YES(?,O(n^1)) * Step 1: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A) -> f1(-1 + A) [A >= 202] (?,1) 1. f0(A) -> f1(A) True (1,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{0},1->{0}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = -201 + x1 p(f1) = -201 + x1 Following rules are strictly oriented: [A >= 202] ==> f1(A) = -201 + A > -202 + A = f1(-1 + A) Following rules are weakly oriented: True ==> f0(A) = -201 + A >= -201 + A = f1(A) * Step 2: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A) -> f1(-1 + A) [A >= 202] (201 + A,1) 1. f0(A) -> f1(A) True (1,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{0},1->{0}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))