* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
U11(mark(X1),X2) -> mark(U11(X1,X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U12(mark(X1),X2) -> mark(U12(X1,X2))
U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
U13(mark(X)) -> mark(U13(X))
U13(ok(X)) -> ok(U13(X))
U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
U25(mark(X1),X2) -> mark(U25(X1,X2))
U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
U26(mark(X)) -> mark(U26(X))
U26(ok(X)) -> ok(U26(X))
U31(mark(X1),X2) -> mark(U31(X1,X2))
U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
U32(mark(X1),X2) -> mark(U32(X1,X2))
U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
U33(mark(X)) -> mark(U33(X))
U33(ok(X)) -> ok(U33(X))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
U45(mark(X1),X2) -> mark(U45(X1,X2))
U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
U46(mark(X)) -> mark(U46(X))
U46(ok(X)) -> ok(U46(X))
U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
U55(mark(X1),X2) -> mark(U55(X1,X2))
U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
U56(mark(X)) -> mark(U56(X))
U56(ok(X)) -> ok(U56(X))
U61(mark(X1),X2) -> mark(U61(X1,X2))
U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
U62(mark(X1),X2) -> mark(U62(X1,X2))
U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
U63(mark(X)) -> mark(U63(X))
U63(ok(X)) -> ok(U63(X))
U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
U72(mark(X1),X2) -> mark(U72(X1,X2))
U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
U73(mark(X1),X2) -> mark(U73(X1,X2))
U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
U74(mark(X)) -> mark(U74(X))
U74(ok(X)) -> ok(U74(X))
U81(mark(X1),X2) -> mark(U81(X1,X2))
U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
U82(mark(X1),X2) -> mark(U82(X1,X2))
U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
U83(mark(X)) -> mark(U83(X))
U83(ok(X)) -> ok(U83(X))
U91(mark(X1),X2) -> mark(U91(X1,X2))
U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
U92(mark(X)) -> mark(U92(X))
U92(ok(X)) -> ok(U92(X))
__(X1,mark(X2)) -> mark(__(X1,X2))
__(mark(X1),X2) -> mark(__(X1,X2))
__(ok(X1),ok(X2)) -> ok(__(X1,X2))
active(U11(X1,X2)) -> U11(active(X1),X2)
active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
active(U12(X1,X2)) -> U12(active(X1),X2)
active(U12(tt(),V)) -> mark(U13(isNeList(V)))
active(U13(X)) -> U13(active(X))
active(U13(tt())) -> mark(tt())
active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
active(U25(X1,X2)) -> U25(active(X1),X2)
active(U25(tt(),V2)) -> mark(U26(isList(V2)))
active(U26(X)) -> U26(active(X))
active(U26(tt())) -> mark(tt())
active(U31(X1,X2)) -> U31(active(X1),X2)
active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
active(U32(X1,X2)) -> U32(active(X1),X2)
active(U32(tt(),V)) -> mark(U33(isQid(V)))
active(U33(X)) -> U33(active(X))
active(U33(tt())) -> mark(tt())
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
active(U45(X1,X2)) -> U45(active(X1),X2)
active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
active(U46(X)) -> U46(active(X))
active(U46(tt())) -> mark(tt())
active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
active(U55(X1,X2)) -> U55(active(X1),X2)
active(U55(tt(),V2)) -> mark(U56(isList(V2)))
active(U56(X)) -> U56(active(X))
active(U56(tt())) -> mark(tt())
active(U61(X1,X2)) -> U61(active(X1),X2)
active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
active(U62(X1,X2)) -> U62(active(X1),X2)
active(U62(tt(),V)) -> mark(U63(isQid(V)))
active(U63(X)) -> U63(active(X))
active(U63(tt())) -> mark(tt())
active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
active(U72(X1,X2)) -> U72(active(X1),X2)
active(U72(tt(),P)) -> mark(U73(isPal(P),P))
active(U73(X1,X2)) -> U73(active(X1),X2)
active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
active(U74(X)) -> U74(active(X))
active(U74(tt())) -> mark(tt())
active(U81(X1,X2)) -> U81(active(X1),X2)
active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
active(U82(X1,X2)) -> U82(active(X1),X2)
active(U82(tt(),V)) -> mark(U83(isNePal(V)))
active(U83(X)) -> U83(active(X))
active(U83(tt())) -> mark(tt())
active(U91(X1,X2)) -> U91(active(X1),X2)
active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
active(U92(X)) -> U92(active(X))
active(U92(tt())) -> mark(tt())
active(__(X,nil())) -> mark(X)
active(__(X1,X2)) -> __(X1,active(X2))
active(__(X1,X2)) -> __(active(X1),X2)
active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
active(__(nil(),X)) -> mark(X)
active(isList(V)) -> mark(U11(isPalListKind(V),V))
active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
active(isList(nil())) -> mark(tt())
active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
active(isPal(V)) -> mark(U81(isPalListKind(V),V))
active(isPal(nil())) -> mark(tt())
