YES(?,O(n^1)) * Step 1: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B) -> f1(A,B) [A >= 1] (1,1) 1. f1(A,B) -> f1(A,-1*A + B) [-1 + A >= 0 && A >= 1 && B >= 0] (?,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{1},1->{1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 1 + x2 p(f1) = 1 + x2 Following rules are strictly oriented: [-1 + A >= 0 && A >= 1 && B >= 0] ==> f1(A,B) = 1 + B > 1 + -1*A + B = f1(A,-1*A + B) Following rules are weakly oriented: [A >= 1] ==> f0(A,B) = 1 + B >= 1 + B = f1(A,B) * Step 2: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B) -> f1(A,B) [A >= 1] (1,1) 1. f1(A,B) -> f1(A,-1*A + B) [-1 + A >= 0 && A >= 1 && B >= 0] (1 + B,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{1},1->{1}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))