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