* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: help(x,y,c) -> if(lt(c,y),x,y,c) if(false(),x,y,c) -> 0() if(true(),x,y,c) -> plus(x,help(x,y,s(c))) lt(0(),s(x)) -> true() lt(s(x),0()) -> false() lt(s(x),s(y)) -> lt(x,y) plus(x,0()) -> x plus(x,s(y)) -> s(plus(x,y)) plus(0(),x) -> x plus(s(x),y) -> s(plus(x,y)) times(x,y) -> help(x,y,0()) - Signature: {help/3,if/4,lt/2,plus/2,times/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {help,if,lt,plus,times} 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,y,c) -> if(lt(c,y),x,y,c) if(false(),x,y,c) -> 0() if(true(),x,y,c) -> plus(x,help(x,y,s(c))) lt(0(),s(x)) -> true() lt(s(x),0()) -> false() lt(s(x),s(y)) -> lt(x,y) plus(x,0()) -> x plus(x,s(y)) -> s(plus(x,y)) plus(0(),x) -> x plus(s(x),y) -> s(plus(x,y)) times(x,y) -> help(x,y,0()) - Signature: {help/3,if/4,lt/2,plus/2,times/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {help,if,lt,plus,times} 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),?)