*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: f(a()) -> g(h(a())) h(g(x)) -> g(h(f(x))) k(x,h(x),a()) -> h(x) k(f(x),y,x) -> f(x) Weak DP Rules: Weak TRS Rules: Signature: {f/1,h/1,k/3} / {a/0,g/1} Obligation: Innermost basic terms: {f,h,k}/{a,g} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 2 a_1() -> 4 f_0(2) -> 1 f_1(2) -> 4 f_2(3) -> 6 g_0(2) -> 2 g_1(3) -> 1 g_1(3) -> 4 g_2(5) -> 3 h_0(2) -> 1 h_1(4) -> 3 h_2(6) -> 5 k_0(2,2,2) -> 1 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: f(a()) -> g(h(a())) h(g(x)) -> g(h(f(x))) k(x,h(x),a()) -> h(x) k(f(x),y,x) -> f(x) Signature: {f/1,h/1,k/3} / {a/0,g/1} Obligation: Innermost basic terms: {f,h,k}/{a,g} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).