* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(a(),g(y)) -> g(g(y)) f(g(x),a()) -> f(x,g(a())) f(g(x),g(y)) -> h(g(y),x,g(y)) h(a(),y,z) -> z h(g(x),y,z) -> f(y,h(x,y,z)) - Signature: {f/2,h/3} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,h} and constructors {a,g} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(a(),g(y)) -> g(g(y)) f(g(x),a()) -> f(x,g(a())) f(g(x),g(y)) -> h(g(y),x,g(y)) h(a(),y,z) -> z h(g(x),y,z) -> f(y,h(x,y,z)) - Signature: {f/2,h/3} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,h} and constructors {a,g} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: h(x,y,z){x -> g(x)} = h(g(x),y,z) ->^+ f(y,h(x,y,z)) = C[h(x,y,z) = h(x,y,z){}] WORST_CASE(Omega(n^1),?)