*** 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(c(f(g(f(a()))))) active(g(X)) -> g(active(X)) c(ok(X)) -> ok(c(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) 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,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} Obligation: Innermost basic terms: {active,c,f,g,proper,top}/{a,mark,ok} 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() -> 13 active_0(1) -> 2 active_0(6) -> 2 active_0(7) -> 2 active_1(1) -> 14 active_1(6) -> 14 active_1(7) -> 14 active_2(13) -> 15 c_0(1) -> 3 c_0(6) -> 3 c_0(7) -> 3 c_1(1) -> 10 c_1(6) -> 10 c_1(7) -> 10 f_0(1) -> 4 f_0(6) -> 4 f_0(7) -> 4 f_1(1) -> 11 f_1(6) -> 11 f_1(7) -> 11 g_0(1) -> 5 g_0(6) -> 5 g_0(7) -> 5 g_1(1) -> 12 g_1(6) -> 12 g_1(7) -> 12 mark_0(1) -> 6 mark_0(6) -> 6 mark_0(7) -> 6 mark_1(11) -> 4 mark_1(11) -> 11 mark_1(12) -> 5 mark_1(12) -> 12 ok_0(1) -> 7 ok_0(6) -> 7 ok_0(7) -> 7 ok_1(10) -> 3 ok_1(10) -> 10 ok_1(11) -> 4 ok_1(11) -> 11 ok_1(12) -> 5 ok_1(12) -> 12 ok_1(13) -> 8 ok_1(13) -> 14 proper_0(1) -> 8 proper_0(6) -> 8 proper_0(7) -> 8 proper_1(1) -> 14 proper_1(6) -> 14 proper_1(7) -> 14 top_0(1) -> 9 top_0(6) -> 9 top_0(7) -> 9 top_1(14) -> 9 top_2(15) -> 9 *** 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(c(f(g(f(a()))))) active(g(X)) -> g(active(X)) c(ok(X)) -> ok(c(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) 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,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} Obligation: Innermost basic terms: {active,c,f,g,proper,top}/{a,mark,ok} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).