WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f13(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f13(A,B,C,D,E,F,G,H,I,1 + J,1,0,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D >= J] (?,1)
2. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[C1 >= 2 && D >= J] (?,1)
,A1)
3. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[0 >= C1 && D >= J] (?,1)
,A1)
4. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f24(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= J] (?,1)
5. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f31(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= J] (?,1)
6. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [N >= O] (?,1)
7. f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= J] (?,1)
10. f50(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f50(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= J] (?,1)
11. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f57(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= J] (?,1)
12. f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,0,Q,R,S,T,U,V,W,X,Y,Z,A1) [0 >= Q && P = 0] (?,1)
13. f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f64(A,B,C,D,E,F,G,H,I,2 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [E >= J] (?,1)
14. f71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f71(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,2*J,C1,1 + -1*C1,U,V,W,X,Y,Z,A1) [D >= J] (?,1)
15. f86(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,J,K,0,M,N,O,P,Q,R,S,T,0,V,W,X,Y,Z,A1) [L = 0] (?,1)
16. f86(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [0 >= 1 + L] (?,1)
17. f86(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [L >= 1] (?,1)
18. f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f99(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,2*J,S,T,U,0,W,X,Y,Z,A1) [A >= J] (?,1)
19. f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f99(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,2*J,S,T,U,B1^2,W,X,Y,Z,A1) [0 >= 1 + B1 && A >= J] (?,1)
20. f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f99(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,2*J,S,T,U,B1^2,W,X,Y,Z,A1) [B1 >= 1 && A >= J] (?,1)
21. f99(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f103(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,0,X,Y,Z,A1) [L = 0] (?,1)
22. f99(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f103(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,L^2,X,Y,Z,A1) [0 >= 1 + L] (?,1)
23. f99(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f103(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,L^2,X,Y,Z,A1) [L >= 1] (?,1)
24. f103(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f107(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,0,Y,Z,A1) [L = 0] (?,1)
25. f103(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f107(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,L^2,Y,Z,A1) [0 >= 1 + L] (?,1)
26. f103(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f107(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,L^2,Y,Z,A1) [L >= 1] (?,1)
27. f107(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,1 + J,K,0,M,N,O,P,Q,R,S,T,U,V,W,X,0,Z,A1) [L = 0] (?,1)
28. f107(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,L^2,Z,A1) [0 >= 1 + L] (?,1)
29. f107(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,L^2,Z,A1) [L >= 1] (?,1)
30. f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f118(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= J] (?,1)
31. f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + A] (?,1)
32. f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f37(A,B,B + C,D,E,F,G,H,I,J,K,L,M,N,1 + O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + A] (?,1)
33. f71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [J >= 1 + D] (?,1)
34. f71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,1 + Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + E] (?,1)
37. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,1 + Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + A] (?,1)
38. f50(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,D + Q) [J >= 1 + A] (?,1)
39. f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f50(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + A] (?,1)
40. f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [Q >= 1] (?,1)
41. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f118(A,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [O >= 1 + N] (?,1)
42. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + A] (?,1)
43. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [0 >= 1 + P && J >= 1 + A] (?,1)
44. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [P >= 1 && J >= 1 + A] (?,1)
45. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,0,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + A && P = 0] (?,1)
46. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + D] (?,1)
Signature:
{(f1,27)
;(f103,27)
;(f107,27)
;(f118,27)
;(f13,27)
;(f2,27)
;(f24,27)
;(f31,27)
;(f37,27)
;(f40,27)
;(f44,27)
;(f50,27)
;(f57,27)
;(f64,27)
;(f71,27)
;(f86,27)
;(f91,27)
;(f99,27)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},5->{5,42},6->{7,8,12,40},7->{9
,39},8->{9,39},9->{9,39},10->{10,38},11->{11,37},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32}
,16->{18,19,20,32},17->{18,19,20,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25
,26},23->{24,25,26},24->{27,28,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18
,19,20,32},30->{30,31},31->{},32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7
,8,12,40},38->{11,37},39->{10,38},40->{14,33,34,35},41->{30,31},42->{6,41},43->{5,42},44->{5,42},45->{6,41}
,46->{4,43,44,45}]
+ Applied Processor:
RestrictVarsProcessor
+ Details:
We removed the arguments [C,F,G,H,I,K,M,R,S,T,U,V,W,X,Y,Z,A1] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
5. f31(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
10. f50(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
11. f57(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (?,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (?,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (?,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
31. f118(A,B,D,E,J,L,N,O,P,Q) -> f1(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (?,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (?,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (?,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},5->{5,42},6->{7,8,12,40},7->{9
