* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: div(x,y) -> if1(ge(x,y),x,y) ge(x,0()) -> true() ge(0(),s(x)) -> false() ge(s(x),s(y)) -> ge(x,y) gt(0(),y) -> false() gt(s(x),0()) -> true() gt(s(x),s(y)) -> gt(x,y) if(false(),x,y) -> 0() if(true(),x,y) -> s(minus(p(x),y)) if1(false(),x,y) -> 0() if1(true(),x,y) -> if2(gt(y,0()),x,y) if2(false(),x,y) -> 0() if2(true(),x,y) -> s(div(minus(x,y),y)) minus(x,y) -> if(gt(x,y),x,y) p(0()) -> 0() p(s(x)) -> x - Signature: {div/2,ge/2,gt/2,if/3,if1/3,if2/3,minus/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {div,ge,gt,if,if1,if2,minus,p} 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) -> if1(ge(x,y),x,y) ge(x,0()) -> true() ge(0(),s(x)) -> false() ge(s(x),s(y)) -> ge(x,y) gt(0(),y) -> false() gt(s(x),0()) -> true() gt(s(x),s(y)) -> gt(x,y) if(false(),x,y) -> 0() if(true(),x,y) -> s(minus(p(x),y)) if1(false(),x,y) -> 0() if1(true(),x,y) -> if2(gt(y,0()),x,y) if2(false(),x,y) -> 0() if2(true(),x,y) -> s(div(minus(x,y),y)) minus(x,y) -> if(gt(x,y),x,y) p(0()) -> 0() p(s(x)) -> x - Signature: {div/2,ge/2,gt/2,if/3,if1/3,if2/3,minus/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {div,ge,gt,if,if1,if2,minus,p} and constructors {0,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),?)