YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. f5(A,B) -> f5(-1 + A,B) [A >= 0 && A >= 1] (?,1) 1. f5(A,B) -> f1(A,C) [A >= 0 && 0 >= A] (?,1) 2. f300(A,B) -> f5(-1 + A,B) [A >= 1] (1,1) 3. f300(A,B) -> f1(A,C) [0 >= A] (1,1) Signature: {(f1,2);(f300,2);(f5,2)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. f5(A,B) -> f5(-1 + A,B) [A >= 0 && A >= 1] (?,1) 1. f5(A,B) -> f1(A,C) [A >= 0 && 0 >= A] (1,1) 2. f300(A,B) -> f5(-1 + A,B) [A >= 1] (1,1) 3. f300(A,B) -> f1(A,C) [0 >= A] (1,1) Signature: {(f1,2);(f300,2);(f5,2)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3] | `- p:[0] c: [0] YES