,39},8->{9,39},9->{9,39},10->{10,38},11->{11,37},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32}
,16->{18,19,20,32},17->{18,19,20,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25
,26},23->{24,25,26},24->{27,28,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18
,19,20,32},30->{30,31},31->{},32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7
,8,12,40},38->{11,37},39->{10,38},40->{14,33,34,35},41->{30,31},42->{6,41},43->{5,42},44->{5,42},45->{6,41}
,46->{4,43,44,45}]
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(< 0,0,A>, A, .= 0) (< 0,0,B>, 0, .= 0) (< 0,0,D>, 2*A, .?) (< 0,0,E>, 4*A, .?) (< 0,0,J>, J, .= 0) (< 0,0,L>, L, .= 0) (< 0,0,N>, N, .= 0) (< 0,0,O>, O, .= 0) (< 0,0,P>, P, .= 0) (< 0,0,Q>, Q, .= 0)
(< 1,0,A>, A, .= 0) (< 1,0,B>, B, .= 0) (< 1,0,D>, D, .= 0) (< 1,0,E>, E, .= 0) (< 1,0,J>, 1 + J, .+ 1) (< 1,0,L>, 0, .= 0) (< 1,0,N>, N, .= 0) (< 1,0,O>, O, .= 0) (< 1,0,P>, P, .= 0) (< 1,0,Q>, Q, .= 0)
(< 2,0,A>, A, .= 0) (< 2,0,B>, ?, .?) (< 2,0,D>, D, .= 0) (< 2,0,E>, E, .= 0) (< 2,0,J>, 1 + J, .+ 1) (< 2,0,L>, ?, .?) (< 2,0,N>, N, .= 0) (< 2,0,O>, O, .= 0) (< 2,0,P>, P, .= 0) (< 2,0,Q>, Q, .= 0)
(< 3,0,A>, A, .= 0) (< 3,0,B>, ?, .?) (< 3,0,D>, D, .= 0) (< 3,0,E>, E, .= 0) (< 3,0,J>, 1 + J, .+ 1) (< 3,0,L>, ?, .?) (< 3,0,N>, N, .= 0) (< 3,0,O>, O, .= 0) (< 3,0,P>, P, .= 0) (< 3,0,Q>, Q, .= 0)
(< 4,0,A>, A, .= 0) (< 4,0,B>, B, .= 0) (< 4,0,D>, D, .= 0) (< 4,0,E>, E, .= 0) (< 4,0,J>, 1 + J, .+ 1) (< 4,0,L>, L, .= 0) (< 4,0,N>, N, .= 0) (< 4,0,O>, O, .= 0) (< 4,0,P>, P, .= 0) (< 4,0,Q>, Q, .= 0)
(< 5,0,A>, A, .= 0) (< 5,0,B>, B, .= 0) (< 5,0,D>, D, .= 0) (< 5,0,E>, E, .= 0) (< 5,0,J>, 1 + J, .+ 1) (< 5,0,L>, L, .= 0) (< 5,0,N>, N, .= 0) (< 5,0,O>, O, .= 0) (< 5,0,P>, P, .= 0) (< 5,0,Q>, Q, .= 0)
(< 6,0,A>, A, .= 0) (< 6,0,B>, B, .= 0) (< 6,0,D>, D, .= 0) (< 6,0,E>, E, .= 0) (< 6,0,J>, J, .= 0) (< 6,0,L>, L, .= 0) (< 6,0,N>, N, .= 0) (< 6,0,O>, O, .= 0) (< 6,0,P>, P, .= 0) (< 6,0,Q>, Q, .= 0)
(< 7,0,A>, A, .= 0) (< 7,0,B>, B, .= 0) (< 7,0,D>, D, .= 0) (< 7,0,E>, E, .= 0) (< 7,0,J>, J, .= 0) (< 7,0,L>, L, .= 0) (< 7,0,N>, N, .= 0) (< 7,0,O>, O, .= 0) (< 7,0,P>, P, .= 0) (< 7,0,Q>, Q, .= 0)
(< 8,0,A>, A, .= 0) (< 8,0,B>, B, .= 0) (< 8,0,D>, D, .= 0) (< 8,0,E>, E, .= 0) (< 8,0,J>, J, .= 0) (< 8,0,L>, L, .= 0) (< 8,0,N>, N, .= 0) (< 8,0,O>, O, .= 0) (< 8,0,P>, P, .= 0) (< 8,0,Q>, Q, .= 0)
(< 9,0,A>, A, .= 0) (< 9,0,B>, B, .= 0) (< 9,0,D>, D, .= 0) (< 9,0,E>, E, .= 0) (< 9,0,J>, 1 + J, .+ 1) (< 9,0,L>, L, .= 0) (< 9,0,N>, N, .= 0) (< 9,0,O>, O, .= 0) (< 9,0,P>, P, .= 0) (< 9,0,Q>, Q, .= 0)
(<10,0,A>, A, .= 0) (<10,0,B>, B, .= 0) (<10,0,D>, D, .= 0) (<10,0,E>, E, .= 0) (<10,0,J>, 1 + J, .+ 1) (<10,0,L>, L, .= 0) (<10,0,N>, N, .= 0) (<10,0,O>, O, .= 0) (<10,0,P>, P, .= 0) (<10,0,Q>, Q, .= 0)
(<11,0,A>, A, .= 0) (<11,0,B>, B, .= 0) (<11,0,D>, D, .= 0) (<11,0,E>, E, .= 0) (<11,0,J>, 1 + J, .+ 1) (<11,0,L>, L, .= 0) (<11,0,N>, N, .= 0) (<11,0,O>, O, .= 0) (<11,0,P>, P, .= 0) (<11,0,Q>, Q, .= 0)
(<12,0,A>, A, .= 0) (<12,0,B>, B, .= 0) (<12,0,D>, D, .= 0) (<12,0,E>, E, .= 0) (<12,0,J>, J, .= 0) (<12,0,L>, L, .= 0) (<12,0,N>, N, .= 0) (<12,0,O>, O, .= 0) (<12,0,P>, 0, .= 0) (<12,0,Q>, Q, .= 0)
(<13,0,A>, A, .= 0) (<13,0,B>, B, .= 0) (<13,0,D>, D, .= 0) (<13,0,E>, E, .= 0) (<13,0,J>, 2 + J, .+ 2) (<13,0,L>, L, .= 0) (<13,0,N>, N, .= 0) (<13,0,O>, O, .= 0) (<13,0,P>, P, .= 0) (<13,0,Q>, Q, .= 0)
(<14,0,A>, A, .= 0) (<14,0,B>, B, .= 0) (<14,0,D>, D, .= 0) (<14,0,E>, E, .= 0) (<14,0,J>, 1 + J, .+ 1) (<14,0,L>, L, .= 0) (<14,0,N>, N, .= 0) (<14,0,O>, O, .= 0) (<14,0,P>, P, .= 0) (<14,0,Q>, Q, .= 0)
(<15,0,A>, A, .= 0) (<15,0,B>, B, .= 0) (<15,0,D>, D, .= 0) (<15,0,E>, E, .= 0) (<15,0,J>, J, .= 0) (<15,0,L>, 0, .= 0) (<15,0,N>, N, .= 0) (<15,0,O>, O, .= 0) (<15,0,P>, P, .= 0) (<15,0,Q>, Q, .= 0)
(<16,0,A>, A, .= 0) (<16,0,B>, B, .= 0) (<16,0,D>, D, .= 0) (<16,0,E>, E, .= 0) (<16,0,J>, J, .= 0) (<16,0,L>, L, .= 0) (<16,0,N>, N, .= 0) (<16,0,O>, O, .= 0) (<16,0,P>, P, .= 0) (<16,0,Q>, Q, .= 0)
(<17,0,A>, A, .= 0) (<17,0,B>, B, .= 0) (<17,0,D>, D, .= 0) (<17,0,E>, E, .= 0) (<17,0,J>, J, .= 0) (<17,0,L>, L, .= 0) (<17,0,N>, N, .= 0) (<17,0,O>, O, .= 0) (<17,0,P>, P, .= 0) (<17,0,Q>, Q, .= 0)
(<18,0,A>, A, .= 0) (<18,0,B>, B, .= 0) (<18,0,D>, D, .= 0) (<18,0,E>, E, .= 0) (<18,0,J>, J, .= 0) (<18,0,L>, ?, .?) (<18,0,N>, N, .= 0) (<18,0,O>, O, .= 0) (<18,0,P>, P, .= 0) (<18,0,Q>, Q, .= 0)
(<19,0,A>, A, .= 0) (<19,0,B>, B, .= 0) (<19,0,D>, D, .= 0) (<19,0,E>, E, .= 0) (<19,0,J>, J, .= 0) (<19,0,L>, ?, .?) (<19,0,N>, N, .= 0) (<19,0,O>, O, .= 0) (<19,0,P>, P, .= 0) (<19,0,Q>, Q, .= 0)
(<20,0,A>, A, .= 0) (<20,0,B>, B, .= 0) (<20,0,D>, D, .= 0) (<20,0,E>, E, .= 0) (<20,0,J>, J, .= 0) (<20,0,L>, ?, .?) (<20,0,N>, N, .= 0) (<20,0,O>, O, .= 0) (<20,0,P>, P, .= 0) (<20,0,Q>, Q, .= 0)
(<21,0,A>, A, .= 0) (<21,0,B>, B, .= 0) (<21,0,D>, D, .= 0) (<21,0,E>, E, .= 0) (<21,0,J>, J, .= 0) (<21,0,L>, ?, .?) (<21,0,N>, N, .= 0) (<21,0,O>, O, .= 0) (<21,0,P>, P, .= 0) (<21,0,Q>, Q, .= 0)
(<22,0,A>, A, .= 0) (<22,0,B>, B, .= 0) (<22,0,D>, D, .= 0) (<22,0,E>, E, .= 0) (<22,0,J>, J, .= 0) (<22,0,L>, ?, .?) (<22,0,N>, N, .= 0) (<22,0,O>, O, .= 0) (<22,0,P>, P, .= 0) (<22,0,Q>, Q, .= 0)
(<23,0,A>, A, .= 0) (<23,0,B>, B, .= 0) (<23,0,D>, D, .= 0) (<23,0,E>, E, .= 0) (<23,0,J>, J, .= 0) (<23,0,L>, ?, .?) (<23,0,N>, N, .= 0) (<23,0,O>, O, .= 0) (<23,0,P>, P, .= 0) (<23,0,Q>, Q, .= 0)
(<24,0,A>, A, .= 0) (<24,0,B>, B, .= 0) (<24,0,D>, D, .= 0) (<24,0,E>, E, .= 0) (<24,0,J>, J, .= 0) (<24,0,L>, ?, .?) (<24,0,N>, N, .= 0) (<24,0,O>, O, .= 0) (<24,0,P>, P, .= 0) (<24,0,Q>, Q, .= 0)
(<25,0,A>, A, .= 0) (<25,0,B>, B, .= 0) (<25,0,D>, D, .= 0) (<25,0,E>, E, .= 0) (<25,0,J>, J, .= 0) (<25,0,L>, ?, .?) (<25,0,N>, N, .= 0) (<25,0,O>, O, .= 0) (<25,0,P>, P, .= 0) (<25,0,Q>, Q, .= 0)
(<26,0,A>, A, .= 0) (<26,0,B>, B, .= 0) (<26,0,D>, D, .= 0) (<26,0,E>, E, .= 0) (<26,0,J>, J, .= 0) (<26,0,L>, ?, .?) (<26,0,N>, N, .= 0) (<26,0,O>, O, .= 0) (<26,0,P>, P, .= 0) (<26,0,Q>, Q, .= 0)
(<27,0,A>, A, .= 0) (<27,0,B>, B, .= 0) (<27,0,D>, D, .= 0) (<27,0,E>, E, .= 0) (<27,0,J>, 1 + J, .+ 1) (<27,0,L>, 0, .= 0) (<27,0,N>, N, .= 0) (<27,0,O>, O, .= 0) (<27,0,P>, P, .= 0) (<27,0,Q>, Q, .= 0)
(<28,0,A>, A, .= 0) (<28,0,B>, B, .= 0) (<28,0,D>, D, .= 0) (<28,0,E>, E, .= 0) (<28,0,J>, 1 + J, .+ 1) (<28,0,L>, L, .= 0) (<28,0,N>, N, .= 0) (<28,0,O>, O, .= 0) (<28,0,P>, P, .= 0) (<28,0,Q>, Q, .= 0)
