* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0())) -> g(f(s(0()))) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0())) -> g(f(s(0()))) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x){x -> s(x)} = f(s(x)) ->^+ f(x) = C[f(x) = f(x){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0())) -> g(f(s(0()))) - Signature: {f/1,g/1} / {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() -> 2 0_1() -> 5 f_0(2) -> 1 f_1(2) -> 1 f_1(4) -> 3 f_2(5) -> 3 g_0(2) -> 1 g_1(3) -> 1 s_0(2) -> 2 s_1(5) -> 4 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0())) -> g(f(s(0()))) - Signature: {f/1,g/1} / {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(Omega(n^1),O(n^1))