*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: active(f(X)) -> f(active(X)) active(f(f(a()))) -> mark(f(g(f(a())))) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Weak DP Rules: Weak TRS Rules: Signature: {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} Obligation: Full basic terms: {active,f,g,proper,top}/{a,mark,ok} 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() -> 3 active_0(2) -> 1 active_1(2) -> 4 active_2(2) -> 6 active_2(3) -> 5 f_0(2) -> 1 f_1(2) -> 3 f_2(6) -> 5 g_0(2) -> 1 g_1(2) -> 3 mark_0(2) -> 2 mark_1(3) -> 1 mark_1(3) -> 3 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 3 ok_1(3) -> 4 proper_0(2) -> 1 proper_1(2) -> 4 top_0(2) -> 1 top_1(4) -> 1 top_2(5) -> 1 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: active(f(X)) -> f(active(X)) active(f(f(a()))) -> mark(f(g(f(a())))) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Signature: {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} Obligation: Full basic terms: {active,f,g,proper,top}/{a,mark,ok} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).