* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(f(a())) -> c(f(g(f(a())))) mark(a()) -> a() mark(c(X)) -> c(X) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(mark(X)) - Signature: {a__f/1,mark/1} / {a/0,c/1,f/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {a,c,f,g} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 2 a_1() -> 1 a_1() -> 6 a_1() -> 7 a_2() -> 11 a__f_0(2) -> 1 a__f_1(7) -> 1 a__f_1(7) -> 7 c_0(2) -> 2 c_1(2) -> 1 c_1(2) -> 7 c_1(3) -> 1 c_2(8) -> 1 c_2(8) -> 7 f_0(2) -> 2 f_1(2) -> 1 f_1(4) -> 3 f_1(6) -> 5 f_2(7) -> 1 f_2(7) -> 7 f_2(9) -> 8 f_2(11) -> 10 g_0(2) -> 2 g_1(5) -> 4 g_1(7) -> 1 g_1(7) -> 7 g_2(10) -> 9 mark_0(2) -> 1 mark_1(2) -> 7 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: a__f(X) -> f(X) a__f(f(a())) -> c(f(g(f(a())))) mark(a()) -> a() mark(c(X)) -> c(X) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(mark(X)) - Signature: {a__f/1,mark/1} / {a/0,c/1,f/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {a,c,f,g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))