NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. f0(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f1(A,-1 + B,D) [-1*A >= 0 && A >= 0 && B >= 1] (?,1) 2. f1(A,B,C) -> f4(A,B,D) [-1*A >= 0 && A >= 0 && 0 >= B] (?,1) 3. f4(A,B,C) -> f4(1,B,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] (?,1) Signature: {(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree NO + Considered Problem: Rules: 0. f0(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f1(A,-1 + B,D) [-1*A >= 0 && A >= 0 && B >= 1] (?,1) 2. f1(A,B,C) -> f4(A,B,D) [-1*A >= 0 && A >= 0 && 0 >= B] (1,1) 3. f4(A,B,C) -> f4(1,B,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] (?,1) Signature: {(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3] | +- p:[1] c: [1] | `- p:[3] c: [] NO