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