),V) -> c_26(activate#(V))
28: U73#(tt(),P) -> c_30(isPalListKind#(activate(P)),activate#(P))
37: isPalListKind#(n____(V1,V2)) -> c_59(U91#(isPalListKind(activate(V1)),activate(V2))
,isPalListKind#(activate(V1))
,activate#(V1)
,activate#(V2))
29: U91#(tt(),V2) -> c_35(isPalListKind#(activate(V2)),activate#(V2))
30: activate#(n____(X1,X2)) -> c_40(activate#(X1),activate#(X2))
*** Step 1.b:7.b:5: SimplifyRHS WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
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))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/4,c_29/4,c_30/2,c_31/0
,c_32/4,c_33/2,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/4,c_57/4,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P))
-->_1 U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P))
,isPal#(activate(P))
,activate#(P)
,activate#(P)):2
2:S:U72#(tt(),P) -> c_29(U73#(isPal(activate(P)),activate(P)),isPal#(activate(P)),activate#(P),activate#(P))
-->_2 isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):6
3:S:U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_1 U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V)):4
4:S:U82#(tt(),V) -> c_33(isNePal#(activate(V)),activate#(V))
-->_1 isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P)):5
5:S:isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))
,activate#(I)
,activate#(I)
,activate#(P))
-->_1 U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))
,isPalListKind#(activate(I))
,activate#(I)
,activate#(P)):1
6:S:isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V))
-->_1 U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))
,isPalListKind#(activate(V))
,activate#(V)
,activate#(V)):3
Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
U72#(tt(),P) -> c_29(isPal#(activate(P)))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
U82#(tt(),V) -> c_33(isNePal#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V)))
*** Step 1.b:7.b:6: UsableRules WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
U72#(tt(),P) -> c_29(isPal#(activate(P)))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
U82#(tt(),V) -> c_33(isNePal#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),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()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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,n____(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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/1,c_29/1,c_30/2,c_31/0
,c_32/1,c_33/1,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/1,c_57/1,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
U91(tt(),V2) -> U92(isPalListKind(activate(V2)))
U92(tt()) -> tt()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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()
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()
U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
U72#(tt(),P) -> c_29(isPal#(activate(P)))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
U82#(tt(),V) -> c_33(isNePal#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V)))
*** Step 1.b:7.b:7: PredecessorEstimationCP WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
U72#(tt(),P) -> c_29(isPal#(activate(P)))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
U82#(tt(),V) -> c_33(isNePal#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V)))
- Weak TRS:
U91(tt(),V2) -> U92(isPalListKind(activate(V2)))
