WORST_CASE(?,O(n^2))
* Step 1: UnsatRules WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1entryin(A,B,C) True (1,1)
1. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (?,1)
2. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (?,1)
3. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [A >= 1 + B] (?,1)
4. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [B >= A] (?,1)
5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= C] (?,1)
6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [C >= 1] (?,1)
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
14. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && D >= 0 && 0 >= 2*D && 1 + 2*D >= 0 && 1 + C = 0] (?,1)
15. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && 0 >= D && 1 + C = 0 && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
16. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 1 && D >= 0 && 0 >= 2*D && 1 + 2*D >= 0 && 1 + C = 0] (?,1)
17. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && E >= 0 && 0 >= 2*E && 1 + 2*E >= 0 && D >= 0 && 0 >= 2*D && 1 + 2*D >= 0 && 1 + C = 0] (?,1)
18. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && E >= 0 && 0 >= 2*E && 1 + 2*E >= 0 && 0 >= D && 1 + C = 0 && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
19. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 1 && 0 >= D && 1 + C = 0 && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
20. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && 0 >= E && D >= 0 && 0 >= 2*D && 1 + 2*D >= 0 && 1 + C = 0 && 2*E >= 1 + C && 2 + C >= 2*E] (?,1)
21. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && 0 >= E && 0 >= D && 1 + C = 0 && 2*E >= 1 + C && 2 + C >= 2*E && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
22. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 1 && D >= 0 && 0 >= 2*D && 1 + 2*D >= 0 && 1 + C = 0] (?,1)
23. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && E >= 0 && 0 >= 2*E && 1 + 2*E >= 0 && D >= 0 && 0 >= 2*D && 1 + 2*D >= 0 && 1 + C = 0] (?,1)
24. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && E >= 0 && 0 >= 2*E && 1 + 2*E >= 0 && 0 >= D && 1 + C = 0 && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
25. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 1 && D >= 0 && 0 >= 2*D && 1 + 2*D >= 0 && E >= 0 && 0 >= 2*E && 1 + 2*E >= 0 && 1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
27. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& 0 >= 2 + C
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
28. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 1 && D >= 0 && 0 >= 2*D && 1 + 2*D >= 0 && 0 >= E && 1 + C = 0 && 2*E >= 1 + C && 2 + C >= 2*E] (?,1)
29. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& 0 >= 2 + C
&& 0 >= F
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 2*F >= 1 + C
&& 2 + C >= 2*F]
30. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& 0 >= 2 + C
&& 0 >= F
&& 0 >= D
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
31. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 1 && 0 >= D && 1 + C = 0 && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
32. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && 0 >= E && D >= 0 && 0 >= 2*D && 1 + 2*D >= 0 && 1 + C = 0 && 2*E >= 1 + C && 2 + C >= 2*E] (?,1)
33. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 1 && 0 >= E && 0 >= D && 1 + C = 0 && 2*E >= 1 + C && 2 + C >= 2*E && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
34. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 1 && 0 >= D && E >= 0 && 0 >= 2*E && 1 + 2*E >= 0 && 1 + C = 0 && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
35. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& C >= 0
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 2*E >= 1 + C
&& 2 + C >= 2*E]
36. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& C >= 0
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
37. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 1 && 0 >= D && 0 >= E && 1 + C = 0 && 2*D >= 1 + C && 2 + C >= 2*D && 2*E >= 1 + C && 2 + C >= 2*E] (?,1)
38. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& C >= 0
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[0->{1,2},1->{3,4},2->{41},3->{5,6},4->{41},5->{40},6->{7,8,9,10,11,12},7->{13,14,15,16,17,18,19,20,21,22
,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39},8->{13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29
,30,31,32,33,34,35,36,37,38,39},9->{13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36
,37,38,39},10->{40},11->{40},12->{40},13->{5,6},14->{5,6},15->{5,6},16->{5,6},17->{5,6},18->{5,6},19->{5,6}
,20->{5,6},21->{5,6},22->{5,6},23->{5,6},24->{5,6},25->{5,6},26->{5,6},27->{5,6},28->{5,6},29->{5,6},30->{5
,6},31->{5,6},32->{5,6},33->{5,6},34->{5,6},35->{5,6},36->{5,6},37->{5,6},38->{5,6},39->{5,6},40->{3,4}
