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