MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f4(C,0) True (1,1) 1. f4(A,B) -> f4(A,1 + B) [B >= 0 && 0 >= 1 + C] (?,1) 2. f4(A,B) -> f4(A,1 + B) [B >= 0] (?,1) 3. f4(A,B) -> f14(A,B) [B >= 0 && A >= 0 && B >= 1 + A] (?,1) 4. f4(A,B) -> f14(A,B) [B >= 0 && 0 >= 1 + A] (?,1) 5. f4(A,B) -> f14(A,B) [B >= 0 && A >= 0 && A >= B] (?,1) 6. f4(A,B) -> f14(A,B) [B >= 0 && 0 >= 1 + C && A >= 0 && B >= 1 + A] (?,1) Signature: {(f0,2);(f14,2);(f4,2)} Flow Graph: [0->{1,2,3,4,5,6},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{},4->{},5->{},6->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(0,6)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f4(C,0) True (1,1) 1. f4(A,B) -> f4(A,1 + B) [B >= 0 && 0 >= 1 + C] (?,1) 2. f4(A,B) -> f4(A,1 + B) [B >= 0] (?,1) 3. f4(A,B) -> f14(A,B) [B >= 0 && A >= 0 && B >= 1 + A] (?,1) 4. f4(A,B) -> f14(A,B) [B >= 0 && 0 >= 1 + A] (?,1) 5. f4(A,B) -> f14(A,B) [B >= 0 && A >= 0 && A >= B] (?,1) 6. f4(A,B) -> f14(A,B) [B >= 0 && 0 >= 1 + C && A >= 0 && B >= 1 + A] (?,1) Signature: {(f0,2);(f14,2);(f4,2)} Flow Graph: [0->{1,2,4,5},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{},4->{},5->{},6->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks MAYBE + Considered Problem: Rules: f0(A,B) -> f4(C,0) True f4(A,B) -> f4(A,1 + B) [B >= 0 && 0 >= 1 + C] f4(A,B) -> f4(A,1 + B) [B >= 0] f4(A,B) -> f14(A,B) [B >= 0 && A >= 0 && B >= 1 + A] f4(A,B) -> f14(A,B) [B >= 0 && 0 >= 1 + A] f4(A,B) -> f14(A,B) [B >= 0 && A >= 0 && A >= B] f4(A,B) -> f14(A,B) [B >= 0 && 0 >= 1 + C && A >= 0 && B >= 1 + A] Signature: {(f0,2);(f14,2);(f4,2)} Rule Graph: [0->{1,2,4,5},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{},4->{},5->{},6->{}] + Applied Processor: AddSinks + Details: () * Step 4: Failure MAYBE + Considered Problem: Rules: f0(A,B) -> f4(C,0) True f4(A,B) -> f4(A,1 + B) [B >= 0 && 0 >= 1 + C] f4(A,B) -> f4(A,1 + B) [B >= 0] f4(A,B) -> f14(A,B) [B >= 0 && A >= 0 && B >= 1 + A] f4(A,B) -> f14(A,B) [B >= 0 && 0 >= 1 + A] f4(A,B) -> f14(A,B) [B >= 0 && A >= 0 && A >= B] f4(A,B) -> f14(A,B) [B >= 0 && 0 >= 1 + C && A >= 0 && B >= 1 + A] f14(A,B) -> exitus616(A,B) True f14(A,B) -> exitus616(A,B) True f14(A,B) -> exitus616(A,B) True f14(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0,2);(f14,2);(f4,2)} Rule Graph: [0->{1,2,4,5},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{10},4->{9},5->{8},6->{7}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[1,2] c: [] MAYBE