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