U92(tt()) -> tt()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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()
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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/1,c_29/1,c_30/2,c_31/0
,c_32/1,c_33/1,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/1,c_57/1,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
5: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
Consider the set of all dependency pairs
1: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
2: U72#(tt(),P) -> c_29(isPal#(activate(P)))
3: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
4: U82#(tt(),V) -> c_33(isNePal#(activate(V)))
5: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
6: isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V)))
Processor NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
SPACE(?,?)on application of the dependency pairs
{5}
These cover all (indirect) predecessors of dependency pairs
{1,2,3,4,5,6}
their number of applications is equally bounded.
The dependency pairs are shifted into the weak component.
**** Step 1.b:7.b:7.a:1: NaturalMI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
U72#(tt(),P) -> c_29(isPal#(activate(P)))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
U82#(tt(),V) -> c_33(isNePal#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V)))
- Weak TRS:
U91(tt(),V2) -> U92(isPalListKind(activate(V2)))
U92(tt()) -> tt()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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()
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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/1,c_29/1,c_30/2,c_31/0
,c_32/1,c_33/1,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/1,c_57/1,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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 = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
The following argument positions are considered usable:
uargs(c_28) = {1},
uargs(c_29) = {1},
uargs(c_32) = {1},
uargs(c_33) = {1},
uargs(c_56) = {1},
uargs(c_57) = {1}
Following symbols are considered usable:
{__,a,activate,e,i,isQid,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 0] x1 + [1 0] x2 + [0]
[2 0] [1 0] [2]
p(U12) = [1]
[0]
p(U13) = [0 0] x1 + [0]
[2 1] [0]
p(U21) = [0 0] x1 + [1 2] x2 + [0 0] x3 + [0]
[0 1] [0 1] [1 0] [2]
p(U22) = [2]
[1]
p(U23) = [1 2] x1 + [0 2] x2 + [0]
[0 0] [1 0] [0]
p(U24) = [0 1] x3 + [0]
[0 2] [0]
p(U25) = [0]
[1]
p(U26) = [0]
[1]
p(U31) = [1 1] x1 + [0 0] x2 + [1]
[1 0] [0 1] [0]
p(U32) = [0 0] x2 + [0]
[2 0] [0]
p(U33) = [0]
[0]
p(U41) = [0 0] x2 + [0 1] x3 + [0]
[2 1] [1 2] [2]
p(U42) = [0 0] x2 + [0 0] x3 + [0]
[1 2] [2 0] [0]
p(U43) = [0 1] x2 + [2]
[1 1] [0]
p(U44) = [2 2] x2 + [2]
[0 0] [0]
p(U45) = [0]
[0]
p(U46) = [0]
[0]
p(U51) = [1 2] x2 + [0]
[0 2] [2]
p(U52) = [0 2] x2 + [0]
[2 0] [2]
p(U53) = [0 1] x2 + [2 2] x3 + [0]
[0 1] [1 0] [0]
p(U54) = [0 2] x1 + [1 0] x2 + [0 1] x3 + [0]
[0 0] [0 1] [0 0] [0]
p(U55) = [0 2] x2 + [1]
[0 0] [0]
p(U56) = [1]
[0]
p(U61) = [1]
[2]
p(U62) = [0 0] x1 + [0 0] x2 + [0]
[0 2] [1 2] [1]
p(U63) = [0]
[1]
p(U71) = [0 0] x1 + [0]
[0 2] [0]
p(U72) = [0 0] x1 + [0]
[1 0] [0]
p(U73) = [0 0] x2 + [1]
[1 1] [2]
p(U74) = [0 0] x1 + [0]
[1 2] [2]
p(U81) = [0 1] x1 + [0 0] x2 + [0]
[0 0] [1 1] [0]
p(U82) = [1 1] x2 + [0]
[1 0] [0]
p(U83) = [0 2] x1 + [0]
[1 0] [1]
p(U91) = [0 3] x1 + [1 0] x2 + [3]
[2 0] [0 0] [0]
