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