* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(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: {__/2,and/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 {__,and,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. ___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 and_0(2,2) -> 1 and_1(2,2) -> 3 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: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(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: {__/2,and/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 {__,and,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))