p(U92) = [0 2] x1 + [0]
[0 0] [1]
p(__) = [0 3] x1 + [0 0] x2 + [1]
[0 1] [0 1] [1]
p(a) = [2]
[0]
p(activate) = [1 0] x1 + [2]
[0 1] [0]
p(e) = [3]
[0]
p(i) = [0]
[0]
p(isList) = [2]
[0]
p(isNeList) = [1]
[1]
p(isNePal) = [0]
[0]
p(isPal) = [0]
[0]
p(isPalListKind) = [0]
[0]
p(isQid) = [0 1] x1 + [1]
[0 2] [2]
p(n____) = [0 3] x1 + [0 0] x2 + [1]
[0 1] [0 1] [1]
p(n__a) = [0]
[0]
p(n__e) = [3]
[0]
p(n__i) = [0]
[0]
p(n__nil) = [1]
[0]
p(n__o) = [2]
[2]
p(n__u) = [0]
[0]
p(nil) = [3]
[0]
p(o) = [2]
[2]
p(tt) = [0]
[1]
p(u) = [0]
[0]
p(U11#) = [0 2] x1 + [2]
[2 0] [0]
p(U12#) = [1 2] x1 + [0]
[0 2] [0]
p(U13#) = [0 1] x1 + [1]
[1 0] [0]
p(U21#) = [0 0] x1 + [0 0] x2 + [1 0] x3 + [0]
[2 2] [0 1] [0 2] [0]
p(U22#) = [1 2] x1 + [0 1] x2 + [0 0] x3 + [2]
[2 0] [0 2] [2 0] [0]
p(U23#) = [0 2] x2 + [0 0] x3 + [0]
[0 0] [1 0] [1]
p(U24#) = [1 0] x1 + [0 1] x3 + [0]
[1 0] [2 0] [0]
p(U25#) = [0]
[0]
p(U26#) = [0 1] x1 + [1]
[0 0] [0]
p(U31#) = [0 0] x1 + [0]
[0 2] [0]
p(U32#) = [1]
[0]
p(U33#) = [2]
[0]
p(U41#) = [0 2] x1 + [2 2] x2 + [2]
[1 0] [1 0] [0]
p(U42#) = [0 0] x1 + [0 0] x3 + [0]
[0 1] [0 2] [1]
p(U43#) = [0 0] x2 + [1 0] x3 + [0]
[1 0] [0 0] [0]
p(U44#) = [0 0] x1 + [0]
[0 1] [0]
p(U45#) = [2 0] x2 + [0]
[0 2] [0]
p(U46#) = [0]
[0]
p(U51#) = [0 0] x1 + [0 0] x3 + [0]
[2 0] [0 1] [0]
p(U52#) = [2]
[0]
p(U53#) = [0 0] x2 + [1]
[2 0] [0]
p(U54#) = [0]
[0]
p(U55#) = [0 1] x1 + [0]
[0 0] [1]
p(U56#) = [2]
[0]
p(U61#) = [0]
[0]
p(U62#) = [2]
[1]
p(U63#) = [0 0] x1 + [0]
[1 0] [2]
p(U71#) = [0 1] x1 + [0 2] x2 + [0 2] x3 + [1]
[1 0] [0 0] [0 2] [0]
p(U72#) = [0 2] x2 + [2]
[0 2] [1]
p(U73#) = [0 0] x2 + [0]
[1 0] [1]
p(U74#) = [0 1] x1 + [2]
[1 0] [2]
p(U81#) = [0 2] x2 + [2]
[0 1] [1]
p(U82#) = [0 2] x2 + [2]
[1 0] [2]
p(U83#) = [0 1] x1 + [1]
[2 0] [2]
p(U91#) = [0 0] x1 + [2 2] x2 + [0]
[0 2] [0 0] [0]
p(U92#) = [0 1] x1 + [0]
[1 1] [2]
p(__#) = [0 2] x1 + [0 0] x2 + [2]
[0 0] [0 1] [0]
p(a#) = [2]
[0]
p(activate#) = [1]
[2]
p(e#) = [0]
[1]
p(i#) = [2]
[1]
p(isList#) = [0 0] x1 + [0]
[0 1] [0]
p(isNeList#) = [0]
[2]
p(isNePal#) = [0 2] x1 + [2]
[1 0] [0]
p(isPal#) = [0 2] x1 + [2]
[0 0] [2]
p(isPalListKind#) = [2 0] x1 + [1]
[0 1] [1]
p(isQid#) = [0]
[0]
p(nil#) = [1]
[0]
p(o#) = [2]
[1]
p(u#) = [0]
[0]
p(c_1) = [0 1] x2 + [0 0] x3 + [0 0] x4 + [0]
[1 0] [0 1] [2 0] [1]
p(c_2) = [0 0] x1 + [0 0] x2 + [1]
[0 2] [1 1] [0]
p(c_3) = [0]
[0]
p(c_4) = [1 0] x3 + [2 0] x4 + [1]
[0 0] [0 0] [2]
p(c_5) = [0 2] x3 + [1 1] x4 + [2 1] x5 + [1]
[2 0] [1 1] [2 0] [1]
p(c_6) = [0 2] x3 + [0 1] x5 + [0]
[1 0] [2 2] [0]
p(c_7) = [0 2] x4 + [2]
[1 1] [2]
p(c_8) = [0 1] x2 + [0]
[0 1] [0]
p(c_9) = [1]
[0]
p(c_10) = [2 0] x2 + [2 0] x4 + [2]
[2 1] [0 2] [0]
p(c_11) = [0 0] x1 + [0]
[0 1] [1]
p(c_12) = [0]
[0]
p(c_13) = [0 0] x1 + [0 0] x2 + [2 2] x3 + [2 0] x5 + [0]
[0 2] [1 0] [0 1] [1 0] [2]
p(c_14) = [0 2] x3 + [2 0] x5 + [0]
[1 2] [1 0] [0]
p(c_15) = [0 0] x2 + [0 2] x5 + [0]
[1 2] [0 2] [0]
p(c_16) = [1 0] x2 + [1]
[0 1] [2]
p(c_17) = [2 0] x1 + [2 1] x2 + [2]
[2 0] [0 1] [0]
p(c_18) = [0]
[0]
p(c_19) = [0 0] x2 + [0 0] x3 + [0]
[1 2] [1 0] [0]
p(c_20) = [0 0] x1 + [2 0] x3 + [2 2] x4 + [1]
[0 2] [0 1] [2 1] [1]
p(c_21) = [1 2] x1 + [2 0] x2 + [2]
[0 0] [0 0] [0]
p(c_22) = [2 0] x1 + [0 0] x3 + [2]
[0 2] [0 2] [0]
p(c_23) = [1 0] x1 + [1 2] x2 + [0]
[0 0] [0 1] [0]
p(c_24) = [0]
[1]
p(c_25) = [0 1] x2 + [0 0] x3 + [0]
[0 2] [1 0] [1]
p(c_26) = [0 2] x1 + [2]
[0 0] [0]
p(c_27) = [1]
[0]
p(c_28) = [1 0] x1 + [0]
