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