MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) 1. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 3. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 4. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 6. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 7. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{},1->{0,1,2,3,4,5,6},2->{0,1,2,3,4,5,6},3->{0,1,2,3,4,5,6},4->{0,1,2,3,4,5,6},5->{0,1,2,3,4,5,6} ,6->{0,1,2,3,4,5,6},7->{0,1,2,3,4,5,6}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,0) ,(1,4) ,(1,5) ,(1,6) ,(2,1) ,(2,2) ,(2,3) ,(2,4) ,(2,5) ,(2,6) ,(3,1) ,(3,2) ,(3,3) ,(3,4) ,(3,5) ,(3,6) ,(4,0) ,(4,1) ,(4,2) ,(4,3) ,(5,0) ,(6,0)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) 1. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 3. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 4. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 6. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 7. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{},1->{1,2,3},2->{0},3->{0},4->{4,5,6},5->{1,2,3,4,5,6},6->{1,2,3,4,5,6},7->{0,1,2,3,4,5,6}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f2(A,B,C,D) -> f1(A,B,C,D) True Signature: {(f1,4);(f2,4);(f300,4)} Rule Graph: [0->{},1->{1,2,3},2->{0},3->{0},4->{4,5,6},5->{1,2,3,4,5,6},6->{1,2,3,4,5,6},7->{0,1,2,3,4,5,6}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f1.0(A,B,C,D) -> f300.8(A,B,C,E) [A >= B && A >= 1 + B] f1.1(A,B,C,D) -> f1.1(A,A,0,D) [B >= E && A = B] f1.1(A,B,C,D) -> f1.2(A,A,0,D) [B >= E && A = B] f1.1(A,B,C,D) -> f1.3(A,A,0,D) [B >= E && A = B] f1.2(A,B,C,D) -> f1.0(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] f1.3(A,B,C,D) -> f1.0(1 + A,A,E,D) [E >= 1 && B >= F && A = B] f1.4(A,B,C,D) -> f1.4(A,B,0,D) [B >= 1 + A] f1.4(A,B,C,D) -> f1.5(A,B,0,D) [B >= 1 + A] f1.4(A,B,C,D) -> f1.6(A,B,0,D) [B >= 1 + A] f1.5(A,B,C,D) -> f1.1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.2(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.3(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.4(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.5(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.6(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.6(A,B,C,D) -> f1.1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.2(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.3(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.4(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.5(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.6(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f2.7(A,B,C,D) -> f1.0(A,B,C,D) True f2.7(A,B,C,D) -> f1.1(A,B,C,D) True f2.7(A,B,C,D) -> f1.2(A,B,C,D) True f2.7(A,B,C,D) -> f1.3(A,B,C,D) True f2.7(A,B,C,D) -> f1.4(A,B,C,D) True f2.7(A,B,C,D) -> f1.5(A,B,C,D) True f2.7(A,B,C,D) -> f1.6(A,B,C,D) True Signature: {(f1.0,4);(f1.1,4);(f1.2,4);(f1.3,4);(f1.4,4);(f1.5,4);(f1.6,4);(f2.7,4);(f300.8,4)} Rule Graph: [0->{},1->{1,2,3},2->{4},3->{5},4->{0},5->{0},6->{6,7,8},7->{9,10,11,12,13,14},8->{15,16,17,18,19,20} ,9->{1,2,3},10->{4},11->{5},12->{6,7,8},13->{9,10,11,12,13,14},14->{15,16,17,18,19,20},15->{1,2,3},16->{4} ,17->{5},18->{6,7,8},19->{9,10,11,12,13,14},20->{15,16,17,18,19,20},21->{0},22->{1,2,3},23->{4},24->{5} ,25->{6,7,8},26->{9,10,11,12,13,14},27->{15,16,17,18,19,20}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f1.0(A,B,C,D) -> f300.8(A,B,C,E) [A >= B && A >= 1 + B] f1.1(A,B,C,D) -> f1.1(A,A,0,D) [B >= E && A = B] f1.1(A,B,C,D) -> f1.2(A,A,0,D) [B >= E && A = B] f1.1(A,B,C,D) -> f1.3(A,A,0,D) [B >= E && A = B] f1.2(A,B,C,D) -> f1.0(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] f1.3(A,B,C,D) -> f1.0(1 + A,A,E,D) [E >= 1 && B >= F && A = B] f1.4(A,B,C,D) -> f1.4(A,B,0,D) [B >= 1 + A] f1.4(A,B,C,D) -> f1.5(A,B,0,D) [B >= 1 + A] f1.4(A,B,C,D) -> f1.6(A,B,0,D) [B >= 1 + A] f1.5(A,B,C,D) -> f1.1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.2(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.3(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.4(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.5(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.5(A,B,C,D) -> f1.6(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.6(A,B,C,D) -> f1.1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.2(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.3(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.4(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.5(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.6(A,B,C,D) -> f1.6(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f2.7(A,B,C,D) -> f1.0(A,B,C,D) True f2.7(A,B,C,D) -> f1.1(A,B,C,D) True f2.7(A,B,C,D) -> f1.2(A,B,C,D) True f2.7(A,B,C,D) -> f1.3(A,B,C,D) True f2.7(A,B,C,D) -> f1.4(A,B,C,D) True f2.7(A,B,C,D) -> f1.5(A,B,C,D) True f2.7(A,B,C,D) -> f1.6(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True f300.8(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f1.0,4);(f1.1,4);(f1.2,4);(f1.3,4);(f1.4,4);(f1.5,4);(f1.6,4);(f2.7,4);(f300.8,4)} Rule Graph: [0->{28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56},1->{1,2,3} ,2->{4},3->{5},4->{0},5->{0},6->{6,7,8},7->{9,10,11,12,13,14},8->{15,16,17,18,19,20},9->{1,2,3},10->{4} ,11->{5},12->{6,7,8},13->{9,10,11,12,13,14},14->{15,16,17,18,19,20},15->{1,2,3},16->{4},17->{5},18->{6,7,8} ,19->{9,10,11,12,13,14},20->{15,16,17,18,19,20},21->{0},22->{1,2,3},23->{4},24->{5},25->{6,7,8},26->{9,10,11 ,12,13,14},27->{15,16,17,18,19,20}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56] | +- p:[6,12,7,18,8,14,13,19,20] c: [7,8,12,13,14,18,19,20] | | | `- p:[6] c: [] | `- p:[1] c: [] MAYBE