* Step 1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> s(0()) f(s(x)) -> s(s(g(x))) g(0()) -> 0() g(s(x)) -> f(x) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f,g} 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(x)) -> s(s(g(x))) g(0()) -> 0() g(s(x)) -> f(x) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 1 0_1() -> 3 0_1() -> 4 f_0(2) -> 1 f_1(2) -> 1 f_1(2) -> 4 g_0(2) -> 1 g_1(2) -> 4 s_0(2) -> 2 s_1(3) -> 1 s_1(4) -> 3 s_1(4) -> 4 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(0()) -> s(0()) f(s(x)) -> s(s(g(x))) g(0()) -> 0() g(s(x)) -> f(x) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))