*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: h(f(x,y)) -> f(y,f(h(h(x)),a())) Weak DP Rules: Weak TRS Rules: Signature: {h/1} / {a/0,f/2} Obligation: Innermost basic terms: {h}/{a,f} Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} Proof: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 1 a_1() -> 6 a_2() -> 10 f_0(1,1) -> 2 f_0(1,2) -> 2 f_0(2,1) -> 2 f_0(2,2) -> 2 f_1(1,4) -> 3 f_1(1,4) -> 7 f_1(1,4) -> 11 f_1(2,4) -> 3 f_1(2,4) -> 7 f_1(2,4) -> 11 f_1(5,6) -> 4 f_2(4,8) -> 5 f_2(4,8) -> 9 f_2(9,10) -> 8 h_0(1) -> 3 h_0(2) -> 3 h_1(1) -> 7 h_1(2) -> 7 h_1(7) -> 5 h_2(1) -> 11 h_2(2) -> 11 h_2(11) -> 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(y,f(h(h(x)),a())) 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).