(<29,0,A>, A, .= 0) (<29,0,B>, B, .= 0) (<29,0,D>, D, .= 0) (<29,0,E>, E, .= 0) (<29,0,J>, 1 + J, .+ 1) (<29,0,L>, L, .= 0) (<29,0,N>, N, .= 0) (<29,0,O>, O, .= 0) (<29,0,P>, P, .= 0) (<29,0,Q>, Q, .= 0)
(<30,0,A>, A, .= 0) (<30,0,B>, B, .= 0) (<30,0,D>, D, .= 0) (<30,0,E>, E, .= 0) (<30,0,J>, 1 + J, .+ 1) (<30,0,L>, L, .= 0) (<30,0,N>, N, .= 0) (<30,0,O>, O, .= 0) (<30,0,P>, P, .= 0) (<30,0,Q>, Q, .= 0)
(<31,0,A>, A, .= 0) (<31,0,B>, B, .= 0) (<31,0,D>, D, .= 0) (<31,0,E>, E, .= 0) (<31,0,J>, J, .= 0) (<31,0,L>, L, .= 0) (<31,0,N>, N, .= 0) (<31,0,O>, O, .= 0) (<31,0,P>, P, .= 0) (<31,0,Q>, Q, .= 0)
(<32,0,A>, A, .= 0) (<32,0,B>, B, .= 0) (<32,0,D>, D, .= 0) (<32,0,E>, E, .= 0) (<32,0,J>, J, .= 0) (<32,0,L>, L, .= 0) (<32,0,N>, N, .= 0) (<32,0,O>, 1 + O, .+ 1) (<32,0,P>, P, .= 0) (<32,0,Q>, Q, .= 0)
(<33,0,A>, A, .= 0) (<33,0,B>, B, .= 0) (<33,0,D>, D, .= 0) (<33,0,E>, E, .= 0) (<33,0,J>, J, .= 0) (<33,0,L>, ?, .?) (<33,0,N>, N, .= 0) (<33,0,O>, O, .= 0) (<33,0,P>, P, .= 0) (<33,0,Q>, Q, .= 0)
(<34,0,A>, A, .= 0) (<34,0,B>, B, .= 0) (<34,0,D>, D, .= 0) (<34,0,E>, E, .= 0) (<34,0,J>, J, .= 0) (<34,0,L>, ?, .?) (<34,0,N>, N, .= 0) (<34,0,O>, O, .= 0) (<34,0,P>, P, .= 0) (<34,0,Q>, Q, .= 0)
(<35,0,A>, A, .= 0) (<35,0,B>, B, .= 0) (<35,0,D>, D, .= 0) (<35,0,E>, E, .= 0) (<35,0,J>, J, .= 0) (<35,0,L>, ?, .?) (<35,0,N>, N, .= 0) (<35,0,O>, O, .= 0) (<35,0,P>, P, .= 0) (<35,0,Q>, Q, .= 0)
(<36,0,A>, A, .= 0) (<36,0,B>, B, .= 0) (<36,0,D>, D, .= 0) (<36,0,E>, E, .= 0) (<36,0,J>, J, .= 0) (<36,0,L>, L, .= 0) (<36,0,N>, N, .= 0) (<36,0,O>, O, .= 0) (<36,0,P>, P, .= 0) (<36,0,Q>, 1 + Q, .+ 1)
(<37,0,A>, A, .= 0) (<37,0,B>, B, .= 0) (<37,0,D>, D, .= 0) (<37,0,E>, E, .= 0) (<37,0,J>, J, .= 0) (<37,0,L>, L, .= 0) (<37,0,N>, N, .= 0) (<37,0,O>, O, .= 0) (<37,0,P>, P, .= 0) (<37,0,Q>, 1 + Q, .+ 1)
(<38,0,A>, A, .= 0) (<38,0,B>, B, .= 0) (<38,0,D>, D, .= 0) (<38,0,E>, E, .= 0) (<38,0,J>, J, .= 0) (<38,0,L>, L, .= 0) (<38,0,N>, N, .= 0) (<38,0,O>, O, .= 0) (<38,0,P>, P, .= 0) (<38,0,Q>, Q, .= 0)
(<39,0,A>, A, .= 0) (<39,0,B>, B, .= 0) (<39,0,D>, D, .= 0) (<39,0,E>, E, .= 0) (<39,0,J>, J, .= 0) (<39,0,L>, L, .= 0) (<39,0,N>, N, .= 0) (<39,0,O>, O, .= 0) (<39,0,P>, P, .= 0) (<39,0,Q>, Q, .= 0)
(<40,0,A>, A, .= 0) (<40,0,B>, B, .= 0) (<40,0,D>, D, .= 0) (<40,0,E>, E, .= 0) (<40,0,J>, J, .= 0) (<40,0,L>, L, .= 0) (<40,0,N>, N, .= 0) (<40,0,O>, O, .= 0) (<40,0,P>, P, .= 0) (<40,0,Q>, Q, .= 0)
(<41,0,A>, A, .= 0) (<41,0,B>, B, .= 0) (<41,0,D>, D, .= 0) (<41,0,E>, E, .= 0) (<41,0,J>, J, .= 0) (<41,0,L>, L, .= 0) (<41,0,N>, N, .= 0) (<41,0,O>, O, .= 0) (<41,0,P>, P, .= 0) (<41,0,Q>, Q, .= 0)
(<42,0,A>, A, .= 0) (<42,0,B>, B, .= 0) (<42,0,D>, D, .= 0) (<42,0,E>, E, .= 0) (<42,0,J>, J, .= 0) (<42,0,L>, L, .= 0) (<42,0,N>, N, .= 0) (<42,0,O>, O, .= 0) (<42,0,P>, P, .= 0) (<42,0,Q>, Q, .= 0)
(<43,0,A>, A, .= 0) (<43,0,B>, B, .= 0) (<43,0,D>, D, .= 0) (<43,0,E>, E, .= 0) (<43,0,J>, J, .= 0) (<43,0,L>, L, .= 0) (<43,0,N>, N, .= 0) (<43,0,O>, O, .= 0) (<43,0,P>, P, .= 0) (<43,0,Q>, Q, .= 0)
(<44,0,A>, A, .= 0) (<44,0,B>, B, .= 0) (<44,0,D>, D, .= 0) (<44,0,E>, E, .= 0) (<44,0,J>, J, .= 0) (<44,0,L>, L, .= 0) (<44,0,N>, N, .= 0) (<44,0,O>, O, .= 0) (<44,0,P>, P, .= 0) (<44,0,Q>, Q, .= 0)
(<45,0,A>, A, .= 0) (<45,0,B>, B, .= 0) (<45,0,D>, D, .= 0) (<45,0,E>, E, .= 0) (<45,0,J>, J, .= 0) (<45,0,L>, L, .= 0) (<45,0,N>, N, .= 0) (<45,0,O>, O, .= 0) (<45,0,P>, 0, .= 0) (<45,0,Q>, Q, .= 0)
(<46,0,A>, A, .= 0) (<46,0,B>, B, .= 0) (<46,0,D>, D, .= 0) (<46,0,E>, E, .= 0) (<46,0,J>, J, .= 0) (<46,0,L>, L, .= 0) (<46,0,N>, N, .= 0) (<46,0,O>, O, .= 0) (<46,0,P>, P, .= 0) (<46,0,Q>, Q, .= 0)
* Step 3: SizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
5. f31(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
10. f50(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
11. f57(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (?,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (?,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (?,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
31. f118(A,B,D,E,J,L,N,O,P,Q) -> f1(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (?,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (?,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (?,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},5->{5,42},6->{7,8,12,40},7->{9
,39},8->{9,39},9->{9,39},10->{10,38},11->{11,37},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32}
,16->{18,19,20,32},17->{18,19,20,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25
,26},23->{24,25,26},24->{27,28,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18
,19,20,32},30->{30,31},31->{},32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7
,8,12,40},38->{11,37},39->{10,38},40->{14,33,34,35},41->{30,31},42->{6,41},43->{5,42},44->{5,42},45->{6,41}
,46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, ?) (< 0,0,B>, ?) (< 0,0,D>, ?) (< 0,0,E>, ?) (< 0,0,J>, ?) (< 0,0,L>, ?) (< 0,0,N>, ?) (< 0,0,O>, ?) (< 0,0,P>, ?) (< 0,0,Q>, ?)
(< 1,0,A>, ?) (< 1,0,B>, ?) (< 1,0,D>, ?) (< 1,0,E>, ?) (< 1,0,J>, ?) (< 1,0,L>, ?) (< 1,0,N>, ?) (< 1,0,O>, ?) (< 1,0,P>, ?) (< 1,0,Q>, ?)
(< 2,0,A>, ?) (< 2,0,B>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 2,0,J>, ?) (< 2,0,L>, ?) (< 2,0,N>, ?) (< 2,0,O>, ?) (< 2,0,P>, ?) (< 2,0,Q>, ?)
(< 3,0,A>, ?) (< 3,0,B>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?) (< 3,0,J>, ?) (< 3,0,L>, ?) (< 3,0,N>, ?) (< 3,0,O>, ?) (< 3,0,P>, ?) (< 3,0,Q>, ?)
(< 4,0,A>, ?) (< 4,0,B>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?) (< 4,0,J>, ?) (< 4,0,L>, ?) (< 4,0,N>, ?) (< 4,0,O>, ?) (< 4,0,P>, ?) (< 4,0,Q>, ?)
(< 5,0,A>, ?) (< 5,0,B>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 5,0,J>, ?) (< 5,0,L>, ?) (< 5,0,N>, ?) (< 5,0,O>, ?) (< 5,0,P>, ?) (< 5,0,Q>, ?)
(< 6,0,A>, ?) (< 6,0,B>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, ?) (< 6,0,O>, ?) (< 6,0,P>, ?) (< 6,0,Q>, ?)
(< 7,0,A>, ?) (< 7,0,B>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, ?) (< 7,0,O>, ?) (< 7,0,P>, ?) (< 7,0,Q>, ?)
(< 8,0,A>, ?) (< 8,0,B>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, ?) (< 8,0,O>, ?) (< 8,0,P>, ?) (< 8,0,Q>, ?)
(< 9,0,A>, ?) (< 9,0,B>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?) (< 9,0,J>, ?) (< 9,0,L>, ?) (< 9,0,N>, ?) (< 9,0,O>, ?) (< 9,0,P>, ?) (< 9,0,Q>, ?)
(<10,0,A>, ?) (<10,0,B>, ?) (<10,0,D>, ?) (<10,0,E>, ?) (<10,0,J>, ?) (<10,0,L>, ?) (<10,0,N>, ?) (<10,0,O>, ?) (<10,0,P>, ?) (<10,0,Q>, ?)
(<11,0,A>, ?) (<11,0,B>, ?) (<11,0,D>, ?) (<11,0,E>, ?) (<11,0,J>, ?) (<11,0,L>, ?) (<11,0,N>, ?) (<11,0,O>, ?) (<11,0,P>, ?) (<11,0,Q>, ?)
