* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U12/1,__/2,isNePal/1,proper/1,top/1} / {active/1,mark/1,nil/0,ok/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,__,isNePal,proper,top} and constructors {active ,mark,nil,ok,tt} + 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 U12_0(2) -> 1 U12_1(2) -> 3 ___0(2,2) -> 1 ___1(2,2) -> 3 active_0(2) -> 2 active_1(2) -> 4 active_2(3) -> 5 isNePal_0(2) -> 1 isNePal_1(2) -> 3 mark_0(2) -> 2 mark_1(3) -> 1 mark_1(3) -> 3 nil_0() -> 2 nil_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 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U12/1,__/2,isNePal/1,proper/1,top/1} / {active/1,mark/1,nil/0,ok/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,__,isNePal,proper,top} and constructors {active ,mark,nil,ok,tt} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))