WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> 0() f(s(x)) -> s(s(f(p(s(x))))) p(s(x)) -> x - Signature: {f/1,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,s} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 3 0_0() -> 7 0_1() -> 2 0_1() -> 6 f_0(1) -> 2 f_0(4) -> 2 f_1(7) -> 6 p_0(1) -> 3 p_0(4) -> 3 p_1(8) -> 7 s_0(1) -> 3 s_0(1) -> 4 s_0(1) -> 7 s_0(4) -> 3 s_0(4) -> 4 s_0(4) -> 7 s_1(1) -> 8 s_1(4) -> 8 s_1(5) -> 2 s_1(5) -> 6 s_1(6) -> 5 1 -> 3 1 -> 7 4 -> 3 4 -> 7 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(0()) -> 0() f(s(x)) -> s(s(f(p(s(x))))) p(s(x)) -> x - Signature: {f/1,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))