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