MAYBE * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) 1. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 2. f2(A,B,C) -> f300(A,B,D) [A = B] (?,1) 3. f1(A,B,C) -> f2(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,1,2},1->{0,1,2},2->{},3->{0,1,2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) 1. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 2. f2(A,B,C) -> f300(A,B,D) [A = B] (1,1) 3. f1(A,B,C) -> f2(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,1,2},1->{0,1,2},2->{},3->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(1,0),(1,2)] * Step 3: AddSinks MAYBE + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) 1. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 2. f2(A,B,C) -> f300(A,B,D) [A = B] (1,1) 3. f1(A,B,C) -> f2(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,2},1->{1},2->{},3->{0,1,2}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths MAYBE + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) 1. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 2. f2(A,B,C) -> f300(A,B,D) [A = B] (?,1) 3. f1(A,B,C) -> f2(A,B,C) True (1,1) 4. f2(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,1,2,4},1->{0,1,2,4},2->{},3->{0,1,2,4},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(1,0),(1,2)] * Step 5: Failure MAYBE + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,B,C) [B >= 1 + A] (?,1) 1. f2(A,B,C) -> f2(1 + A,B,C) [A >= 1 + B && A >= B] (?,1) 2. f2(A,B,C) -> f300(A,B,D) [A = B] (?,1) 3. f1(A,B,C) -> f2(A,B,C) True (1,1) 4. f2(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,2,4},1->{1,4},2->{},3->{0,1,2,4},4->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4] | +- p:[1] c: [] | `- p:[0] c: [0] MAYBE