YES(?,O(n^1)) * Step 1: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A) -> f0(-1 + A) [A >= 0] (?,1) 1. f1(A) -> f0(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) = 1 + x1 p(f1) = 1 + x1 Following rules are strictly oriented: [A >= 0] ==> f0(A) = 1 + A > A = f0(-1 + A) Following rules are weakly oriented: True ==> f1(A) = 1 + A >= 1 + A = f0(A) * Step 2: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A) -> f0(-1 + A) [A >= 0] (1 + A,1) 1. f1(A) -> f0(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))