*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: a__f(X) -> f(X) a__f(X) -> g(h(f(X))) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> h(mark(X)) Weak DP Rules: Weak TRS Rules: Signature: {a__f/1,mark/1} / {f/1,g/1,h/1} Obligation: Innermost basic terms: {a__f,mark}/{f,g,h} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a__f_0(2) -> 1 a__f_1(4) -> 1 a__f_1(4) -> 4 f_0(2) -> 2 f_1(2) -> 1 f_2(4) -> 1 f_2(4) -> 4 g_0(2) -> 2 g_1(2) -> 1 g_1(2) -> 4 g_1(3) -> 1 g_2(5) -> 1 g_2(5) -> 4 h_0(2) -> 2 h_1(1) -> 3 h_1(4) -> 1 h_1(4) -> 4 h_2(1) -> 5 mark_0(2) -> 1 mark_1(2) -> 4 *** 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(X) -> g(h(f(X))) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> h(mark(X)) Signature: {a__f/1,mark/1} / {f/1,g/1,h/1} Obligation: Innermost basic terms: {a__f,mark}/{f,g,h} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).