active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
active(isPalListKind(a())) -> mark(tt())
active(isPalListKind(e())) -> mark(tt())
active(isPalListKind(i())) -> mark(tt())
active(isPalListKind(nil())) -> mark(tt())
active(isPalListKind(o())) -> mark(tt())
active(isPalListKind(u())) -> mark(tt())
active(isQid(a())) -> mark(tt())
active(isQid(e())) -> mark(tt())
active(isQid(i())) -> mark(tt())
active(isQid(o())) -> mark(tt())
active(isQid(u())) -> mark(tt())
isList(ok(X)) -> ok(isList(X))
isNeList(ok(X)) -> ok(isNeList(X))
isNePal(ok(X)) -> ok(isNePal(X))
isPal(ok(X)) -> ok(isPal(X))
isPalListKind(ok(X)) -> ok(isPalListKind(X))
isQid(ok(X)) -> ok(isQid(X))
proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
proper(U13(X)) -> U13(proper(X))
proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
proper(U26(X)) -> U26(proper(X))
proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
proper(U33(X)) -> U33(proper(X))
proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
proper(U46(X)) -> U46(proper(X))
proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
proper(U56(X)) -> U56(proper(X))
proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
proper(U63(X)) -> U63(proper(X))
proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
proper(U74(X)) -> U74(proper(X))
proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
proper(U83(X)) -> U83(proper(X))
proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
proper(U92(X)) -> U92(proper(X))
proper(__(X1,X2)) -> __(proper(X1),proper(X2))
proper(a()) -> ok(a())
proper(e()) -> ok(e())
proper(i()) -> ok(i())
proper(isList(X)) -> isList(proper(X))
proper(isNeList(X)) -> isNeList(proper(X))
proper(isNePal(X)) -> isNePal(proper(X))
proper(isPal(X)) -> isPal(proper(X))
proper(isPalListKind(X)) -> isPalListKind(proper(X))
proper(isQid(X)) -> isQid(proper(X))
proper(nil()) -> ok(nil())
proper(o()) -> ok(o())
proper(tt()) -> ok(tt())
proper(u()) -> ok(u())
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- 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,active/1,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0
,mark/1,nil/0,o/0,ok/1,tt/0,u/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,__,active,isList
,isNeList,isNePal,isPal,isPalListKind,isQid,proper,top} and constructors {a,e,i,mark,nil,o,ok,tt,u}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
U11(mark(X1),X2) -> mark(U11(X1,X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U12(mark(X1),X2) -> mark(U12(X1,X2))
U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
U13(mark(X)) -> mark(U13(X))
U13(ok(X)) -> ok(U13(X))
U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
U25(mark(X1),X2) -> mark(U25(X1,X2))
U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
U26(mark(X)) -> mark(U26(X))
U26(ok(X)) -> ok(U26(X))
U31(mark(X1),X2) -> mark(U31(X1,X2))
U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
U32(mark(X1),X2) -> mark(U32(X1,X2))
U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
U33(mark(X)) -> mark(U33(X))
U33(ok(X)) -> ok(U33(X))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
U45(mark(X1),X2) -> mark(U45(X1,X2))
U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
U46(mark(X)) -> mark(U46(X))
U46(ok(X)) -> ok(U46(X))
U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
U55(mark(X1),X2) -> mark(U55(X1,X2))
U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
U56(mark(X)) -> mark(U56(X))
U56(ok(X)) -> ok(U56(X))
U61(mark(X1),X2) -> mark(U61(X1,X2))
U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
U62(mark(X1),X2) -> mark(U62(X1,X2))
U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
U63(mark(X)) -> mark(U63(X))
U63(ok(X)) -> ok(U63(X))
U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
U72(mark(X1),X2) -> mark(U72(X1,X2))
U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
U73(mark(X1),X2) -> mark(U73(X1,X2))
U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
U74(mark(X)) -> mark(U74(X))
U74(ok(X)) -> ok(U74(X))
U81(mark(X1),X2) -> mark(U81(X1,X2))
U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
U82(mark(X1),X2) -> mark(U82(X1,X2))
U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
U83(mark(X)) -> mark(U83(X))
U83(ok(X)) -> ok(U83(X))
U91(mark(X1),X2) -> mark(U91(X1,X2))
U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
U92(mark(X)) -> mark(U92(X))
U92(ok(X)) -> ok(U92(X))
__(X1,mark(X2)) -> mark(__(X1,X2))
__(mark(X1),X2) -> mark(__(X1,X2))
__(ok(X1),ok(X2)) -> ok(__(X1,X2))
active(U11(X1,X2)) -> U11(active(X1),X2)
active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
active(U12(X1,X2)) -> U12(active(X1),X2)
active(U12(tt(),V)) -> mark(U13(isNeList(V)))
active(U13(X)) -> U13(active(X))
active(U13(tt())) -> mark(tt())
active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
