*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: f(0()) -> s(0()) f(s(0())) -> s(0()) f(s(s(x))) -> f(f(s(x))) Weak DP Rules: Weak TRS Rules: Signature: {f/1} / {0/0,s/1} Obligation: Innermost basic terms: {f}/{0,s} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 3 0_2() -> 6 f_0(2) -> 1 f_1(4) -> 1 f_1(4) -> 4 f_1(5) -> 4 s_0(2) -> 2 s_1(2) -> 5 s_1(3) -> 1 s_1(3) -> 4 s_2(6) -> 1 s_2(6) -> 4 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: f(0()) -> s(0()) f(s(0())) -> s(0()) f(s(s(x))) -> f(f(s(x))) Signature: {f/1} / {0/0,s/1} Obligation: Innermost basic terms: {f}/{0,s} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).