NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I) -> f1(A,B,C,D,E,F,G,K,L) True (1,1) 1. f1(A,B,C,D,E,F,G,H,I) -> f300(A,B,K,L,E,F,J,H,I) [A >= B] (?,1) 2. f1(A,B,C,D,E,F,G,H,I) -> f1(A,B,K,L,0,F,G,H,I) [B >= 1 + A] (?,1) 3. f1(A,B,C,D,E,F,G,H,I) -> f1(A,B,K,L,J,M,G,H,I) [0 >= 1 + J && B >= 1 + A] (?,1) 4. f1(A,B,C,D,E,F,G,H,I) -> f1(A,B,K,L,J,M,G,H,I) [J >= 1 && B >= 1 + A] (?,1) Signature: {(f1,9);(f2,9);(f300,9)} Flow Graph: [0->{1,2,3,4},1->{},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths NO + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I) -> f1(A,B,C,D,E,F,G,K,L) True (1,1) 1. f1(A,B,C,D,E,F,G,H,I) -> f300(A,B,K,L,E,F,J,H,I) [A >= B] (1,1) 2. f1(A,B,C,D,E,F,G,H,I) -> f1(A,B,K,L,0,F,G,H,I) [B >= 1 + A] (?,1) 3. f1(A,B,C,D,E,F,G,H,I) -> f1(A,B,K,L,J,M,G,H,I) [0 >= 1 + J && B >= 1 + A] (?,1) 4. f1(A,B,C,D,E,F,G,H,I) -> f1(A,B,K,L,J,M,G,H,I) [J >= 1 && B >= 1 + A] (?,1) Signature: {(f1,9);(f2,9);(f300,9)} Flow Graph: [0->{1,2,3,4},1->{},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,1),(3,1),(4,1)] * Step 3: Looptree NO + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I) -> f1(A,B,C,D,E,F,G,K,L) True (1,1) 1. f1(A,B,C,D,E,F,G,H,I) -> f300(A,B,K,L,E,F,J,H,I) [A >= B] (1,1) 2. f1(A,B,C,D,E,F,G,H,I) -> f1(A,B,K,L,0,F,G,H,I) [B >= 1 + A] (?,1) 3. f1(A,B,C,D,E,F,G,H,I) -> f1(A,B,K,L,J,M,G,H,I) [0 >= 1 + J && B >= 1 + A] (?,1) 4. f1(A,B,C,D,E,F,G,H,I) -> f1(A,B,K,L,J,M,G,H,I) [J >= 1 && B >= 1 + A] (?,1) Signature: {(f1,9);(f2,9);(f300,9)} Flow Graph: [0->{1,2,3,4},1->{},2->{2,3,4},3->{2,3,4},4->{2,3,4}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[2,3,4] c: [] NO