YES(?,O(n^1)) * Step 1: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,-1 + B) [A >= 1 && B >= 1] (?,1) 1. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0},1->{0}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = x2 p(start) = x2 Following rules are strictly oriented: [A >= 1 && B >= 1] ==> eval(A,B) = B > -1 + B = eval(-1 + A,-1 + B) Following rules are weakly oriented: True ==> start(A,B) = B >= B = eval(A,B) * Step 2: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,-1 + B) [A >= 1 && B >= 1] (B,1) 1. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0},1->{0}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))