(<12,0,A>, ?) (<12,0,B>, ?) (<12,0,D>, ?) (<12,0,E>, ?) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, ?) (<12,0,O>, ?) (<12,0,P>, ?) (<12,0,Q>, ?)
(<13,0,A>, ?) (<13,0,B>, ?) (<13,0,D>, ?) (<13,0,E>, ?) (<13,0,J>, ?) (<13,0,L>, ?) (<13,0,N>, ?) (<13,0,O>, ?) (<13,0,P>, ?) (<13,0,Q>, ?)
(<14,0,A>, ?) (<14,0,B>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<14,0,J>, ?) (<14,0,L>, ?) (<14,0,N>, ?) (<14,0,O>, ?) (<14,0,P>, ?) (<14,0,Q>, ?)
(<15,0,A>, ?) (<15,0,B>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<15,0,J>, ?) (<15,0,L>, ?) (<15,0,N>, ?) (<15,0,O>, ?) (<15,0,P>, ?) (<15,0,Q>, ?)
(<16,0,A>, ?) (<16,0,B>, ?) (<16,0,D>, ?) (<16,0,E>, ?) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, ?) (<16,0,O>, ?) (<16,0,P>, ?) (<16,0,Q>, ?)
(<17,0,A>, ?) (<17,0,B>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, ?) (<17,0,O>, ?) (<17,0,P>, ?) (<17,0,Q>, ?)
(<18,0,A>, ?) (<18,0,B>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<18,0,J>, ?) (<18,0,L>, ?) (<18,0,N>, ?) (<18,0,O>, ?) (<18,0,P>, ?) (<18,0,Q>, ?)
(<19,0,A>, ?) (<19,0,B>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<19,0,J>, ?) (<19,0,L>, ?) (<19,0,N>, ?) (<19,0,O>, ?) (<19,0,P>, ?) (<19,0,Q>, ?)
(<20,0,A>, ?) (<20,0,B>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<20,0,J>, ?) (<20,0,L>, ?) (<20,0,N>, ?) (<20,0,O>, ?) (<20,0,P>, ?) (<20,0,Q>, ?)
(<21,0,A>, ?) (<21,0,B>, ?) (<21,0,D>, ?) (<21,0,E>, ?) (<21,0,J>, ?) (<21,0,L>, ?) (<21,0,N>, ?) (<21,0,O>, ?) (<21,0,P>, ?) (<21,0,Q>, ?)
(<22,0,A>, ?) (<22,0,B>, ?) (<22,0,D>, ?) (<22,0,E>, ?) (<22,0,J>, ?) (<22,0,L>, ?) (<22,0,N>, ?) (<22,0,O>, ?) (<22,0,P>, ?) (<22,0,Q>, ?)
(<23,0,A>, ?) (<23,0,B>, ?) (<23,0,D>, ?) (<23,0,E>, ?) (<23,0,J>, ?) (<23,0,L>, ?) (<23,0,N>, ?) (<23,0,O>, ?) (<23,0,P>, ?) (<23,0,Q>, ?)
(<24,0,A>, ?) (<24,0,B>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<24,0,J>, ?) (<24,0,L>, ?) (<24,0,N>, ?) (<24,0,O>, ?) (<24,0,P>, ?) (<24,0,Q>, ?)
(<25,0,A>, ?) (<25,0,B>, ?) (<25,0,D>, ?) (<25,0,E>, ?) (<25,0,J>, ?) (<25,0,L>, ?) (<25,0,N>, ?) (<25,0,O>, ?) (<25,0,P>, ?) (<25,0,Q>, ?)
(<26,0,A>, ?) (<26,0,B>, ?) (<26,0,D>, ?) (<26,0,E>, ?) (<26,0,J>, ?) (<26,0,L>, ?) (<26,0,N>, ?) (<26,0,O>, ?) (<26,0,P>, ?) (<26,0,Q>, ?)
(<27,0,A>, ?) (<27,0,B>, ?) (<27,0,D>, ?) (<27,0,E>, ?) (<27,0,J>, ?) (<27,0,L>, ?) (<27,0,N>, ?) (<27,0,O>, ?) (<27,0,P>, ?) (<27,0,Q>, ?)
(<28,0,A>, ?) (<28,0,B>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<28,0,J>, ?) (<28,0,L>, ?) (<28,0,N>, ?) (<28,0,O>, ?) (<28,0,P>, ?) (<28,0,Q>, ?)
(<29,0,A>, ?) (<29,0,B>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<29,0,J>, ?) (<29,0,L>, ?) (<29,0,N>, ?) (<29,0,O>, ?) (<29,0,P>, ?) (<29,0,Q>, ?)
(<30,0,A>, ?) (<30,0,B>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<30,0,J>, ?) (<30,0,L>, ?) (<30,0,N>, ?) (<30,0,O>, ?) (<30,0,P>, ?) (<30,0,Q>, ?)
(<31,0,A>, ?) (<31,0,B>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<31,0,J>, ?) (<31,0,L>, ?) (<31,0,N>, ?) (<31,0,O>, ?) (<31,0,P>, ?) (<31,0,Q>, ?)
(<32,0,A>, ?) (<32,0,B>, ?) (<32,0,D>, ?) (<32,0,E>, ?) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, ?) (<32,0,O>, ?) (<32,0,P>, ?) (<32,0,Q>, ?)
(<33,0,A>, ?) (<33,0,B>, ?) (<33,0,D>, ?) (<33,0,E>, ?) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, ?) (<33,0,O>, ?) (<33,0,P>, ?) (<33,0,Q>, ?)
(<34,0,A>, ?) (<34,0,B>, ?) (<34,0,D>, ?) (<34,0,E>, ?) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, ?) (<34,0,O>, ?) (<34,0,P>, ?) (<34,0,Q>, ?)
(<35,0,A>, ?) (<35,0,B>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, ?) (<35,0,O>, ?) (<35,0,P>, ?) (<35,0,Q>, ?)
(<36,0,A>, ?) (<36,0,B>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, ?) (<36,0,O>, ?) (<36,0,P>, ?) (<36,0,Q>, ?)
(<37,0,A>, ?) (<37,0,B>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, ?) (<37,0,O>, ?) (<37,0,P>, ?) (<37,0,Q>, ?)
(<38,0,A>, ?) (<38,0,B>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, ?) (<38,0,O>, ?) (<38,0,P>, ?) (<38,0,Q>, ?)
(<39,0,A>, ?) (<39,0,B>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, ?) (<39,0,O>, ?) (<39,0,P>, ?) (<39,0,Q>, ?)
(<40,0,A>, ?) (<40,0,B>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, ?) (<40,0,O>, ?) (<40,0,P>, ?) (<40,0,Q>, ?)
(<41,0,A>, ?) (<41,0,B>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, ?) (<41,0,O>, ?) (<41,0,P>, ?) (<41,0,Q>, ?)
(<42,0,A>, ?) (<42,0,B>, ?) (<42,0,D>, ?) (<42,0,E>, ?) (<42,0,J>, ?) (<42,0,L>, ?) (<42,0,N>, ?) (<42,0,O>, ?) (<42,0,P>, ?) (<42,0,Q>, ?)
(<43,0,A>, ?) (<43,0,B>, ?) (<43,0,D>, ?) (<43,0,E>, ?) (<43,0,J>, ?) (<43,0,L>, ?) (<43,0,N>, ?) (<43,0,O>, ?) (<43,0,P>, ?) (<43,0,Q>, ?)
(<44,0,A>, ?) (<44,0,B>, ?) (<44,0,D>, ?) (<44,0,E>, ?) (<44,0,J>, ?) (<44,0,L>, ?) (<44,0,N>, ?) (<44,0,O>, ?) (<44,0,P>, ?) (<44,0,Q>, ?)
(<45,0,A>, ?) (<45,0,B>, ?) (<45,0,D>, ?) (<45,0,E>, ?) (<45,0,J>, ?) (<45,0,L>, ?) (<45,0,N>, ?) (<45,0,O>, ?) (<45,0,P>, ?) (<45,0,Q>, ?)
