* Step 1: Bounds WORST_CASE(?,O(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))
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(a()) -> ok(a())
proper(e()) -> ok(e())
proper(i()) -> ok(i())
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,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,proper/1,top/1} / {a/0,active/1,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,__,isList,isNeList
,isNePal,isPal,isPalListKind,isQid,proper,top} and constructors {a,active,e,i,mark,nil,o,ok,tt,u}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
U11_0(2,2) -> 1
U11_1(2,2) -> 3
U12_0(2,2) -> 1
U12_1(2,2) -> 3
U13_0(2) -> 1
U13_1(2) -> 3
U21_0(2,2,2) -> 1
U21_1(2,2,2) -> 3
U22_0(2,2,2) -> 1
U22_1(2,2,2) -> 3
U23_0(2,2,2) -> 1
U23_1(2,2,2) -> 3
U24_0(2,2,2) -> 1
U24_1(2,2,2) -> 3
U25_0(2,2) -> 1
U25_1(2,2) -> 3
U26_0(2) -> 1
U26_1(2) -> 3
U31_0(2,2) -> 1
U31_1(2,2) -> 3
U32_0(2,2) -> 1
U32_1(2,2) -> 3
U33_0(2) -> 1
U33_1(2) -> 3
U41_0(2,2,2) -> 1
U41_1(2,2,2) -> 3
U42_0(2,2,2) -> 1
U42_1(2,2,2) -> 3
U43_0(2,2,2) -> 1
U43_1(2,2,2) -> 3
U44_0(2,2,2) -> 1
U44_1(2,2,2) -> 3
U45_0(2,2) -> 1
U45_1(2,2) -> 3
U46_0(2) -> 1
U46_1(2) -> 3
U51_0(2,2,2) -> 1
U51_1(2,2,2) -> 3
U52_0(2,2,2) -> 1
U52_1(2,2,2) -> 3
U53_0(2,2,2) -> 1
U53_1(2,2,2) -> 3
U54_0(2,2,2) -> 1
U54_1(2,2,2) -> 3
U55_0(2,2) -> 1
U55_1(2,2) -> 3
U56_0(2) -> 1
U56_1(2) -> 3
U61_0(2,2) -> 1
U61_1(2,2) -> 3
U62_0(2,2) -> 1
U62_1(2,2) -> 3
U63_0(2) -> 1
U63_1(2) -> 3
U71_0(2,2,2) -> 1
U71_1(2,2,2) -> 3
U72_0(2,2) -> 1
U72_1(2,2) -> 3
U73_0(2,2) -> 1
U73_1(2,2) -> 3
U74_0(2) -> 1
U74_1(2) -> 3
U81_0(2,2) -> 1
U81_1(2,2) -> 3
U82_0(2,2) -> 1
U82_1(2,2) -> 3
U83_0(2) -> 1
U83_1(2) -> 3
U91_0(2,2) -> 1
U91_1(2,2) -> 3
U92_0(2) -> 1
U92_1(2) -> 3
___0(2,2) -> 1
___1(2,2) -> 3
a_0() -> 2
a_1() -> 3
active_0(2) -> 2
active_1(2) -> 4
active_2(3) -> 5
e_0() -> 2
e_1() -> 3
i_0() -> 2
i_1() -> 3
isList_0(2) -> 1
isList_1(2) -> 3
isNeList_0(2) -> 1
isNeList_1(2) -> 3
isNePal_0(2) -> 1
isNePal_1(2) -> 3
isPal_0(2) -> 1
isPal_1(2) -> 3
isPalListKind_0(2) -> 1
isPalListKind_1(2) -> 3
isQid_0(2) -> 1
isQid_1(2) -> 3
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 3
nil_0() -> 2
nil_1() -> 3
o_0() -> 2
o_1() -> 3
ok_0(2) -> 2
ok_1(3) -> 1
ok_1(3) -> 3
ok_1(3) -> 4
proper_0(2) -> 1
proper_1(2) -> 4
top_0(2) -> 1
top_1(4) -> 1
top_2(5) -> 1
tt_0() -> 2
tt_1() -> 3
u_0() -> 2
u_1() -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak 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))
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(a()) -> ok(a())
proper(e()) -> ok(e())
proper(i()) -> ok(i())
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,isList/1,isNeList/1,isNePal/1,isPal/1,isPalListKind/1,isQid/1,proper/1,top/1} / {a/0,active/1,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,__,isList,isNeList
,isNePal,isPal,isPalListKind,isQid,proper,top} and constructors {a,active,e,i,mark,nil,o,ok,tt,u}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))