* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(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)) 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: {U11/1,U21/2,U22/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/1,U71/2,U72/1,U81/1,__/2,isList/1,isNeList/1,isNePal/1 ,isPal/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,U21,U22,U31,U41,U42,U51,U52,U61,U71,U72,U81,__,isList ,isNeList,isNePal,isPal,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) -> 1 U11_1(2) -> 3 U21_0(2,2) -> 1 U21_1(2,2) -> 3 U22_0(2) -> 1 U22_1(2) -> 3 U31_0(2) -> 1 U31_1(2) -> 3 U41_0(2,2) -> 1 U41_1(2,2) -> 3 U42_0(2) -> 1 U42_1(2) -> 3 U51_0(2,2) -> 1 U51_1(2,2) -> 3 U52_0(2) -> 1 U52_1(2) -> 3 U61_0(2) -> 1 U61_1(2) -> 3 U71_0(2,2) -> 1 U71_1(2,2) -> 3 U72_0(2) -> 1 U72_1(2) -> 3 U81_0(2) -> 1 U81_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 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(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(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)) 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: {U11/1,U21/2,U22/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/1,U71/2,U72/1,U81/1,__/2,isList/1,isNeList/1,isNePal/1 ,isPal/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,U21,U22,U31,U41,U42,U51,U52,U61,U71,U72,U81,__,isList ,isNeList,isNePal,isPal,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))