(<46,0,A>, ?) (<46,0,B>, ?) (<46,0,D>, ?) (<46,0,E>, ?) (<46,0,J>, ?) (<46,0,L>, ?) (<46,0,N>, ?) (<46,0,O>, ?) (<46,0,P>, ?) (<46,0,Q>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 5,0,A>, A) (< 5,0,B>, ?) (< 5,0,D>, 2*A) (< 5,0,E>, 4*A) (< 5,0,J>, 1 + A) (< 5,0,L>, ?) (< 5,0,N>, N) (< 5,0,O>, O) (< 5,0,P>, P) (< 5,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,D>, 2*A) (<10,0,E>, 4*A) (<10,0,J>, 1 + A) (<10,0,L>, ?) (<10,0,N>, N) (<10,0,O>, ?) (<10,0,P>, P) (<10,0,Q>, 0)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,D>, 2*A) (<11,0,E>, 4*A) (<11,0,J>, 1 + A) (<11,0,L>, ?) (<11,0,N>, N) (<11,0,O>, ?) (<11,0,P>, P) (<11,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<31,0,A>, A) (<31,0,B>, ?) (<31,0,D>, 2*A) (<31,0,E>, 4*A) (<31,0,J>, ?) (<31,0,L>, ?) (<31,0,N>, N) (<31,0,O>, ?) (<31,0,P>, P) (<31,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
* Step 4: UnsatPaths WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
5. f31(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
10. f50(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
11. f57(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (?,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (?,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (?,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
31. f118(A,B,D,E,J,L,N,O,P,Q) -> f1(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (?,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (?,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (?,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},5->{5,42},6->{7,8,12,40},7->{9
,39},8->{9,39},9->{9,39},10->{10,38},11->{11,37},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32}
,16->{18,19,20,32},17->{18,19,20,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25
,26},23->{24,25,26},24->{27,28,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18
,19,20,32},30->{30,31},31->{},32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7
,8,12,40},38->{11,37},39->{10,38},40->{14,33,34,35},41->{30,31},42->{6,41},43->{5,42},44->{5,42},45->{6,41}
,46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 5,0,A>, A) (< 5,0,B>, ?) (< 5,0,D>, 2*A) (< 5,0,E>, 4*A) (< 5,0,J>, 1 + A) (< 5,0,L>, ?) (< 5,0,N>, N) (< 5,0,O>, O) (< 5,0,P>, P) (< 5,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,D>, 2*A) (<10,0,E>, 4*A) (<10,0,J>, 1 + A) (<10,0,L>, ?) (<10,0,N>, N) (<10,0,O>, ?) (<10,0,P>, P) (<10,0,Q>, 0)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,D>, 2*A) (<11,0,E>, 4*A) (<11,0,J>, 1 + A) (<11,0,L>, ?) (<11,0,N>, N) (<11,0,O>, ?) (<11,0,P>, P) (<11,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<31,0,A>, A) (<31,0,B>, ?) (<31,0,D>, 2*A) (<31,0,E>, 4*A) (<31,0,J>, ?) (<31,0,L>, ?) (<31,0,N>, N) (<31,0,O>, ?) (<31,0,P>, P) (<31,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(38,11),(39,10),(43,5),(44,5)]
* Step 5: UnreachableRules WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
5. f31(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
10. f50(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
11. f57(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (?,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (?,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (?,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
31. f118(A,B,D,E,J,L,N,O,P,Q) -> f1(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (?,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (?,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (?,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},5->{5,42},6->{7,8,12,40},7->{9
,39},8->{9,39},9->{9,39},10->{10,38},11->{11,37},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32}
,16->{18,19,20,32},17->{18,19,20,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25
,26},23->{24,25,26},24->{27,28,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18
,19,20,32},30->{30,31},31->{},32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7
,8,12,40},38->{37},39->{38},40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43
,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 5,0,A>, A) (< 5,0,B>, ?) (< 5,0,D>, 2*A) (< 5,0,E>, 4*A) (< 5,0,J>, 1 + A) (< 5,0,L>, ?) (< 5,0,N>, N) (< 5,0,O>, O) (< 5,0,P>, P) (< 5,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,D>, 2*A) (<10,0,E>, 4*A) (<10,0,J>, 1 + A) (<10,0,L>, ?) (<10,0,N>, N) (<10,0,O>, ?) (<10,0,P>, P) (<10,0,Q>, 0)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,D>, 2*A) (<11,0,E>, 4*A) (<11,0,J>, 1 + A) (<11,0,L>, ?) (<11,0,N>, N) (<11,0,O>, ?) (<11,0,P>, P) (<11,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<31,0,A>, A) (<31,0,B>, ?) (<31,0,D>, 2*A) (<31,0,E>, 4*A) (<31,0,J>, ?) (<31,0,L>, ?) (<31,0,N>, N) (<31,0,O>, ?) (<31,0,P>, P) (<31,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [5,10,11]
* Step 6: LeafRules WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (?,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (?,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (?,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
31. f118(A,B,D,E,J,L,N,O,P,Q) -> f1(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (?,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (?,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (?,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{}
,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38}
,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<31,0,A>, A) (<31,0,B>, ?) (<31,0,D>, 2*A) (<31,0,E>, 4*A) (<31,0,J>, ?) (<31,0,L>, ?) (<31,0,N>, N) (<31,0,O>, ?) (<31,0,P>, P) (<31,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
LeafRules
+ Details:
The following transitions are estimated by its predecessors and are removed [31]
* Step 7: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (?,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (?,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (?,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (?,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (?,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (?,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = 0
p(f107) = 0
p(f118) = 0
p(f13) = 1
p(f2) = 1
p(f24) = 0
p(f31) = 0
p(f37) = 0
p(f40) = 0
p(f44) = 0
p(f50) = 0
p(f57) = 0
p(f64) = 0
p(f71) = 0
p(f86) = 0
p(f91) = 0
p(f99) = 0
The following rules are strictly oriented:
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1
> 0
= f24(A,B,D,E,J,L,N,O,P,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f40(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f64(A,B,D,E,J,L,N,O,0,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f37(A,B,D,E,J,L,N,O,0,Q)
* Step 8: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (?,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (?,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (?,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (?,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (?,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (?,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (?,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = x1 + -1*x5
p(f107) = x1 + -1*x5
p(f118) = 1 + x1 + -1*x5
p(f13) = x1 + -1*x3
p(f2) = -1*x1
p(f24) = 1 + x1 + -1*x5
p(f31) = 1 + x1 + -1*x5
p(f37) = 1 + x1 + -1*x5
p(f40) = 1 + x1 + -1*x5
p(f44) = 1 + x1 + -1*x5
p(f50) = 1 + x1 + -1*x5
p(f57) = 1 + x1 + -1*x5
p(f64) = 1 + x1 + -1*x5
p(f71) = 1 + x1 + -1*x5
p(f86) = 1 + x1 + -1*x5
p(f91) = 1 + x1 + -1*x5
p(f99) = x1 + -1*x5
The following rules are strictly oriented:
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
> A + -1*J
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
> A + -1*J
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
> A + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
> A + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
> A + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
> A + -1*J
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = -1*A
>= -1*A
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = A + -1*D
>= A + -1*D
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = A + -1*D
>= A + -1*D
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = A + -1*D
>= A + -1*D
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f40(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f64(A,B,D,E,J,L,N,O,0,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= -1 + A + -1*J
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= A + -1*J
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = A + -1*J
>= A + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = A + -1*J
>= A + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = A + -1*J
>= A + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = A + -1*J
>= A + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = A + -1*J
>= A + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = A + -1*J
>= A + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = A + -1*J
>= A + -1*J
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = A + -1*J
>= A + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = A + -1*J
>= A + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + A + -1*J
>= 1 + A + -1*J
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = A + -1*D
>= 1 + A + -1*J
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 9: KnowledgePropagation WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (?,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (?,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (?,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (?,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 10: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = 1
p(f107) = 1
p(f118) = 0
p(f13) = 1
p(f2) = 1
p(f24) = 1
p(f31) = 1
p(f37) = 1
p(f40) = 1
p(f44) = 1
p(f50) = 1
p(f57) = 1
p(f64) = 1
p(f71) = 1
p(f86) = 1
p(f91) = 1
p(f99) = 1
The following rules are strictly oriented:
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1
> 0
= f118(A,B,D,E,J,L,N,O,P,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f40(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f64(A,B,D,E,J,L,N,O,0,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f71(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1
>= 1
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 11: KnowledgePropagation WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (?,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (?,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 12: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = 1 + x3 + -1*x5
p(f107) = 1 + x3 + -1*x5
p(f118) = 1 + x3 + -1*x5
p(f13) = 0
p(f2) = 0
p(f24) = 1 + x3 + -1*x5
p(f31) = 1 + x3 + -1*x5
p(f37) = 1 + x3 + -1*x5
