* Step 1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(b(x)) -> b(b(a(x))) - Signature: {a/1} / {b/1} - Obligation: runtime complexity wrt. defined symbols {a} and constructors {b} + 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: a(b(x)) -> b(b(a(x))) - Signature: {a/1} / {b/1} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {b} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. a_0(2) -> 1 a_1(2) -> 4 b_0(2) -> 2 b_1(3) -> 1 b_1(3) -> 4 b_1(4) -> 3 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: a(b(x)) -> b(b(a(x))) - Signature: {a/1} / {b/1} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {b} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))