* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(c(s(x),y)) -> f(c(x,s(y))) f(c(s(x),s(y))) -> g(c(x,y)) g(c(x,s(y))) -> g(c(s(x),y)) g(c(s(x),s(y))) -> f(c(x,y)) - 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 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(c(s(x),y)) -> f(c(x,s(y))) f(c(s(x),s(y))) -> g(c(x,y)) g(c(x,s(y))) -> g(c(s(x),y)) g(c(s(x),s(y))) -> f(c(x,y)) - 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)}] WORST_CASE(Omega(n^1),?)