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