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