p(f40) = 1 + x3 + -1*x5
p(f44) = 1 + x3 + -1*x5
p(f50) = 1 + x3 + -1*x5
p(f57) = 1 + x3 + -1*x5
p(f64) = 1 + x3 + -1*x5
p(f71) = 1 + x3 + -1*x5
p(f86) = 1 + x3 + -1*x5
p(f91) = 1 + x3 + -1*x5
p(f99) = 1 + x3 + -1*x5
The following rules are strictly oriented:
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 0
>= 0
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f64(A,B,D,E,J,L,N,O,0,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= -1 + D + -1*J
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 0
>= 1 + D + -1*J
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 13: KnowledgePropagation WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 14: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = x4 + -1*x5
p(f107) = x4 + -1*x5
p(f118) = 1 + x4 + -1*x5
p(f13) = -1*x3 + x4
p(f2) = 2*x1
p(f24) = 1 + x4 + -1*x5
p(f31) = 1 + x4 + -1*x5
p(f37) = 1 + x4 + -1*x5
p(f40) = 1 + x4 + -1*x5
p(f44) = 1 + x4 + -1*x5
p(f50) = 1 + x4 + -1*x5
p(f57) = 1 + x4 + -1*x5
p(f64) = 1 + x4 + -1*x5
p(f71) = 1 + x4 + -1*x5
p(f86) = 1 + x4 + -1*x5
p(f91) = 1 + x4 + -1*x5
p(f99) = x4 + -1*x5
The following rules are strictly oriented:
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
> -1 + E + -1*J
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 2*A
>= 2*A
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = -1*D + E
>= -1*D + E
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = -1*D + E
>= -1*D + E
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = -1*D + E
>= -1*D + E
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= E + -1*J
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f40(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= E + -1*J
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f64(A,B,D,E,J,L,N,O,0,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= E + -1*J
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= E + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= E + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= E + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = E + -1*J
>= E + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = E + -1*J
>= E + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = E + -1*J
>= E + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = E + -1*J
>= E + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = E + -1*J
>= E + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = E + -1*J
>= E + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = E + -1*J
>= E + -1*J
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = E + -1*J
>= E + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = E + -1*J
>= E + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= E + -1*J
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + E + -1*J
>= 1 + E + -1*J
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = -1*D + E
>= 1 + E + -1*J
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 15: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (?,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = x3 + -1*x5
p(f107) = x3 + -1*x5
p(f118) = 1 + x3 + -1*x5
p(f13) = 1 + x3 + -1*x5
p(f2) = 1 + 2*x1 + -1*x5
p(f24) = 1 + x3 + -1*x5
p(f31) = 1 + x3 + -1*x5
p(f37) = 1 + x3 + -1*x5
p(f40) = 1 + x3 + -1*x5
p(f44) = 1 + x3 + -1*x5
p(f50) = 1 + x3 + -1*x5
p(f57) = 1 + x3 + -1*x5
p(f64) = 1 + x3 + -1*x5
p(f71) = 1 + x3 + -1*x5
p(f86) = 1 + x3 + -1*x5
p(f91) = 1 + x3 + -1*x5
p(f99) = x3 + -1*x5
The following rules are strictly oriented:
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 1 + 2*A + -1*J
>= 1 + 2*A + -1*J
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f64(A,B,D,E,J,L,N,O,0,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= -1 + D + -1*J
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 16: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (?,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (1 + 2*A + J,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = x3 + -1*x5
p(f107) = x3 + -1*x5
p(f118) = 1 + x3 + -1*x5
p(f13) = 1 + x3 + -1*x5
p(f2) = 1 + 2*x1 + -1*x5
p(f24) = 1 + x3 + -1*x5
p(f31) = 1 + x3 + -1*x5
p(f37) = 1 + x3 + -1*x5
p(f40) = 1 + x3 + -1*x5
p(f44) = 1 + x3 + -1*x5
p(f50) = 1 + x3 + -1*x5
p(f57) = 1 + x3 + -1*x5
p(f64) = 1 + x3 + -1*x5
p(f71) = 1 + x3 + -1*x5
p(f86) = 1 + x3 + -1*x5
p(f91) = 1 + x3 + -1*x5
p(f99) = x3 + -1*x5
The following rules are strictly oriented:
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 1 + 2*A + -1*J
>= 1 + 2*A + -1*J
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f64(A,B,D,E,J,L,N,O,0,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= -1 + D + -1*J
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 17: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (?,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (1 + 2*A + J,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (1 + 2*A + J,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = x3 + -1*x5
p(f107) = x3 + -1*x5
p(f118) = 1 + x3 + -1*x5
p(f13) = 1 + x3 + -1*x5
p(f2) = 1 + 2*x1 + -1*x5
p(f24) = 1 + x3 + -1*x5
p(f31) = 1 + x3 + -1*x5
p(f37) = 1 + x3 + -1*x5
p(f40) = 1 + x3 + -1*x5
p(f44) = 1 + x3 + -1*x5
p(f50) = 1 + x3 + -1*x5
p(f57) = 1 + x3 + -1*x5
p(f64) = 1 + x3 + -1*x5
p(f71) = 1 + x3 + -1*x5
p(f86) = 1 + x3 + -1*x5
p(f91) = 1 + x3 + -1*x5
p(f99) = x3 + -1*x5
The following rules are strictly oriented:
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
> D + -1*J
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 1 + 2*A + -1*J
>= 1 + 2*A + -1*J
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f64(A,B,D,E,J,L,N,O,0,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= -1 + D + -1*J
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = D + -1*J
>= D + -1*J
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= D + -1*J
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + D + -1*J
>= 1 + D + -1*J
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 18: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (1 + 2*A + J,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (1 + 2*A + J,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (1 + 2*A + J,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (?,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = x7 + -1*x8
p(f107) = x7 + -1*x8
p(f118) = 1 + x7 + -1*x8
p(f13) = 1 + x7 + -1*x8
p(f2) = 1 + x7 + -1*x8
p(f24) = 1 + x7 + -1*x8
p(f31) = 1 + x7 + -1*x8
p(f37) = 1 + x7 + -1*x8
p(f40) = x7 + -1*x8
p(f44) = x7 + -1*x8
p(f50) = x7 + -1*x8
p(f57) = x7 + -1*x8
p(f64) = x7 + -1*x8
p(f71) = x7 + -1*x8
p(f86) = x7 + -1*x8
p(f91) = x7 + -1*x8
p(f99) = x7 + -1*x8
The following rules are strictly oriented:
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
> N + -1*O
= f40(A,B,D,E,J,L,N,O,P,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f64(A,B,D,E,J,L,N,O,0,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = N + -1*O
>= N + -1*O
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + N + -1*O
>= 1 + N + -1*O
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 19: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (1 + 2*A + J,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (1 + 2*A + J,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (1 + 2*A + J,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (1 + N + O,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = 1 + -1*x10
p(f107) = 1 + -1*x10
p(f118) = 1 + -1*x10
p(f13) = 1 + -1*x10
p(f2) = 1 + -1*x10
p(f24) = 1 + -1*x10
p(f31) = 1 + -1*x10
p(f37) = 1 + -1*x10
p(f40) = 1 + -1*x10
p(f44) = 1 + -1*x10
p(f50) = 1 + -1*x10
p(f57) = -1*x10
p(f64) = -1*x10
p(f71) = 1 + -1*x10
p(f86) = 1 + -1*x10
p(f91) = 1 + -1*x10
p(f99) = 1 + -1*x10
The following rules are strictly oriented:
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
> -1*Q
= f64(A,B,D,E,J,L,N,O,0,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f40(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= -1*Q
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 20: KnowledgePropagation WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (1 + 2*A + J,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (1 + 2*A + J,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (1 + 2*A + J,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (1 + N + O,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (1 + Q,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 21: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (1 + 2*A + J,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (1 + 2*A + J,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (1 + 2*A + J,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (1 + N + O,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (1 + Q,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (1 + 2*A + Q,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = 1 + -1*x10
p(f107) = 1 + -1*x10
p(f118) = 1 + -1*x10
p(f13) = 1 + -1*x10
p(f2) = 1 + -1*x10
p(f24) = 1 + -1*x10
p(f31) = 1 + -1*x10
p(f37) = 1 + -1*x10
p(f40) = 1 + -1*x10
p(f44) = -1*x10
p(f50) = -1*x10
p(f57) = -1*x10
p(f64) = -1*x10
p(f71) = 1 + -1*x10
p(f86) = 1 + -1*x10
p(f91) = 1 + -1*x10
p(f99) = 1 + -1*x10
The following rules are strictly oriented:
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
> -1*Q
= f44(A,B,D,E,J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
> -1*Q
= f64(A,B,D,E,J,L,N,O,0,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f40(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= -1*Q
= f44(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 22: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (1 + 2*A + J,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (1 + 2*A + J,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (1 + 2*A + J,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (1 + N + O,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (1 + Q,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (1 + 2*A + Q,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f103) = 1 + -1*x10
p(f107) = 1 + -1*x10
p(f118) = 1 + -1*x10
p(f13) = 1 + -1*x10
p(f2) = 1 + -1*x10
p(f24) = 1 + -1*x10
p(f31) = 1 + -1*x10
p(f37) = 1 + -1*x10
p(f40) = 1 + -1*x10
p(f44) = -1*x10
p(f50) = -1*x10
p(f57) = -1*x10
p(f64) = -1*x10
p(f71) = 1 + -1*x10
p(f86) = 1 + -1*x10
p(f91) = 1 + -1*x10
p(f99) = 1 + -1*x10
The following rules are strictly oriented:
[0 >= 1 + P && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
> -1*Q
= f44(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && 0 >= Q] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
> -1*Q
= f44(A,B,D,E,J,L,N,O,P,Q)
[0 >= Q && P = 0] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
> -1*Q
= f64(A,B,D,E,J,L,N,O,0,Q)
The following rules are weakly oriented:
