* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(0()) -> s(0()) f(s(x)) -> minus(s(x),g(f(x))) g(0()) -> 0() g(s(x)) -> minus(s(x),f(g(x))) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) - Signature: {f/1,g/1,minus/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,minus} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(0()) -> s(0()) f(s(x)) -> minus(s(x),g(f(x))) g(0()) -> 0() g(s(x)) -> minus(s(x),f(g(x))) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) - Signature: {f/1,g/1,minus/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,minus} 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)) ->^+ minus(s(x),g(f(x))) = C[f(x) = f(x){}] WORST_CASE(Omega(n^1),?)