* Step 1: ToInnermost 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: runtime complexity wrt. defined symbols {f,p} 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()) -> 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 = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 2 0_0() -> 5 0_1() -> 1 0_1() -> 4 f_0(2) -> 1 f_1(5) -> 4 p_0(2) -> 1 p_1(6) -> 5 s_0(2) -> 1 s_0(2) -> 2 s_0(2) -> 5 s_1(2) -> 6 s_1(3) -> 1 s_1(3) -> 4 s_1(4) -> 3 2 -> 1 2 -> 5 * Step 3: 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))