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