* 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(x,y),s(y))) f(x,0(),b) -> x f(x,s(y),b) -> div(f(x,minus(s(y),s(0())),b),b) minus(x,x) -> 0() minus(x,0()) -> x minus(0(),x) -> 0() minus(s(x),s(y)) -> minus(x,y) - Signature: {div/2,f/3,minus/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {div,f,minus} 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(x,y),s(y))) f(x,0(),b) -> x f(x,s(y),b) -> div(f(x,minus(s(y),s(0())),b),b) minus(x,x) -> 0() minus(x,0()) -> x minus(0(),x) -> 0() minus(s(x),s(y)) -> minus(x,y) - Signature: {div/2,f/3,minus/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {div,f,minus} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: minus(x,y){x -> s(x),y -> s(y)} = minus(s(x),s(y)) ->^+ minus(x,y) = C[minus(x,y) = minus(x,y){}] WORST_CASE(Omega(n^1),?)