* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(0(),x2) -> 0() f(S(x),0()) -> 0() f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x)) g(0(),x2) -> 0() g(S(x),0()) -> 0() g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x')))) h(0(),0()) -> 0() h(0(),S(x)) -> h(0(),x) h(S(x),x2) -> h(x,x2) - Signature: {f/2,g/2,h/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,h} 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(),x2) -> 0() f(S(x),0()) -> 0() f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x)) g(0(),x2) -> 0() g(S(x),0()) -> 0() g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x')))) h(0(),0()) -> 0() h(0(),S(x)) -> h(0(),x) h(S(x),x2) -> h(x,x2) - Signature: {f/2,g/2,h/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,h} and constructors {0,S} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(S(x),y){y -> S(y)} = f(S(x),S(y)) ->^+ h(g(x,S(y)),f(S(S(x)),y)) = C[f(S(S(x)),y) = f(S(x),y){x -> S(x)}] WORST_CASE(Omega(n^1),?)