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