YES(?,O(n^1)) * Step 1: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1) 1. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(start,3);(zip3,3)} Flow Graph: [0->{0},1->{0}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(start) = x1 p(zip3) = x1 Following rules are strictly oriented: [A >= 1 && B >= 1 && C >= 1] ==> zip3(A,B,C) = A > -1 + A = zip3(-1 + A,-1 + B,-1 + C) Following rules are weakly oriented: True ==> start(A,B,C) = A >= A = zip3(A,B,C) * Step 2: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (A,1) 1. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(start,3);(zip3,3)} Flow Graph: [0->{0},1->{0}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))