MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f11(D,E,D) True (1,1) 1. f11(A,B,C) -> f20(A,B,C) [5 >= A && B >= 1] (?,1) 2. f11(A,B,C) -> f14(A,B,C) [5 >= A && 0 >= B] (?,1) 3. f11(A,B,C) -> f14(A,B,C) [A >= 6] (?,1) 4. f20(A,B,C) -> f11(A,D,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && 2 >= A] (?,1) 5. f20(A,B,C) -> f20(-1 + A,B,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && A >= 3] (?,1) 6. f14(A,B,C) -> f11(1 + A,D,C) [5 >= A] (?,1) 7. f14(A,B,C) -> f11(1 + A,D,C) [A >= 6] (?,1) Signature: {(f0,3);(f11,3);(f14,3);(f20,3)} Flow Graph: [0->{1,2,3},1->{4,5},2->{6,7},3->{6,7},4->{1,2,3},5->{4,5},6->{1,2,3},7->{1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7),(3,6),(4,3),(7,1),(7,2)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f11(D,E,D) True (1,1) 1. f11(A,B,C) -> f20(A,B,C) [5 >= A && B >= 1] (?,1) 2. f11(A,B,C) -> f14(A,B,C) [5 >= A && 0 >= B] (?,1) 3. f11(A,B,C) -> f14(A,B,C) [A >= 6] (?,1) 4. f20(A,B,C) -> f11(A,D,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && 2 >= A] (?,1) 5. f20(A,B,C) -> f20(-1 + A,B,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && A >= 3] (?,1) 6. f14(A,B,C) -> f11(1 + A,D,C) [5 >= A] (?,1) 7. f14(A,B,C) -> f11(1 + A,D,C) [A >= 6] (?,1) Signature: {(f0,3);(f11,3);(f14,3);(f20,3)} Flow Graph: [0->{1,2,3},1->{4,5},2->{6},3->{7},4->{1,2},5->{4,5},6->{1,2,3},7->{3}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f0(A,B,C) -> f11(D,E,D) True f11(A,B,C) -> f20(A,B,C) [5 >= A && B >= 1] f11(A,B,C) -> f14(A,B,C) [5 >= A && 0 >= B] f11(A,B,C) -> f14(A,B,C) [A >= 6] f20(A,B,C) -> f11(A,D,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && 2 >= A] f20(A,B,C) -> f20(-1 + A,B,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && A >= 3] f14(A,B,C) -> f11(1 + A,D,C) [5 >= A] f14(A,B,C) -> f11(1 + A,D,C) [A >= 6] Signature: {(f0,3);(f11,3);(f14,3);(f20,3)} Rule Graph: [0->{1,2,3},1->{4,5},2->{6},3->{7},4->{1,2},5->{4,5},6->{1,2,3},7->{3}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f0.0(A,B,C) -> f11.1(D,E,D) True f0.0(A,B,C) -> f11.2(D,E,D) True f0.0(A,B,C) -> f11.3(D,E,D) True f11.1(A,B,C) -> f20.4(A,B,C) [5 >= A && B >= 1] f11.1(A,B,C) -> f20.5(A,B,C) [5 >= A && B >= 1] f11.2(A,B,C) -> f14.6(A,B,C) [5 >= A && 0 >= B] f11.3(A,B,C) -> f14.7(A,B,C) [A >= 6] f20.4(A,B,C) -> f11.1(A,D,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && 2 >= A] f20.4(A,B,C) -> f11.2(A,D,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && 2 >= A] f20.5(A,B,C) -> f20.4(-1 + A,B,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && A >= 3] f20.5(A,B,C) -> f20.5(-1 + A,B,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && A >= 3] f14.6(A,B,C) -> f11.1(1 + A,D,C) [5 >= A] f14.6(A,B,C) -> f11.2(1 + A,D,C) [5 >= A] f14.6(A,B,C) -> f11.3(1 + A,D,C) [5 >= A] f14.7(A,B,C) -> f11.3(1 + A,D,C) [A >= 6] Signature: {(f0.0,3);(f11.1,3);(f11.2,3);(f11.3,3);(f14.6,3);(f14.7,3);(f20.4,3);(f20.5,3)} Rule Graph: [0->{3,4},1->{5},2->{6},3->{7,8},4->{9,10},5->{11,12,13},6->{14},7->{3,4},8->{5},9->{7,8},10->{9,10} ,11->{3,4},12->{5},13->{6},14->{6}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f0.0(A,B,C) -> f11.1(D,E,D) True f0.0(A,B,C) -> f11.2(D,E,D) True f0.0(A,B,C) -> f11.3(D,E,D) True f11.1(A,B,C) -> f20.4(A,B,C) [5 >= A && B >= 1] f11.1(A,B,C) -> f20.5(A,B,C) [5 >= A && B >= 1] f11.2(A,B,C) -> f14.6(A,B,C) [5 >= A && 0 >= B] f11.3(A,B,C) -> f14.7(A,B,C) [A >= 6] f20.4(A,B,C) -> f11.1(A,D,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && 2 >= A] f20.4(A,B,C) -> f11.2(A,D,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && 2 >= A] f20.5(A,B,C) -> f20.4(-1 + A,B,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && A >= 3] f20.5(A,B,C) -> f20.5(-1 + A,B,C) [-1 + B >= 0 && 4 + -1*A + B >= 0 && 5 + -1*A >= 0 && A >= 3] f14.6(A,B,C) -> f11.1(1 + A,D,C) [5 >= A] f14.6(A,B,C) -> f11.2(1 + A,D,C) [5 >= A] f14.6(A,B,C) -> f11.3(1 + A,D,C) [5 >= A] f14.7(A,B,C) -> f11.3(1 + A,D,C) [A >= 6] f14.7(A,B,C) -> exitus616(A,B,C) True f11.3(A,B,C) -> exitus616(A,B,C) True f14.7(A,B,C) -> exitus616(A,B,C) True f11.3(A,B,C) -> exitus616(A,B,C) True f14.7(A,B,C) -> exitus616(A,B,C) True f11.3(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0.0,3);(f11.1,3);(f11.2,3);(f11.3,3);(f14.6,3);(f14.7,3);(f20.4,3);(f20.5,3)} Rule Graph: [0->{3,4},1->{5},2->{6},3->{7,8},4->{9,10},5->{11,12,13},6->{14,15,17,19},7->{3,4},8->{5},9->{7,8},10->{9 ,10},11->{3,4},12->{5},13->{6},14->{6,16,18,20}] + 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] | +- p:[3,7,9,4,11,5,8,12,10] c: [] | `- p:[6,14] c: [] MAYBE