MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f2(3,C) True (1,1) 1. f0(A,B) -> f2(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] (1,1) 2. f2(A,B) -> f2(4 + 6*B,C) [-3 + A >= 0 && 6*B >= 1 && 2 + 6*B >= 0 && 1 + 6*B >= 0 && A = 1 + 2*B] (?,1) 3. f2(A,B) -> f2(B,C) [-3 + A >= 0 && B = 3 && A = 6] (?,1) 4. f2(A,B) -> f2(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] (?,1) Signature: {(f0,2);(f2,2)} Flow Graph: [0->{2,3,4},1->{2,3,4},2->{2,3,4},3->{2,3,4},4->{2,3,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(0,4),(2,3),(3,3),(3,4)] * Step 2: AddSinks MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f2(3,C) True (1,1) 1. f0(A,B) -> f2(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] (1,1) 2. f2(A,B) -> f2(4 + 6*B,C) [-3 + A >= 0 && 6*B >= 1 && 2 + 6*B >= 0 && 1 + 6*B >= 0 && A = 1 + 2*B] (?,1) 3. f2(A,B) -> f2(B,C) [-3 + A >= 0 && B = 3 && A = 6] (?,1) 4. f2(A,B) -> f2(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] (?,1) Signature: {(f0,2);(f2,2)} Flow Graph: [0->{2},1->{2,3,4},2->{2,4},3->{2},4->{2,3,4}] + Applied Processor: AddSinks + Details: () * Step 3: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f2(3,C) True (1,1) 1. f0(A,B) -> f2(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] (1,1) 2. f2(A,B) -> f2(4 + 6*B,C) [-3 + A >= 0 && 6*B >= 1 && 2 + 6*B >= 0 && 1 + 6*B >= 0 && A = 1 + 2*B] (?,1) 3. f2(A,B) -> f2(B,C) [-3 + A >= 0 && B = 3 && A = 6] (?,1) 4. f2(A,B) -> f2(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] (?,1) 5. f2(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,2);(f2,2)} Flow Graph: [0->{2,3,4,5},1->{2,3,4,5},2->{2,3,4,5},3->{2,3,4,5},4->{2,3,4,5},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(0,4),(2,3),(3,3),(3,4)] * Step 4: Failure MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f2(3,C) True (1,1) 1. f0(A,B) -> f2(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] (1,1) 2. f2(A,B) -> f2(4 + 6*B,C) [-3 + A >= 0 && 6*B >= 1 && 2 + 6*B >= 0 && 1 + 6*B >= 0 && A = 1 + 2*B] (?,1) 3. f2(A,B) -> f2(B,C) [-3 + A >= 0 && B = 3 && A = 6] (?,1) 4. f2(A,B) -> f2(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] (?,1) 5. f2(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,2);(f2,2)} Flow Graph: [0->{2,5},1->{2,3,4,5},2->{2,4,5},3->{2,5},4->{2,3,4,5},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[2,3,4] c: [] MAYBE