* Step 1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> s(0()) f(s(0())) -> s(0()) f(s(s(x))) -> f(f(s(x))) - Signature: {f/1} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f} and constructors {0,s} + Applied Processor: ToInnermost + Details: switch to innermost, as the system is overlay and right linear and does not contain weak rules * Step 2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> s(0()) f(s(0())) -> s(0()) f(s(s(x))) -> f(f(s(x))) - Signature: {f/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {0,s} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 3 0_2() -> 6 f_0(2) -> 1 f_1(4) -> 1 f_1(4) -> 4 f_1(5) -> 4 s_0(2) -> 2 s_1(2) -> 5 s_1(3) -> 1 s_1(3) -> 4 s_2(6) -> 1 s_2(6) -> 4 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(0()) -> s(0()) f(s(0())) -> s(0()) f(s(s(x))) -> f(f(s(x))) - Signature: {f/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {0,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))