* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: div(x,y,z) -> if(lt(x,y),x,y,inc(z)) division(x,y) -> div(x,y,0()) if(false(),x,s(y),z) -> div(minus(x,s(y)),s(y),z) if(true(),x,y,z) -> z inc(0()) -> s(0()) inc(s(x)) -> s(inc(x)) lt(x,0()) -> false() lt(0(),s(y)) -> true() lt(s(x),s(y)) -> lt(x,y) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) - Signature: {div/3,division/2,if/4,inc/1,lt/2,minus/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {div,division,if,inc,lt,minus} and constructors {0,false,s ,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: div(x,y,z) -> if(lt(x,y),x,y,inc(z)) division(x,y) -> div(x,y,0()) if(false(),x,s(y),z) -> div(minus(x,s(y)),s(y),z) if(true(),x,y,z) -> z inc(0()) -> s(0()) inc(s(x)) -> s(inc(x)) lt(x,0()) -> false() lt(0(),s(y)) -> true() lt(s(x),s(y)) -> lt(x,y) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) - Signature: {div/3,division/2,if/4,inc/1,lt/2,minus/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {div,division,if,inc,lt,minus} and constructors {0,false,s ,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: inc(x){x -> s(x)} = inc(s(x)) ->^+ s(inc(x)) = C[inc(x) = inc(x){}] WORST_CASE(Omega(n^1),?)