[0 0] [0]
p(c_29) = [1 0] x1 + [0]
[0 0] [1]
p(c_30) = [0 0] x1 + [1]
[0 2] [0]
p(c_31) = [2]
[1]
p(c_32) = [1 0] x1 + [0]
[0 0] [0]
p(c_33) = [1 0] x1 + [0]
[0 1] [0]
p(c_34) = [1]
[2]
p(c_35) = [0 1] x1 + [0]
[0 0] [1]
p(c_36) = [1]
[0]
p(c_37) = [0]
[1]
p(c_38) = [0]
[0]
p(c_39) = [0]
[0]
p(c_40) = [2 0] x1 + [0]
[2 1] [1]
p(c_41) = [0 0] x1 + [1]
[1 0] [0]
p(c_42) = [1]
[0]
p(c_43) = [1]
[0]
p(c_44) = [0 2] x1 + [1]
[2 0] [2]
p(c_45) = [1 2] x1 + [0]
[2 0] [0]
p(c_46) = [0]
[0]
p(c_47) = [0]
[0]
p(c_48) = [1]
[0]
p(c_49) = [0 0] x1 + [1]
[0 2] [0]
p(c_50) = [0 0] x1 + [1 0] x4 + [0 0] x5 + [1]
[1 0] [0 0] [0 2] [0]
p(c_51) = [2]
[2]
p(c_52) = [0 0] x1 + [1 1] x4 + [2]
[2 2] [0 0] [1]
p(c_53) = [1 0] x1 + [1 1] x2 + [1 0] x3 + [0 0] x4 + [0]
[1 2] [2 2] [2 0] [2 0] [0]
p(c_54) = [0 0] x2 + [0 2] x4 + [0 0] x5 + [1]
[1 0] [0 0] [1 0] [0]
p(c_55) = [0 0] x3 + [0 0] x4 + [0]
[1 2] [0 2] [0]
p(c_56) = [1 0] x1 + [1]
[0 0] [0]
p(c_57) = [1 0] x1 + [0]
[0 0] [2]
p(c_58) = [0]
[0]
p(c_59) = [0 0] x1 + [2 2] x2 + [0 0] x3 + [1 0] x4 + [0]
[0 2] [2 0] [1 1] [1 2] [0]
p(c_60) = [0]
[0]
p(c_61) = [0]
[0]
p(c_62) = [0]
[0]
p(c_63) = [2]
[0]
p(c_64) = [0]
[0]
p(c_65) = [1]
[0]
p(c_66) = [1]
[1]
p(c_67) = [1]
[1]
p(c_68) = [0]
[0]
p(c_69) = [1]
[2]
p(c_70) = [1]
[0]
p(c_71) = [2]
[1]
p(c_72) = [0]
[0]
p(c_73) = [1]
[0]
Following rules are strictly oriented:
isNePal#(n____(I,n____(P,I))) = [0 4] I + [0 2] P + [6]
[0 3] [0 0] [1]
> [0 4] I + [0 2] P + [4]
[0 0] [0 0] [0]
= c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
Following rules are (at-least) weakly oriented:
U71#(tt(),I,P) = [0 2] I + [0 2] P + [2]
[0 0] [0 2] [0]
>= [0 2] P + [2]
[0 0] [0]
= c_28(U72#(isPalListKind(activate(I)),activate(P)))
U72#(tt(),P) = [0 2] P + [2]
[0 2] [1]
>= [0 2] P + [2]
[0 0] [1]
= c_29(isPal#(activate(P)))
U81#(tt(),V) = [0 2] V + [2]
[0 1] [1]
>= [0 2] V + [2]
[0 0] [0]
= c_32(U82#(isPalListKind(activate(V)),activate(V)))
U82#(tt(),V) = [0 2] V + [2]
[1 0] [2]
>= [0 2] V + [2]
[1 0] [2]
= c_33(isNePal#(activate(V)))
isPal#(V) = [0 2] V + [2]
[0 0] [2]
>= [0 2] V + [2]
[0 0] [2]
= c_57(U81#(isPalListKind(activate(V)),activate(V)))
__(X1,X2) = [0 3] X1 + [0 0] X2 + [1]
[0 1] [0 1] [1]
>= [0 3] X1 + [0 0] X2 + [1]
[0 1] [0 1] [1]
= n____(X1,X2)
a() = [2]
[0]
>= [0]
[0]
= n__a()
activate(X) = [1 0] X + [2]
[0 1] [0]
>= [1 0] X + [0]
[0 1] [0]
= X
activate(n____(X1,X2)) = [0 3] X1 + [0 0] X2 + [3]
[0 1] [0 1] [1]
>= [0 3] X1 + [0 0] X2 + [1]
[0 1] [0 1] [1]
= __(activate(X1),activate(X2))
activate(n__a()) = [2]
[0]
>= [2]
[0]
= a()
activate(n__e()) = [5]
[0]
>= [3]
[0]
= e()
activate(n__i()) = [2]
[0]
>= [0]
[0]
= i()
activate(n__nil()) = [3]
[0]
>= [3]
[0]
= nil()
activate(n__o()) = [4]
[2]
>= [2]
[2]
= o()
activate(n__u()) = [2]
[0]
>= [0]
[0]
= u()
e() = [3]
[0]
>= [3]
[0]
= n__e()
i() = [0]
[0]
>= [0]
[0]
= n__i()
isQid(n__a()) = [1]
[2]
>= [0]
[1]
= tt()
isQid(n__e()) = [1]
[2]
>= [0]
[1]
= tt()
isQid(n__i()) = [1]
[2]
>= [0]
[1]
= tt()
isQid(n__o()) = [3]
[6]
>= [0]
[1]
= tt()
isQid(n__u()) = [1]
[2]
>= [0]
[1]
= tt()
nil() = [3]
[0]
>= [1]
[0]
= n__nil()
o() = [2]
[2]
>= [2]
[2]
= n__o()
u() = [0]
[0]
>= [0]
[0]
= n__u()
**** Step 1.b:7.b:7.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
U72#(tt(),P) -> c_29(isPal#(activate(P)))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
U82#(tt(),V) -> c_33(isNePal#(activate(V)))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V)))
