YES(?,O(n^1)) * Step 1: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f3(A) -> f1(A) [A >= 0] (1,1) 1. f1(A) -> f1(-1 + A) [A >= 0 && A >= 1] (?,1) Signature: {(f1,1);(f3,1)} Flow Graph: [0->{1},1->{1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = x1 p(f3) = x1 Following rules are strictly oriented: [A >= 0 && A >= 1] ==> f1(A) = A > -1 + A = f1(-1 + A) Following rules are weakly oriented: [A >= 0] ==> f3(A) = A >= A = f1(A) * Step 2: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f3(A) -> f1(A) [A >= 0] (1,1) 1. f1(A) -> f1(-1 + A) [A >= 0 && A >= 1] (A,1) Signature: {(f1,1);(f3,1)} Flow Graph: [0->{1},1->{1}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))