*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: a__f(X) -> f(X) a__f(f(a())) -> a__f(g(f(a()))) mark(a()) -> a() mark(f(X)) -> a__f(X) mark(g(X)) -> g(mark(X)) Weak DP Rules: Weak TRS Rules: Signature: {a__f/1,mark/1} / {a/0,f/1,g/1} Obligation: Innermost basic terms: {a__f,mark}/{a,f,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() -> 1 a_1() -> 5 a_1() -> 6 a__f_0(2) -> 1 a__f_1(2) -> 1 a__f_1(2) -> 6 a__f_1(3) -> 1 a__f_1(3) -> 6 f_0(2) -> 2 f_1(2) -> 1 f_1(5) -> 4 f_2(2) -> 1 f_2(2) -> 6 f_2(3) -> 1 f_2(3) -> 6 g_0(2) -> 2 g_1(4) -> 3 g_1(6) -> 1 g_1(6) -> 6 mark_0(2) -> 1 mark_1(2) -> 6 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: a__f(X) -> f(X) a__f(f(a())) -> a__f(g(f(a()))) mark(a()) -> a() mark(f(X)) -> a__f(X) mark(g(X)) -> g(mark(X)) Signature: {a__f/1,mark/1} / {a/0,f/1,g/1} Obligation: Innermost basic terms: {a__f,mark}/{a,f,g} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).