* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: h(f(x,y)) -> f(f(a(),h(h(y))),x) - Signature: {h/1} / {a/0,f/2} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {a,f} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: h(f(x,y)) -> f(f(a(),h(h(y))),x) - Signature: {h/1} / {a/0,f/2} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {a,f} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: h(y){y -> f(x,y)} = h(f(x,y)) ->^+ f(f(a(),h(h(y))),x) = C[h(y) = h(y){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: h(f(x,y)) -> f(f(a(),h(h(y))),x) - Signature: {h/1} / {a/0,f/2} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {a,f} + 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() -> 4 a_2() -> 8 f_0(2,2) -> 2 f_1(3,2) -> 1 f_1(3,2) -> 6 f_1(3,2) -> 10 f_1(4,5) -> 3 f_2(7,3) -> 5 f_2(7,3) -> 9 f_2(8,9) -> 7 h_0(2) -> 1 h_1(2) -> 6 h_1(6) -> 5 h_2(2) -> 10 h_2(10) -> 9 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: h(f(x,y)) -> f(f(a(),h(h(y))),x) - Signature: {h/1} / {a/0,f/2} - Obligation: innermost runtime complexity wrt. defined symbols {h} and constructors {a,f} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))