MAYBE * Step 1: ArgumentFilter MAYBE + Considered Problem: Rules: 0. f5(A,B,C,D,E) -> f300(A,B,C,D,E) True (1,1) 1. f4(A,B,C,D,E) -> f300(A,B,1 + C,D,E) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && A >= B] (?,1) 2. f4(A,B,C,D,E) -> f4(1 + A,B,C,F,E) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && F >= 1 && B >= 1 + A] (?,1) 3. f4(A,B,C,D,E) -> f4(1 + A,B,C,F,E) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] (?,1) 4. f4(A,B,C,D,E) -> f2(A,B,C,0,E) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && B >= 1 + A] (?,1) 5. f2(A,B,C,D,E) -> f4(1 + A,B,C,F,E) [-1*D >= 0 (?,1) && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && F >= 1 && B >= 1 + A] 6. f2(A,B,C,D,E) -> f4(1 + A,B,C,F,E) [-1*D >= 0 (?,1) && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] 7. f2(A,B,C,D,E) -> f2(A,B,C,0,E) [-1*D >= 0 && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A] (?,1) 8. f300(A,B,C,D,E) -> f1(A,B,C,D,F) [C >= A] (?,1) 9. f300(A,B,C,D,E) -> f300(A,B,1 + C,D,E) [A >= 1 + C && A >= B] (?,1) 10. f300(A,B,C,D,E) -> f4(1 + A,B,C,F,E) [F >= 1 && A >= 1 + C && B >= 1 + A] (?,1) 11. f300(A,B,C,D,E) -> f4(1 + A,B,C,F,E) [0 >= 1 + F && A >= 1 + C && B >= 1 + A] (?,1) 12. f300(A,B,C,D,E) -> f2(A,B,C,0,E) [A >= 1 + C && B >= 1 + A] (?,1) Signature: {(f1,5);(f2,5);(f300,5);(f4,5);(f5,5)} Flow Graph: [0->{8,9,10,11,12},1->{8,9,10,11,12},2->{1,2,3,4},3->{1,2,3,4},4->{5,6,7},5->{1,2,3,4},6->{1,2,3,4},7->{5 ,6,7},8->{},9->{8,9,10,11,12},10->{1,2,3,4},11->{1,2,3,4},12->{5,6,7}] + Applied Processor: ArgumentFilter [4] + Details: We remove following argument positions: [4]. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f5(A,B,C,D) -> f300(A,B,C,D) True (1,1) 1. f4(A,B,C,D) -> f300(A,B,1 + C,D) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && A >= B] (?,1) 2. f4(A,B,C,D) -> f4(1 + A,B,C,F) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && F >= 1 && B >= 1 + A] (?,1) 3. f4(A,B,C,D) -> f4(1 + A,B,C,F) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] (?,1) 4. f4(A,B,C,D) -> f2(A,B,C,0) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && B >= 1 + A] (?,1) 5. f2(A,B,C,D) -> f4(1 + A,B,C,F) [-1*D >= 0 (?,1) && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && F >= 1 && B >= 1 + A] 6. f2(A,B,C,D) -> f4(1 + A,B,C,F) [-1*D >= 0 (?,1) && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] 7. f2(A,B,C,D) -> f2(A,B,C,0) [-1*D >= 0 && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A] (?,1) 8. f300(A,B,C,D) -> f1(A,B,C,D) [C >= A] (?,1) 9. f300(A,B,C,D) -> f300(A,B,1 + C,D) [A >= 1 + C && A >= B] (?,1) 10. f300(A,B,C,D) -> f4(1 + A,B,C,F) [F >= 1 && A >= 1 + C && B >= 1 + A] (?,1) 11. f300(A,B,C,D) -> f4(1 + A,B,C,F) [0 >= 1 + F && A >= 1 + C && B >= 1 + A] (?,1) 12. f300(A,B,C,D) -> f2(A,B,C,0) [A >= 1 + C && B >= 1 + A] (?,1) Signature: {(f1,5);(f2,5);(f300,5);(f4,5);(f5,5)} Flow Graph: [0->{8,9,10,11,12},1->{8,9,10,11,12},2->{1,2,3,4},3->{1,2,3,4},4->{5,6,7},5->{1,2,3,4},6->{1,2,3,4},7->{5 ,6,7},8->{},9->{8,9,10,11,12},10->{1,2,3,4},11->{1,2,3,4},12->{5,6,7}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,8),(1,10),(1,11),(1,12),(9,10),(9,11),(9,12)] * Step 3: FromIts MAYBE + Considered Problem: Rules: 0. f5(A,B,C,D) -> f300(A,B,C,D) True (1,1) 1. f4(A,B,C,D) -> f300(A,B,1 + C,D) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && A >= B] (?,1) 2. f4(A,B,C,D) -> f4(1 + A,B,C,F) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && F >= 1 && B >= 1 + A] (?,1) 3. f4(A,B,C,D) -> f4(1 + A,B,C,F) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] (?,1) 4. f4(A,B,C,D) -> f2(A,B,C,0) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && B >= 1 + A] (?,1) 5. f2(A,B,C,D) -> f4(1 + A,B,C,F) [-1*D >= 0 (?,1) && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && F >= 1 && B >= 1 + A] 6. f2(A,B,C,D) -> f4(1 + A,B,C,F) [-1*D >= 0 (?,1) && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] 7. f2(A,B,C,D) -> f2(A,B,C,0) [-1*D >= 0 && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A] (?,1) 8. f300(A,B,C,D) -> f1(A,B,C,D) [C >= A] (?,1) 9. f300(A,B,C,D) -> f300(A,B,1 + C,D) [A >= 1 + C && A >= B] (?,1) 10. f300(A,B,C,D) -> f4(1 + A,B,C,F) [F >= 1 && A >= 1 + C && B >= 1 + A] (?,1) 11. f300(A,B,C,D) -> f4(1 + A,B,C,F) [0 >= 1 + F && A >= 1 + C && B >= 1 + A] (?,1) 12. f300(A,B,C,D) -> f2(A,B,C,0) [A >= 1 + C && B >= 1 + A] (?,1) Signature: {(f1,5);(f2,5);(f300,5);(f4,5);(f5,5)} Flow Graph: [0->{8,9,10,11,12},1->{9},2->{1,2,3,4},3->{1,2,3,4},4->{5,6,7},5->{1,2,3,4},6->{1,2,3,4},7->{5,6,7},8->{} ,9->{8,9},10->{1,2,3,4},11->{1,2,3,4},12->{5,6,7}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f5(A,B,C,D) -> f300(A,B,C,D) True f4(A,B,C,D) -> f300(A,B,1 + C,D) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && A >= B] f4(A,B,C,D) -> f4(1 + A,B,C,F) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && F >= 1 && B >= 1 + A] f4(A,B,C,D) -> f4(1 + A,B,C,F) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] f4(A,B,C,D) -> f2(A,B,C,0) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && B >= 1 + A] f2(A,B,C,D) -> f4(1 + A,B,C,F) [-1*D >= 0 && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && F >= 1 && B >= 1 + A] f2(A,B,C,D) -> f4(1 + A,B,C,F) [-1*D >= 0 && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] f2(A,B,C,D) -> f2(A,B,C,0) [-1*D >= 0 && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A] f300(A,B,C,D) -> f1(A,B,C,D) [C >= A] f300(A,B,C,D) -> f300(A,B,1 + C,D) [A >= 1 + C && A >= B] f300(A,B,C,D) -> f4(1 + A,B,C,F) [F >= 1 && A >= 1 + C && B >= 1 + A] f300(A,B,C,D) -> f4(1 + A,B,C,F) [0 >= 1 + F && A >= 1 + C && B >= 1 + A] f300(A,B,C,D) -> f2(A,B,C,0) [A >= 1 + C && B >= 1 + A] Signature: {(f1,5);(f2,5);(f300,5);(f4,5);(f5,5)} Rule Graph: [0->{8,9,10,11,12},1->{9},2->{1,2,3,4},3->{1,2,3,4},4->{5,6,7},5->{1,2,3,4},6->{1,2,3,4},7->{5,6,7},8->{} ,9->{8,9},10->{1,2,3,4},11->{1,2,3,4},12->{5,6,7}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f5(A,B,C,D) -> f300(A,B,C,D) True f4(A,B,C,D) -> f300(A,B,1 + C,D) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && A >= B] f4(A,B,C,D) -> f4(1 + A,B,C,F) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && F >= 1 && B >= 1 + A] f4(A,B,C,D) -> f4(1 + A,B,C,F) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] f4(A,B,C,D) -> f2(A,B,C,0) [-2 + B + -1*C >= 0 && -2 + A + -1*C >= 0 && -1*A + B >= 0 && B >= 1 + A] f2(A,B,C,D) -> f4(1 + A,B,C,F) [-1*D >= 0 && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && F >= 1 && B >= 1 + A] f2(A,B,C,D) -> f4(1 + A,B,C,F) [-1*D >= 0 && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && 0 >= 1 + F && B >= 1 + A] f2(A,B,C,D) -> f2(A,B,C,0) [-1*D >= 0 && D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + -1*A + B >= 0 && B >= 1 + A] f300(A,B,C,D) -> f1(A,B,C,D) [C >= A] f300(A,B,C,D) -> f300(A,B,1 + C,D) [A >= 1 + C && A >= B] f300(A,B,C,D) -> f4(1 + A,B,C,F) [F >= 1 && A >= 1 + C && B >= 1 + A] f300(A,B,C,D) -> f4(1 + A,B,C,F) [0 >= 1 + F && A >= 1 + C && B >= 1 + A] f300(A,B,C,D) -> f2(A,B,C,0) [A >= 1 + C && B >= 1 + A] f1(A,B,C,D) -> exitus616(A,B,C,D) True f1(A,B,C,D) -> exitus616(A,B,C,D) True f1(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f1,5);(f2,5);(f300,5);(f4,5);(f5,5)} Rule Graph: [0->{8,9,10,11,12},1->{9},2->{1,2,3,4},3->{1,2,3,4},4->{5,6,7},5->{1,2,3,4},6->{1,2,3,4},7->{5,6,7},8->{13 ,14,15},9->{8,9},10->{1,2,3,4},11->{1,2,3,4},12->{5,6,7}] + 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] | +- p:[2,3,5,4,6,7] c: [2,3,4,5,6] | | | `- p:[7] c: [] | `- p:[9] c: [9] MAYBE