- Weak DPs:
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
- Weak TRS:
U91(tt(),V2) -> U92(isPalListKind(activate(V2)))
U92(tt()) -> tt()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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()
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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/1,c_29/1,c_30/2,c_31/0
,c_32/1,c_33/1,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/1,c_57/1,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()
**** Step 1.b:7.b:7.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
+ Considered Problem:
- Weak DPs:
U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
U72#(tt(),P) -> c_29(isPal#(activate(P)))
U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
U82#(tt(),V) -> c_33(isNePal#(activate(V)))
isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V)))
- Weak TRS:
U91(tt(),V2) -> U92(isPalListKind(activate(V2)))
U92(tt()) -> tt()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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()
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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/1,c_29/1,c_30/2,c_31/0
,c_32/1,c_33/1,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/1,c_57/1,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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:W:U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
-->_1 U72#(tt(),P) -> c_29(isPal#(activate(P))):2
2:W:U72#(tt(),P) -> c_29(isPal#(activate(P)))
-->_1 isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V))):6
3:W:U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
-->_1 U82#(tt(),V) -> c_33(isNePal#(activate(V))):4
4:W:U82#(tt(),V) -> c_33(isNePal#(activate(V)))
-->_1 isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P))):5
5:W:isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
-->_1 U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P))):1
6:W:isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V)))
-->_1 U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V))):3
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
1: U71#(tt(),I,P) -> c_28(U72#(isPalListKind(activate(I)),activate(P)))
5: isNePal#(n____(I,n____(P,I))) -> c_56(U71#(isQid(activate(I)),activate(I),activate(P)))
4: U82#(tt(),V) -> c_33(isNePal#(activate(V)))
3: U81#(tt(),V) -> c_32(U82#(isPalListKind(activate(V)),activate(V)))
6: isPal#(V) -> c_57(U81#(isPalListKind(activate(V)),activate(V)))
2: U72#(tt(),P) -> c_29(isPal#(activate(P)))
**** Step 1.b:7.b:7.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
U91(tt(),V2) -> U92(isPalListKind(activate(V2)))
U92(tt()) -> tt()
__(X1,X2) -> n____(X1,X2)
a() -> n__a()
activate(X) -> X
activate(n____(X1,X2)) -> __(activate(X1),activate(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()
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_2/2,c_3/0,c_4/5,c_5/5,c_6/5,c_7/4,c_8/2,c_9/0,c_10/4,c_11/1,c_12/0,c_13/5,c_14/5,c_15/5,c_16/4
,c_17/2,c_18/0,c_19/5,c_20/5,c_21/5,c_22/4,c_23/2,c_24/0,c_25/4,c_26/1,c_27/0,c_28/1,c_29/1,c_30/2,c_31/0
,c_32/1,c_33/1,c_34/0,c_35/2,c_36/0,c_37/0,c_38/0,c_39/0,c_40/2,c_41/1,c_42/1,c_43/1,c_44/1,c_45/1,c_46/1
,c_47/0,c_48/0,c_49/4,c_50/5,c_51/0,c_52/4,c_53/5,c_54/5,c_55/4,c_56/1,c_57/1,c_58/0,c_59/4,c_60/0,c_61/0
,c_62/0,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}
- 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(Omega(n^1),O(n^3))