NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. f6(A,B,C,D) -> f16(A,B,C,D) [1 + A >= B] (?,1) 1. f6(A,B,C,D) -> f6(E,B,C,E) [B >= 2 + A && C >= E^2] (?,1) 2. f6(A,B,C,D) -> f6(A,E,C,E) [B >= 2 + A && E^2 >= 1 + C] (?,1) 3. f0(A,B,C,D) -> f6(1,C,C,D) True (1,1) Signature: {(f0,4);(f16,4);(f6,4)} Flow Graph: [0->{},1->{0,1,2},2->{0,1,2},3->{0,1,2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree NO + Considered Problem: Rules: 0. f6(A,B,C,D) -> f16(A,B,C,D) [1 + A >= B] (1,1) 1. f6(A,B,C,D) -> f6(E,B,C,E) [B >= 2 + A && C >= E^2] (?,1) 2. f6(A,B,C,D) -> f6(A,E,C,E) [B >= 2 + A && E^2 >= 1 + C] (?,1) 3. f0(A,B,C,D) -> f6(1,C,C,D) True (1,1) Signature: {(f0,4);(f16,4);(f6,4)} Flow Graph: [0->{},1->{0,1,2},2->{0,1,2},3->{0,1,2}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3] | `- p:[1,2] c: [] NO