* Step 1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: h(f(x,y)) -> f(y,f(h(h(x)),a())) - Signature: {h/1} / {a/0,f/2} - Obligation: runtime complexity wrt. defined symbols {h} and constructors {a,f} + 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: h(f(x,y)) -> f(y,f(h(h(x)),a())) - Signature: {h/1} / {a/0,f/2} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {a,f} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 2 a_1() -> 5 a_2() -> 9 f_0(2,2) -> 2 f_1(2,3) -> 1 f_1(2,3) -> 6 f_1(2,3) -> 10 f_1(4,5) -> 3 f_2(3,7) -> 4 f_2(3,7) -> 8 f_2(8,9) -> 7 h_0(2) -> 1 h_1(2) -> 6 h_1(6) -> 4 h_2(2) -> 10 h_2(10) -> 8 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: h(f(x,y)) -> f(y,f(h(h(x)),a())) - Signature: {h/1} / {a/0,f/2} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {a,f} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))