active(U25(X1,X2)) -> U25(active(X1),X2)
active(U25(tt(),V2)) -> mark(U26(isList(V2)))
active(U26(X)) -> U26(active(X))
active(U26(tt())) -> mark(tt())
active(U31(X1,X2)) -> U31(active(X1),X2)
active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
active(U32(X1,X2)) -> U32(active(X1),X2)
active(U32(tt(),V)) -> mark(U33(isQid(V)))
active(U33(X)) -> U33(active(X))
active(U33(tt())) -> mark(tt())
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
active(U45(X1,X2)) -> U45(active(X1),X2)
active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
active(U46(X)) -> U46(active(X))
active(U46(tt())) -> mark(tt())
active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
active(U55(X1,X2)) -> U55(active(X1),X2)
active(U55(tt(),V2)) -> mark(U56(isList(V2)))
active(U56(X)) -> U56(active(X))
active(U56(tt())) -> mark(tt())
active(U61(X1,X2)) -> U61(active(X1),X2)
active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
active(U62(X1,X2)) -> U62(active(X1),X2)
active(U62(tt(),V)) -> mark(U63(isQid(V)))
active(U63(X)) -> U63(active(X))
active(U63(tt())) -> mark(tt())
active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
active(U72(X1,X2)) -> U72(active(X1),X2)
active(U72(tt(),P)) -> mark(U73(isPal(P),P))
active(U73(X1,X2)) -> U73(active(X1),X2)
active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
active(U74(X)) -> U74(active(X))
active(U74(tt())) -> mark(tt())
active(U81(X1,X2)) -> U81(active(X1),X2)
active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
active(U82(X1,X2)) -> U82(active(X1),X2)
active(U82(tt(),V)) -> mark(U83(isNePal(V)))
active(U83(X)) -> U83(active(X))
active(U83(tt())) -> mark(tt())
active(U91(X1,X2)) -> U91(active(X1),X2)
active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
active(U92(X)) -> U92(active(X))
active(U92(tt())) -> mark(tt())
active(__(X,nil())) -> mark(X)
active(__(X1,X2)) -> __(X1,active(X2))
active(__(X1,X2)) -> __(active(X1),X2)
active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
active(__(nil(),X)) -> mark(X)
active(isList(V)) -> mark(U11(isPalListKind(V),V))
active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
active(isList(nil())) -> mark(tt())
active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
active(isPal(V)) -> mark(U81(isPalListKind(V),V))
active(isPal(nil())) -> mark(tt())
active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
active(isPalListKind(a())) -> mark(tt())
active(isPalListKind(e())) -> mark(tt())
active(isPalListKind(i())) -> mark(tt())
active(isPalListKind(nil())) -> mark(tt())
active(isPalListKind(o())) -> mark(tt())
active(isPalListKind(u())) -> mark(tt())
active(isQid(a())) -> mark(tt())
active(isQid(e())) -> mark(tt())
active(isQid(i())) -> mark(tt())
active(isQid(o())) -> mark(tt())
active(isQid(u())) -> mark(tt())
isList(ok(X)) -> ok(isList(X))
isNeList(ok(X)) -> ok(isNeList(X))
isNePal(ok(X)) -> ok(isNePal(X))
isPal(ok(X)) -> ok(isPal(X))
isPalListKind(ok(X)) -> ok(isPalListKind(X))
isQid(ok(X)) -> ok(isQid(X))
proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
proper(U13(X)) -> U13(proper(X))
proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
proper(U26(X)) -> U26(proper(X))
proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
proper(U33(X)) -> U33(proper(X))
proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
proper(U46(X)) -> U46(proper(X))
proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
proper(U56(X)) -> U56(proper(X))
proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
proper(U63(X)) -> U63(proper(X))
proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
proper(U74(X)) -> U74(proper(X))
proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
proper(U83(X)) -> U83(proper(X))
proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
proper(U92(X)) -> U92(proper(X))
proper(__(X1,X2)) -> __(proper(X1),proper(X2))
proper(a()) -> ok(a())
proper(e()) -> ok(e())
proper(i()) -> ok(i())
proper(isList(X)) -> isList(proper(X))
proper(isNeList(X)) -> isNeList(proper(X))
proper(isNePal(X)) -> isNePal(proper(X))
proper(isPal(X)) -> isPal(proper(X))
proper(isPalListKind(X)) -> isPalListKind(proper(X))
proper(isQid(X)) -> isQid(proper(X))
proper(nil()) -> ok(nil())
proper(o()) -> ok(o())
proper(tt()) -> ok(tt())
proper(u()) -> ok(u())
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- 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,active/1,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0
,mark/1,nil/0,o/0,ok/1,tt/0,u/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,__,active,isList
,isNeList,isNePal,isPal,isPalListKind,isQid,proper,top} and constructors {a,e,i,mark,nil,o,ok,tt,u}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
U11(x,y){x -> mark(x)} =
U11(mark(x),y) ->^+ mark(U11(x,y))
= C[U11(x,y) = U11(x,y){}]
WORST_CASE(Omega(n^1),?)