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