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