*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: h(f(x,y)) -> f(f(a(),h(h(y))),x) Weak DP Rules: Weak TRS Rules: Signature: {h/1} / {a/0,f/2} Obligation: Innermost basic terms: {h}/{a,f} 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 a_2() -> 8 f_0(2,2) -> 2 f_1(3,2) -> 1 f_1(3,2) -> 6 f_1(3,2) -> 10 f_1(4,5) -> 3 f_2(7,3) -> 5 f_2(7,3) -> 9 f_2(8,9) -> 7 h_0(2) -> 1 h_1(2) -> 6 h_1(6) -> 5 h_2(2) -> 10 h_2(10) -> 9 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: h(f(x,y)) -> f(f(a(),h(h(y))),x) Signature: {h/1} / {a/0,f/2} Obligation: Innermost basic terms: {h}/{a,f} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).