MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,1 + B) [A >= B && A >= 1 && B >= 1] (1,1) 1. f2(A,B,C) -> f3(A,B,C) [B >= 1 + C] (?,1) 2. f2(A,B,C) -> f3(A,B,C) [C >= 1 + B] (?,1) 3. f3(A,B,C) -> f2(A,B,0) [1 + A >= 0 && C >= 1 && C >= 1 + A] (?,1) 4. f3(A,B,C) -> f2(A,B,1 + C) [A >= C && 1 + C >= 0] (?,1) Signature: {(f1,3);(f2,3);(f3,3)} Flow Graph: [0->{1,2},1->{3,4},2->{3,4},3->{1,2},4->{1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1)] * Step 2: AddSinks MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,1 + B) [A >= B && A >= 1 && B >= 1] (1,1) 1. f2(A,B,C) -> f3(A,B,C) [B >= 1 + C] (?,1) 2. f2(A,B,C) -> f3(A,B,C) [C >= 1 + B] (?,1) 3. f3(A,B,C) -> f2(A,B,0) [1 + A >= 0 && C >= 1 && C >= 1 + A] (?,1) 4. f3(A,B,C) -> f2(A,B,1 + C) [A >= C && 1 + C >= 0] (?,1) Signature: {(f1,3);(f2,3);(f3,3)} Flow Graph: [0->{2},1->{3,4},2->{3,4},3->{1,2},4->{1,2}] + Applied Processor: AddSinks + Details: () * Step 3: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,1 + B) [A >= B && A >= 1 && B >= 1] (1,1) 1. f2(A,B,C) -> f3(A,B,C) [B >= 1 + C] (?,1) 2. f2(A,B,C) -> f3(A,B,C) [C >= 1 + B] (?,1) 3. f3(A,B,C) -> f2(A,B,0) [1 + A >= 0 && C >= 1 && C >= 1 + A] (?,1) 4. f3(A,B,C) -> f2(A,B,1 + C) [A >= C && 1 + C >= 0] (?,1) 5. f2(A,B,C) -> exitus616(A,B,C) True (?,1) 6. f3(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f1,3);(f2,3);(f3,3)} Flow Graph: [0->{1,2,5},1->{3,4,6},2->{3,4,6},3->{1,2,5},4->{1,2,5},5->{},6->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1)] * Step 4: Failure MAYBE + Considered Problem: Rules: 0. f1(A,B,C) -> f2(A,B,1 + B) [A >= B && A >= 1 && B >= 1] (1,1) 1. f2(A,B,C) -> f3(A,B,C) [B >= 1 + C] (?,1) 2. f2(A,B,C) -> f3(A,B,C) [C >= 1 + B] (?,1) 3. f3(A,B,C) -> f2(A,B,0) [1 + A >= 0 && C >= 1 && C >= 1 + A] (?,1) 4. f3(A,B,C) -> f2(A,B,1 + C) [A >= C && 1 + C >= 0] (?,1) 5. f2(A,B,C) -> exitus616(A,B,C) True (?,1) 6. f3(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f1,3);(f2,3);(f3,3)} Flow Graph: [0->{2,5},1->{3,4,6},2->{3,4,6},3->{1,2,5},4->{1,2,5},5->{},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[2,3,1,4] c: [] MAYBE