YES(?,O(n^1)) * Step 1: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C) -> eval(A,B,C) True (1,1) 1. eval(A,B,C) -> eval(C,-1 + B,1 + A) [100 >= A && B >= C] (?,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{1},1->{1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = 101 + -1*x1 + x2 + -1*x3 p(start) = 101 + -1*x1 + x2 + -1*x3 Following rules are strictly oriented: [100 >= A && B >= C] ==> eval(A,B,C) = 101 + -1*A + B + -1*C > 99 + -1*A + B + -1*C = eval(C,-1 + B,1 + A) Following rules are weakly oriented: True ==> start(A,B,C) = 101 + -1*A + B + -1*C >= 101 + -1*A + B + -1*C = eval(A,B,C) * Step 2: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C) -> eval(A,B,C) True (1,1) 1. eval(A,B,C) -> eval(C,-1 + B,1 + A) [100 >= A && B >= C] (101 + A + B + C,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{1},1->{1}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))