WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x1,0()) -> g(x1,0()) f(y,S(x)) -> f(S(y),x) g(0(),x2) -> x2 g(S(x),y) -> g(x,S(y)) - Signature: {f/2,g/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,S} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 2 0_1() -> 1 0_1() -> 3 S_0(2) -> 1 S_0(2) -> 2 S_1(2) -> 1 S_1(2) -> 4 S_1(3) -> 1 S_1(3) -> 3 S_1(4) -> 1 S_1(4) -> 4 S_1(5) -> 1 S_1(5) -> 3 S_2(3) -> 1 S_2(3) -> 5 S_2(5) -> 1 S_2(5) -> 5 f_0(2,2) -> 1 f_1(4,2) -> 1 g_0(2,2) -> 1 g_1(2,3) -> 1 g_1(2,4) -> 1 g_1(4,3) -> 1 g_2(2,5) -> 1 g_2(4,5) -> 1 2 -> 1 3 -> 1 4 -> 1 5 -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(x1,0()) -> g(x1,0()) f(y,S(x)) -> f(S(y),x) g(0(),x2) -> x2 g(S(x),y) -> g(x,S(y)) - Signature: {f/2,g/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,S} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))