* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: f(c(s(x),y)) -> f(c(x,s(y))) g(c(x,s(y))) -> g(c(s(x),y)) g(s(f(x))) -> g(f(x)) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(c(s(x),y)) -> f(c(x,s(y))) g(c(x,s(y))) -> g(c(s(x),y)) g(s(f(x))) -> g(f(x)) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(c(x,y)){x -> s(x)} = f(c(s(x),y)) ->^+ f(c(x,s(y))) = C[f(c(x,s(y))) = f(c(x,y)){y -> s(y)}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(c(s(x),y)) -> f(c(x,s(y))) g(c(x,s(y))) -> g(c(s(x),y)) g(s(f(x))) -> g(f(x)) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. c_0(2,2) -> 2 c_1(2,4) -> 3 c_1(4,2) -> 5 f_0(2) -> 1 f_1(3) -> 1 g_0(2) -> 1 g_1(5) -> 1 s_0(2) -> 2 s_1(2) -> 4 s_1(4) -> 4 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(c(s(x),y)) -> f(c(x,s(y))) g(c(x,s(y))) -> g(c(s(x),y)) g(s(f(x))) -> g(f(x)) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))