[1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==>
f2(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,0,2*A,4*A,J,L,N,O,P,Q)
[D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,B,D,E,1 + J,0,N,O,P,Q)
[C1 >= 2 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[0 >= C1 && D >= J] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q)
[A >= J] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f24(A,B,D,E,1 + J,L,N,O,P,Q)
[N >= O] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f40(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f44(A,B,D,E,1 + J,L,N,O,P,Q)
[E >= J] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f64(A,B,D,E,2 + J,L,N,O,P,Q)
[D >= J] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f71(A,B,D,E,1 + J,L,N,O,P,Q)
[L = 0] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,J,L,N,O,P,Q)
[L >= 1] ==>
f86(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,J,L,N,O,P,Q)
[A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f99(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f99(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && A >= J] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f99(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f103(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f99(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f103(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f107(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + L] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L >= 1] ==>
f103(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f107(A,B,D,E,J,C1,N,O,P,Q)
[L = 0] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,1 + J,0,N,O,P,Q)
[0 >= 1 + L] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[L >= 1] ==>
f107(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f91(A,B,D,E,1 + J,L,N,O,P,Q)
[A >= J] ==>
f118(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f118(A,B,D,E,1 + J,L,N,O,P,Q)
[J >= 1 + A] ==>
f91(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f37(A,B,D,E,J,L,N,1 + O,P,Q)
[J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f86(A,B,D,E,J,C1,N,O,P,Q)
[0 >= 1 + B1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f86(A,B,D,E,J,C1,N,O,P,Q)
[B1 >= 1 && J >= 1 + D] ==>
f71(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f86(A,B,D,E,J,C1,N,O,P,Q)
[J >= 1 + E] ==>
f64(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f57(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f40(A,B,D,E,J,L,N,O,P,1 + Q)
[J >= 1 + A] ==>
f50(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f57(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f44(A,B,D,E,J,L,N,O,P,Q) = -1*Q
>= -1*Q
= f50(A,B,D,E,J,L,N,O,P,Q)
[Q >= 1] ==>
f40(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f71(A,B,D,E,J,L,N,O,P,Q)
[O >= 1 + N] ==>
f37(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f118(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A] ==>
f31(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f37(A,B,D,E,J,L,N,O,P,Q)
[0 >= 1 + P && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f31(A,B,D,E,J,L,N,O,P,Q)
[P >= 1 && J >= 1 + A] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f31(A,B,D,E,J,L,N,O,P,Q)
[J >= 1 + A && P = 0] ==>
f24(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f37(A,B,D,E,J,L,N,O,0,Q)
[J >= 1 + D] ==>
f13(A,B,D,E,J,L,N,O,P,Q) = 1 + -1*Q
>= 1 + -1*Q
= f24(A,B,D,E,J,L,N,O,P,Q)
* Step 23: KnowledgePropagation WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (1 + 2*A + J,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (1 + 2*A + J,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (1 + 2*A + J,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (1 + N + O,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (1 + Q,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (1 + Q,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (?,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (?,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (?,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (?,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (?,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (?,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (1 + 2*A + Q,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (?,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (?,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 24: LocalSizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f2(A,B,D,E,J,L,N,O,P,Q) -> f13(A,0,2*A,4*A,J,L,N,O,P,Q) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1)
1. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,B,D,E,1 + J,0,N,O,P,Q) [D >= J] (1 + 2*A + J,1)
2. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && D >= J] (1 + 2*A + J,1)
3. f13(A,B,D,E,J,L,N,O,P,Q) -> f13(A,1 + B + -2*C1 + C1^2,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && D >= J] (1 + 2*A + J,1)
4. f24(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
6. f37(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,Q) [N >= O] (1 + N + O,1)
7. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1)
8. f40(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (1 + Q,1)
9. f44(A,B,D,E,J,L,N,O,P,Q) -> f44(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
12. f40(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (1 + Q,1)
13. f64(A,B,D,E,J,L,N,O,P,Q) -> f64(A,B,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*A,1)
14. f71(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1)
15. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,0,N,O,P,Q) [L = 0] (12 + 9*A + 3*N + 3*O + 9*Q,1)
16. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (12 + 9*A + 3*N + 3*O + 9*Q,1)
17. f86(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,J,L,N,O,P,Q) [L >= 1] (12 + 9*A + 3*N + 3*O + 9*Q,1)
18. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [A >= J] (A,1)
19. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && A >= J] (A,1)
20. f91(A,B,D,E,J,L,N,O,P,Q) -> f99(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && A >= J] (A,1)
21. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (3*A,1)
22. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (3*A,1)
23. f99(A,B,D,E,J,L,N,O,P,Q) -> f103(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (3*A,1)
24. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L = 0] (9*A,1)
25. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + L] (9*A,1)
26. f103(A,B,D,E,J,L,N,O,P,Q) -> f107(A,B,D,E,J,C1,N,O,P,Q) [L >= 1] (9*A,1)
27. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,0,N,O,P,Q) [L = 0] (27*A,1)
28. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (27*A,1)
29. f107(A,B,D,E,J,L,N,O,P,Q) -> f91(A,B,D,E,1 + J,L,N,O,P,Q) [L >= 1] (27*A,1)
30. f118(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,1 + J,L,N,O,P,Q) [A >= J] (A,1)
32. f91(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,1 + O,P,Q) [J >= 1 + A] (36 + 108*A + 9*N + 9*O + 27*Q,1)
33. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [J >= 1 + D] (4 + 3*A + N + O + 3*Q,1)
34. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [0 >= 1 + B1 && J >= 1 + D] (4 + 3*A + N + O + 3*Q,1)
35. f71(A,B,D,E,J,L,N,O,P,Q) -> f86(A,B,D,E,J,C1,N,O,P,Q) [B1 >= 1 && J >= 1 + D] (4 + 3*A + N + O + 3*Q,1)
36. f64(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (1 + 2*A + Q,1)
37. f57(A,B,D,E,J,L,N,O,P,Q) -> f40(A,B,D,E,J,L,N,O,P,1 + Q) [J >= 1 + A] (2 + A + 2*Q,1)
38. f50(A,B,D,E,J,L,N,O,P,Q) -> f57(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + A + 2*Q,1)
39. f44(A,B,D,E,J,L,N,O,P,Q) -> f50(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + A + 2*Q,1)
40. f40(A,B,D,E,J,L,N,O,P,Q) -> f71(A,B,D,E,J,L,N,O,P,Q) [Q >= 1] (4 + 3*A + N + O + 3*Q,1)
41. f37(A,B,D,E,J,L,N,O,P,Q) -> f118(A,B,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1)
42. f31(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + A] (2 + 2*A,1)
43. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + A] (1 + A,1)
44. f24(A,B,D,E,J,L,N,O,P,Q) -> f31(A,B,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + A] (1 + A,1)
45. f24(A,B,D,E,J,L,N,O,P,Q) -> f37(A,B,D,E,J,L,N,O,0,Q) [J >= 1 + A && P = 0] (1 + A,1)
46. f13(A,B,D,E,J,L,N,O,P,Q) -> f24(A,B,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1)
Signature:
{(f1,10)
;(f103,10)
;(f107,10)
;(f118,10)
;(f13,10)
;(f2,10)
;(f24,10)
;(f31,10)
;(f37,10)
;(f40,10)
;(f44,10)
;(f50,10)
;(f57,10)
;(f64,10)
;(f71,10)
;(f86,10)
;(f91,10)
;(f99,10)}
Flow Graph:
[0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9
,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20
,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28
,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30},32->{6,41}
,33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38},40->{14,33
,34,35},41->{30},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, 0) (< 0,0,D>, 2*A) (< 0,0,E>, 4*A) (< 0,0,J>, J) (< 0,0,L>, L) (< 0,0,N>, N) (< 0,0,O>, O) (< 0,0,P>, P) (< 0,0,Q>, Q)
(< 1,0,A>, A) (< 1,0,B>, ?) (< 1,0,D>, 2*A) (< 1,0,E>, 4*A) (< 1,0,J>, 1 + 2*A) (< 1,0,L>, 0) (< 1,0,N>, N) (< 1,0,O>, O) (< 1,0,P>, P) (< 1,0,Q>, Q)
(< 2,0,A>, A) (< 2,0,B>, ?) (< 2,0,D>, 2*A) (< 2,0,E>, 4*A) (< 2,0,J>, 1 + 2*A) (< 2,0,L>, ?) (< 2,0,N>, N) (< 2,0,O>, O) (< 2,0,P>, P) (< 2,0,Q>, Q)
(< 3,0,A>, A) (< 3,0,B>, ?) (< 3,0,D>, 2*A) (< 3,0,E>, 4*A) (< 3,0,J>, 1 + 2*A) (< 3,0,L>, ?) (< 3,0,N>, N) (< 3,0,O>, O) (< 3,0,P>, P) (< 3,0,Q>, Q)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,D>, 2*A) (< 4,0,E>, 4*A) (< 4,0,J>, 1 + A) (< 4,0,L>, ?) (< 4,0,N>, N) (< 4,0,O>, O) (< 4,0,P>, P) (< 4,0,Q>, Q)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,D>, 2*A) (< 6,0,E>, 4*A) (< 6,0,J>, ?) (< 6,0,L>, ?) (< 6,0,N>, N) (< 6,0,O>, N) (< 6,0,P>, P) (< 6,0,Q>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,D>, 2*A) (< 7,0,E>, 4*A) (< 7,0,J>, ?) (< 7,0,L>, ?) (< 7,0,N>, N) (< 7,0,O>, ?) (< 7,0,P>, P) (< 7,0,Q>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,D>, 2*A) (< 8,0,E>, 4*A) (< 8,0,J>, ?) (< 8,0,L>, ?) (< 8,0,N>, N) (< 8,0,O>, ?) (< 8,0,P>, P) (< 8,0,Q>, 0)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,D>, 2*A) (< 9,0,E>, 4*A) (< 9,0,J>, 1 + A) (< 9,0,L>, ?) (< 9,0,N>, N) (< 9,0,O>, ?) (< 9,0,P>, P) (< 9,0,Q>, 0)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,D>, 2*A) (<12,0,E>, 4*A) (<12,0,J>, ?) (<12,0,L>, ?) (<12,0,N>, N) (<12,0,O>, ?) (<12,0,P>, 0) (<12,0,Q>, P)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,D>, 2*A) (<13,0,E>, 4*A) (<13,0,J>, 2 + 4*A) (<13,0,L>, ?) (<13,0,N>, N) (<13,0,O>, ?) (<13,0,P>, 0) (<13,0,Q>, P)
(<14,0,A>, A) (<14,0,B>, ?) (<14,0,D>, 2*A) (<14,0,E>, 4*A) (<14,0,J>, 1 + 2*A) (<14,0,L>, ?) (<14,0,N>, N) (<14,0,O>, ?) (<14,0,P>, P) (<14,0,Q>, ?)
