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: FromIts 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: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f0(A,B) -> f2(3,C) True f0(A,B) -> f2(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] 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] f2(A,B) -> f2(B,C) [-3 + A >= 0 && B = 3 && A = 6] f2(A,B) -> f2(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] Signature: {(f0,2);(f2,2)} Rule Graph: [0->{2},1->{2,3,4},2->{2,4},3->{2},4->{2,3,4}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f0.0(A,B) -> f2.2(3,C) True f0.1(A,B) -> f2.2(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] f0.1(A,B) -> f2.3(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] f0.1(A,B) -> f2.4(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] f2.2(A,B) -> f2.2(4 + 6*B,C) [-3 + A >= 0 && 6*B >= 1 && 2 + 6*B >= 0 && 1 + 6*B >= 0 && A = 1 + 2*B] f2.2(A,B) -> f2.4(4 + 6*B,C) [-3 + A >= 0 && 6*B >= 1 && 2 + 6*B >= 0 && 1 + 6*B >= 0 && A = 1 + 2*B] f2.3(A,B) -> f2.2(B,C) [-3 + A >= 0 && B = 3 && A = 6] f2.4(A,B) -> f2.2(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] f2.4(A,B) -> f2.3(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] f2.4(A,B) -> f2.4(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] Signature: {(f0.0,2);(f0.1,2);(f2.2,2);(f2.3,2);(f2.4,2)} Rule Graph: [0->{4,5},1->{4,5},2->{6},3->{7,8,9},4->{4,5},5->{7,8,9},6->{4,5},7->{4,5},8->{6},9->{7,8,9}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f0.0(A,B) -> f2.2(3,C) True f0.1(A,B) -> f2.2(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] f0.1(A,B) -> f2.3(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] f0.1(A,B) -> f2.4(C,D) [C >= 1 && C >= 5 && C >= 2 && C >= 3] f2.2(A,B) -> f2.2(4 + 6*B,C) [-3 + A >= 0 && 6*B >= 1 && 2 + 6*B >= 0 && 1 + 6*B >= 0 && A = 1 + 2*B] f2.2(A,B) -> f2.4(4 + 6*B,C) [-3 + A >= 0 && 6*B >= 1 && 2 + 6*B >= 0 && 1 + 6*B >= 0 && A = 1 + 2*B] f2.3(A,B) -> f2.2(B,C) [-3 + A >= 0 && B = 3 && A = 6] f2.4(A,B) -> f2.2(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] f2.4(A,B) -> f2.3(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] f2.4(A,B) -> f2.4(B,C) [-3 + A >= 0 && B >= 5 && B >= 2 && B >= 3 && A = 2*B] f2.2(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.3(A,B) -> exitus616(A,B) True f2.4(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.4(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.3(A,B) -> exitus616(A,B) True f2.4(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.4(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.3(A,B) -> exitus616(A,B) True f2.4(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.4(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.3(A,B) -> exitus616(A,B) True f2.4(A,B) -> exitus616(A,B) True f2.2(A,B) -> exitus616(A,B) True f2.4(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0.0,2);(f0.1,2);(f2.2,2);(f2.3,2);(f2.4,2)} Rule Graph: [0->{4,5},1->{4,5},2->{6},3->{7,8,9},4->{4,5,10,16,22,28},5->{7,8,9,13,19,25,31},6->{4,5,11,17,23,29} ,7->{4,5,14,20,26,32},8->{6,12,18,24,30},9->{7,8,9,15,21,27,33}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33] | `- p:[4,6,8,5,7,9] c: [] MAYBE