* Step 1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,x) -> a() f(g(x),y) -> f(x,y) - Signature: {f/2} / {a/0,g/1} - Obligation: runtime complexity wrt. defined symbols {f} and constructors {a,g} + 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(x,x) -> a() f(g(x),y) -> f(x,y) - Signature: {f/2} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,g} + 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() -> 1 a_2() -> 1 f_0(2,2) -> 1 f_1(2,2) -> 1 g_0(2) -> 2 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(x,x) -> a() f(g(x),y) -> f(x,y) - Signature: {f/2} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))