*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: f(x,a()) -> x f(x,g(y)) -> f(g(x),y) Weak DP Rules: Weak TRS Rules: Signature: {f/2} / {a/0,g/1} Obligation: Innermost basic terms: {f}/{a,g} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. a_0() -> 1 a_0() -> 2 f_0(2,2) -> 1 f_1(3,2) -> 1 g_0(2) -> 1 g_0(2) -> 2 g_1(2) -> 1 g_1(2) -> 3 g_1(3) -> 1 g_1(3) -> 3 2 -> 1 3 -> 1 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: f(x,a()) -> x f(x,g(y)) -> f(g(x),y) Signature: {f/2} / {a/0,g/1} Obligation: Innermost basic terms: {f}/{a,g} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).