(<15,0,A>, A) (<15,0,B>, ?) (<15,0,D>, 2*A) (<15,0,E>, 4*A) (<15,0,J>, ?) (<15,0,L>, 0) (<15,0,N>, N) (<15,0,O>, ?) (<15,0,P>, P) (<15,0,Q>, ?)
(<16,0,A>, A) (<16,0,B>, ?) (<16,0,D>, 2*A) (<16,0,E>, 4*A) (<16,0,J>, ?) (<16,0,L>, ?) (<16,0,N>, N) (<16,0,O>, ?) (<16,0,P>, P) (<16,0,Q>, ?)
(<17,0,A>, A) (<17,0,B>, ?) (<17,0,D>, 2*A) (<17,0,E>, 4*A) (<17,0,J>, ?) (<17,0,L>, ?) (<17,0,N>, N) (<17,0,O>, ?) (<17,0,P>, P) (<17,0,Q>, ?)
(<18,0,A>, A) (<18,0,B>, ?) (<18,0,D>, 2*A) (<18,0,E>, 4*A) (<18,0,J>, A) (<18,0,L>, ?) (<18,0,N>, N) (<18,0,O>, ?) (<18,0,P>, P) (<18,0,Q>, ?)
(<19,0,A>, A) (<19,0,B>, ?) (<19,0,D>, 2*A) (<19,0,E>, 4*A) (<19,0,J>, A) (<19,0,L>, ?) (<19,0,N>, N) (<19,0,O>, ?) (<19,0,P>, P) (<19,0,Q>, ?)
(<20,0,A>, A) (<20,0,B>, ?) (<20,0,D>, 2*A) (<20,0,E>, 4*A) (<20,0,J>, A) (<20,0,L>, ?) (<20,0,N>, N) (<20,0,O>, ?) (<20,0,P>, P) (<20,0,Q>, ?)
(<21,0,A>, A) (<21,0,B>, ?) (<21,0,D>, 2*A) (<21,0,E>, 4*A) (<21,0,J>, A) (<21,0,L>, ?) (<21,0,N>, N) (<21,0,O>, ?) (<21,0,P>, P) (<21,0,Q>, ?)
(<22,0,A>, A) (<22,0,B>, ?) (<22,0,D>, 2*A) (<22,0,E>, 4*A) (<22,0,J>, A) (<22,0,L>, ?) (<22,0,N>, N) (<22,0,O>, ?) (<22,0,P>, P) (<22,0,Q>, ?)
(<23,0,A>, A) (<23,0,B>, ?) (<23,0,D>, 2*A) (<23,0,E>, 4*A) (<23,0,J>, A) (<23,0,L>, ?) (<23,0,N>, N) (<23,0,O>, ?) (<23,0,P>, P) (<23,0,Q>, ?)
(<24,0,A>, A) (<24,0,B>, ?) (<24,0,D>, 2*A) (<24,0,E>, 4*A) (<24,0,J>, A) (<24,0,L>, ?) (<24,0,N>, N) (<24,0,O>, ?) (<24,0,P>, P) (<24,0,Q>, ?)
(<25,0,A>, A) (<25,0,B>, ?) (<25,0,D>, 2*A) (<25,0,E>, 4*A) (<25,0,J>, A) (<25,0,L>, ?) (<25,0,N>, N) (<25,0,O>, ?) (<25,0,P>, P) (<25,0,Q>, ?)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,D>, 2*A) (<26,0,E>, 4*A) (<26,0,J>, A) (<26,0,L>, ?) (<26,0,N>, N) (<26,0,O>, ?) (<26,0,P>, P) (<26,0,Q>, ?)
(<27,0,A>, A) (<27,0,B>, ?) (<27,0,D>, 2*A) (<27,0,E>, 4*A) (<27,0,J>, A) (<27,0,L>, 0) (<27,0,N>, N) (<27,0,O>, ?) (<27,0,P>, P) (<27,0,Q>, ?)
(<28,0,A>, A) (<28,0,B>, ?) (<28,0,D>, 2*A) (<28,0,E>, 4*A) (<28,0,J>, A) (<28,0,L>, ?) (<28,0,N>, N) (<28,0,O>, ?) (<28,0,P>, P) (<28,0,Q>, ?)
(<29,0,A>, A) (<29,0,B>, ?) (<29,0,D>, 2*A) (<29,0,E>, 4*A) (<29,0,J>, A) (<29,0,L>, ?) (<29,0,N>, N) (<29,0,O>, ?) (<29,0,P>, P) (<29,0,Q>, ?)
(<30,0,A>, A) (<30,0,B>, ?) (<30,0,D>, 2*A) (<30,0,E>, 4*A) (<30,0,J>, 1 + A) (<30,0,L>, ?) (<30,0,N>, N) (<30,0,O>, ?) (<30,0,P>, P) (<30,0,Q>, ?)
(<32,0,A>, A) (<32,0,B>, ?) (<32,0,D>, 2*A) (<32,0,E>, 4*A) (<32,0,J>, ?) (<32,0,L>, ?) (<32,0,N>, N) (<32,0,O>, ?) (<32,0,P>, P) (<32,0,Q>, ?)
(<33,0,A>, A) (<33,0,B>, ?) (<33,0,D>, 2*A) (<33,0,E>, 4*A) (<33,0,J>, ?) (<33,0,L>, ?) (<33,0,N>, N) (<33,0,O>, ?) (<33,0,P>, P) (<33,0,Q>, ?)
(<34,0,A>, A) (<34,0,B>, ?) (<34,0,D>, 2*A) (<34,0,E>, 4*A) (<34,0,J>, ?) (<34,0,L>, ?) (<34,0,N>, N) (<34,0,O>, ?) (<34,0,P>, P) (<34,0,Q>, ?)
(<35,0,A>, A) (<35,0,B>, ?) (<35,0,D>, 2*A) (<35,0,E>, 4*A) (<35,0,J>, ?) (<35,0,L>, ?) (<35,0,N>, N) (<35,0,O>, ?) (<35,0,P>, P) (<35,0,Q>, ?)
(<36,0,A>, A) (<36,0,B>, ?) (<36,0,D>, 2*A) (<36,0,E>, 4*A) (<36,0,J>, ?) (<36,0,L>, ?) (<36,0,N>, N) (<36,0,O>, ?) (<36,0,P>, 0) (<36,0,Q>, P)
(<37,0,A>, A) (<37,0,B>, ?) (<37,0,D>, 2*A) (<37,0,E>, 4*A) (<37,0,J>, ?) (<37,0,L>, ?) (<37,0,N>, N) (<37,0,O>, ?) (<37,0,P>, P) (<37,0,Q>, 0)
(<38,0,A>, A) (<38,0,B>, ?) (<38,0,D>, 2*A) (<38,0,E>, 4*A) (<38,0,J>, ?) (<38,0,L>, ?) (<38,0,N>, N) (<38,0,O>, ?) (<38,0,P>, P) (<38,0,Q>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,D>, 2*A) (<39,0,E>, 4*A) (<39,0,J>, ?) (<39,0,L>, ?) (<39,0,N>, N) (<39,0,O>, ?) (<39,0,P>, P) (<39,0,Q>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,D>, 2*A) (<40,0,E>, 4*A) (<40,0,J>, ?) (<40,0,L>, ?) (<40,0,N>, N) (<40,0,O>, ?) (<40,0,P>, P) (<40,0,Q>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,D>, 2*A) (<41,0,E>, 4*A) (<41,0,J>, ?) (<41,0,L>, ?) (<41,0,N>, N) (<41,0,O>, ?) (<41,0,P>, P) (<41,0,Q>, ?)
(<42,0,A>, A) (<42,0,B>, ?) (<42,0,D>, 2*A) (<42,0,E>, 4*A) (<42,0,J>, 1 + 2*A + J) (<42,0,L>, ?) (<42,0,N>, N) (<42,0,O>, O) (<42,0,P>, P) (<42,0,Q>, Q)
(<43,0,A>, A) (<43,0,B>, ?) (<43,0,D>, 2*A) (<43,0,E>, 4*A) (<43,0,J>, 1 + 2*A + J) (<43,0,L>, ?) (<43,0,N>, N) (<43,0,O>, O) (<43,0,P>, P) (<43,0,Q>, Q)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,D>, 2*A) (<44,0,E>, 4*A) (<44,0,J>, 1 + 2*A + J) (<44,0,L>, ?) (<44,0,N>, N) (<44,0,O>, O) (<44,0,P>, P) (<44,0,Q>, Q)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,D>, 2*A) (<45,0,E>, 4*A) (<45,0,J>, 1 + 2*A + J) (<45,0,L>, ?) (<45,0,N>, N) (<45,0,O>, O) (<45,0,P>, 0) (<45,0,Q>, Q)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,D>, 2*A) (<46,0,E>, 4*A) (<46,0,J>, 1 + 2*A + J) (<46,0,L>, ?) (<46,0,N>, N) (<46,0,O>, O) (<46,0,P>, P) (<46,0,Q>, Q)
+ Applied Processor:
LocalSizeboundsProc
+ Details:
The problem is already solved.
WORST_CASE(?,O(n^1))