MAYBE * Step 1: UnsatRules MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 4. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 6. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 7. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) 8. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && B >= 1 + A] (?,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4,5,6,7,8},1->{1,2,3,4,5,6,7,8},2->{1,2,3,4,5,6,7,8},3->{1,2,3,4,5,6,7,8},4->{1,2,3,4,5,6,7,8} ,5->{1,2,3,4,5,6,7,8},6->{1,2,3,4,5,6,7,8},7->{},8->{}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [8] * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 4. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 6. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 7. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4,5,6,7},1->{1,2,3,4,5,6,7},2->{1,2,3,4,5,6,7},3->{1,2,3,4,5,6,7},4->{1,2,3,4,5,6,7},5->{1,2,3 ,4,5,6,7},6->{1,2,3,4,5,6,7},7->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,7) ,(2,7) ,(3,4) ,(3,5) ,(3,6) ,(3,7) ,(4,1) ,(4,2) ,(4,3) ,(4,4) ,(4,5) ,(4,6) ,(5,1) ,(5,2) ,(5,3) ,(5,4) ,(5,5) ,(5,6) ,(6,1) ,(6,2) ,(6,3) ,(6,7)] * Step 3: FromIts MAYBE + Considered Problem: Rules: 0. f2(A,B,C,D) -> f1(A,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f1(A,B,C,D) -> f1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f1(A,B,C,D) -> f1(A,B,0,D) [B >= 1 + A] (?,1) 4. f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && A = B] (?,1) 5. f1(A,B,C,D) -> f1(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] (?,1) 6. f1(A,B,C,D) -> f1(A,A,0,D) [B >= E && A = B] (?,1) 7. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] (?,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4,5,6,7},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{1,2,3},4->{7},5->{7},6->{4,5,6},7->{}] + Applied Processor: FromIts + Details: () * Step 4: Unfold MAYBE + Considered Problem: Rules: f2(A,B,C,D) -> f1(A,B,C,D) True f1(A,B,C,D) -> f1(1 + A,B,E,D) [E >= 1 && 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(A,B,0,D) [B >= 1 + A] f1(A,B,C,D) -> f1(1 + A,A,E,D) [E >= 1 && B >= F && 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(A,A,0,D) [B >= E && A = B] f1(A,B,C,D) -> f300(A,B,C,E) [A >= B && A >= 1 + B] Signature: {(f1,4);(f2,4);(f300,4)} Rule Graph: [0->{1,2,3,4,5,6,7},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{1,2,3},4->{7},5->{7},6->{4,5,6},7->{}] + Applied Processor: Unfold + Details: () * Step 5: AddSinks MAYBE + Considered Problem: Rules: f2.0(A,B,C,D) -> f1.1(A,B,C,D) True f2.0(A,B,C,D) -> f1.2(A,B,C,D) True f2.0(A,B,C,D) -> f1.3(A,B,C,D) True f2.0(A,B,C,D) -> f1.4(A,B,C,D) True f2.0(A,B,C,D) -> f1.5(A,B,C,D) True f2.0(A,B,C,D) -> f1.6(A,B,C,D) True f2.0(A,B,C,D) -> f1.7(A,B,C,D) True f1.1(A,B,C,D) -> f1.1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.2(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.3(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.4(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.5(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.6(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.2(A,B,C,D) -> f1.1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.2(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.3(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.4(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.5(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.6(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.3(A,B,C,D) -> f1.1(A,B,0,D) [B >= 1 + A] f1.3(A,B,C,D) -> f1.2(A,B,0,D) [B >= 1 + A] f1.3(A,B,C,D) -> f1.3(A,B,0,D) [B >= 1 + A] f1.4(A,B,C,D) -> f1.7(1 + A,A,E,D) [E >= 1 && B >= F && A = B] f1.5(A,B,C,D) -> f1.7(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] f1.6(A,B,C,D) -> f1.4(A,A,0,D) [B >= E && A = B] f1.6(A,B,C,D) -> f1.5(A,A,0,D) [B >= E && A = B] f1.6(A,B,C,D) -> f1.6(A,A,0,D) [B >= E && A = B] f1.7(A,B,C,D) -> f300.8(A,B,C,E) [A >= B && A >= 1 + B] Signature: {(f1.1,4);(f1.2,4);(f1.3,4);(f1.4,4);(f1.5,4);(f1.6,4);(f1.7,4);(f2.0,4);(f300.8,4)} Rule Graph: [0->{7,8,9,10,11,12},1->{13,14,15,16,17,18},2->{19,20,21},3->{22},4->{23},5->{24,25,26},6->{27},7->{7,8,9 ,10,11,12},8->{13,14,15,16,17,18},9->{19,20,21},10->{22},11->{23},12->{24,25,26},13->{7,8,9,10,11,12} ,14->{13,14,15,16,17,18},15->{19,20,21},16->{22},17->{23},18->{24,25,26},19->{7,8,9,10,11,12},20->{13,14,15 ,16,17,18},21->{19,20,21},22->{27},23->{27},24->{22},25->{23},26->{24,25,26},27->{}] + Applied Processor: AddSinks + Details: () * Step 6: Failure MAYBE + Considered Problem: Rules: f2.0(A,B,C,D) -> f1.1(A,B,C,D) True f2.0(A,B,C,D) -> f1.2(A,B,C,D) True f2.0(A,B,C,D) -> f1.3(A,B,C,D) True f2.0(A,B,C,D) -> f1.4(A,B,C,D) True f2.0(A,B,C,D) -> f1.5(A,B,C,D) True f2.0(A,B,C,D) -> f1.6(A,B,C,D) True f2.0(A,B,C,D) -> f1.7(A,B,C,D) True f1.1(A,B,C,D) -> f1.1(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.2(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.3(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.4(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.5(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.1(A,B,C,D) -> f1.6(1 + A,B,E,D) [E >= 1 && B >= 1 + A] f1.2(A,B,C,D) -> f1.1(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.2(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.3(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.4(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.5(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.2(A,B,C,D) -> f1.6(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] f1.3(A,B,C,D) -> f1.1(A,B,0,D) [B >= 1 + A] f1.3(A,B,C,D) -> f1.2(A,B,0,D) [B >= 1 + A] f1.3(A,B,C,D) -> f1.3(A,B,0,D) [B >= 1 + A] f1.4(A,B,C,D) -> f1.7(1 + A,A,E,D) [E >= 1 && B >= F && A = B] f1.5(A,B,C,D) -> f1.7(1 + A,A,E,D) [0 >= 1 + E && B >= F && A = B] f1.6(A,B,C,D) -> f1.4(A,A,0,D) [B >= E && A = B] f1.6(A,B,C,D) -> f1.5(A,A,0,D) [B >= E && A = B] f1.6(A,B,C,D) -> f1.6(A,A,0,D) [B >= E && A = B] f1.7(A,B,C,D) -> f300.8(A,B,C,E) [A >= B && A >= 1 + B] 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);(f1.1,4);(f1.2,4);(f1.3,4);(f1.4,4);(f1.5,4);(f1.6,4);(f1.7,4);(f2.0,4);(f300.8,4)} Rule Graph: [0->{7,8,9,10,11,12},1->{13,14,15,16,17,18},2->{19,20,21},3->{22},4->{23},5->{24,25,26},6->{27},7->{7,8,9 ,10,11,12},8->{13,14,15,16,17,18},9->{19,20,21},10->{22},11->{23},12->{24,25,26},13->{7,8,9,10,11,12} ,14->{13,14,15,16,17,18},15->{19,20,21},16->{22},17->{23},18->{24,25,26},19->{7,8,9,10,11,12},20->{13,14,15 ,16,17,18},21->{19,20,21},22->{27},23->{27},24->{22},25->{23},26->{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}] + 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:[7,13,8,19,9,15,14,20,21] c: [7,8,9,13,14,15,19,20] | | | `- p:[21] c: [] | `- p:[26] c: [] MAYBE