,41->{}]
+ Applied Processor:
UnsatRules
+ Details:
The following transitions have unsatisfiable constraints and are removed: [14
,15
,16
,17
,18
,19
,20
,21
,22
,23
,24
,25
,27
,28
,29
,30
,31
,32
,33
,34
,35
,36
,37
,38]
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1entryin(A,B,C) True (1,1)
1. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (?,1)
2. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (?,1)
3. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [A >= 1 + B] (?,1)
4. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [B >= A] (?,1)
5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= C] (?,1)
6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [C >= 1] (?,1)
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[0->{1,2},1->{3,4},2->{41},3->{5,6},4->{41},5->{40},6->{7,8,9,10,11,12},7->{13,26,39},8->{13,26,39},9->{13
,26,39},10->{40},11->{40},12->{40},13->{5,6},26->{5,6},39->{5,6},40->{3,4},41->{}]
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(< 0,0,A>, A, .= 0) (< 0,0,B>, B, .= 0) (< 0,0,C>, C, .= 0)
(< 1,0,A>, A, .= 0) (< 1,0,B>, 1, .= 1) (< 1,0,C>, C, .= 0)
(< 2,0,A>, A, .= 0) (< 2,0,B>, B, .= 0) (< 2,0,C>, C, .= 0)
(< 3,0,A>, A, .= 0) (< 3,0,B>, B, .= 0) (< 3,0,C>, B, .= 0)
(< 4,0,A>, A, .= 0) (< 4,0,B>, B, .= 0) (< 4,0,C>, C, .= 0)
(< 5,0,A>, A, .= 0) (< 5,0,B>, B, .= 0) (< 5,0,C>, C, .= 0)
(< 6,0,A>, A, .= 0) (< 6,0,B>, B, .= 0) (< 6,0,C>, C, .= 0)
(< 7,0,A>, A, .= 0) (< 7,0,B>, B, .= 0) (< 7,0,C>, C, .= 0)
(< 8,0,A>, A, .= 0) (< 8,0,B>, B, .= 0) (< 8,0,C>, C, .= 0)
(< 9,0,A>, A, .= 0) (< 9,0,B>, B, .= 0) (< 9,0,C>, C, .= 0)
(<10,0,A>, A, .= 0) (<10,0,B>, B, .= 0) (<10,0,C>, C, .= 0)
(<11,0,A>, A, .= 0) (<11,0,B>, B, .= 0) (<11,0,C>, C, .= 0)
(<12,0,A>, A, .= 0) (<12,0,B>, B, .= 0) (<12,0,C>, C, .= 0)
(<13,0,A>, A, .= 0) (<13,0,B>, B, .= 0) (<13,0,C>, 1, .= 1)
(<26,0,A>, A, .= 0) (<26,0,B>, B, .= 0) (<26,0,C>, 1 + C, .+ 1)
(<39,0,A>, A, .= 0) (<39,0,B>, B, .= 0) (<39,0,C>, 1 + C, .+ 1)
(<40,0,A>, A, .= 0) (<40,0,B>, 1 + B, .+ 1) (<40,0,C>, C, .= 0)
(<41,0,A>, A, .= 0) (<41,0,B>, B, .= 0) (<41,0,C>, C, .= 0)
* Step 3: SizeboundsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1entryin(A,B,C) True (1,1)
1. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (?,1)
2. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (?,1)
3. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [A >= 1 + B] (?,1)
4. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [B >= A] (?,1)
5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= C] (?,1)
6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [C >= 1] (?,1)
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[0->{1,2},1->{3,4},2->{41},3->{5,6},4->{41},5->{40},6->{7,8,9,10,11,12},7->{13,26,39},8->{13,26,39},9->{13
,26,39},10->{40},11->{40},12->{40},13->{5,6},26->{5,6},39->{5,6},40->{3,4},41->{}]
Sizebounds:
(< 0,0,A>, ?) (< 0,0,B>, ?) (< 0,0,C>, ?)
(< 1,0,A>, ?) (< 1,0,B>, ?) (< 1,0,C>, ?)
(< 2,0,A>, ?) (< 2,0,B>, ?) (< 2,0,C>, ?)
(< 3,0,A>, ?) (< 3,0,B>, ?) (< 3,0,C>, ?)
(< 4,0,A>, ?) (< 4,0,B>, ?) (< 4,0,C>, ?)
(< 5,0,A>, ?) (< 5,0,B>, ?) (< 5,0,C>, ?)
(< 6,0,A>, ?) (< 6,0,B>, ?) (< 6,0,C>, ?)
(< 7,0,A>, ?) (< 7,0,B>, ?) (< 7,0,C>, ?)
(< 8,0,A>, ?) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, ?) (< 9,0,B>, ?) (< 9,0,C>, ?)
(<10,0,A>, ?) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, ?) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, ?) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, ?) (<13,0,B>, ?) (<13,0,C>, ?)
(<26,0,A>, ?) (<26,0,B>, ?) (<26,0,C>, ?)
(<39,0,A>, ?) (<39,0,B>, ?) (<39,0,C>, ?)
(<40,0,A>, ?) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, ?) (<41,0,B>, ?) (<41,0,C>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C)
(< 1,0,A>, A) (< 1,0,B>, 1) (< 1,0,C>, C)
(< 2,0,A>, A) (< 2,0,B>, B) (< 2,0,C>, C)
(< 3,0,A>, A) (< 3,0,B>, A) (< 3,0,C>, ?)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,C>, ?)
(< 5,0,A>, A) (< 5,0,B>, ?) (< 5,0,C>, ?)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,C>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,C>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
* Step 4: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1entryin(A,B,C) True (1,1)
1. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (?,1)
2. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (?,1)
3. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [A >= 1 + B] (?,1)
4. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [B >= A] (?,1)
5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= C] (?,1)
6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [C >= 1] (?,1)
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[0->{1,2},1->{3,4},2->{41},3->{5,6},4->{41},5->{40},6->{7,8,9,10,11,12},7->{13,26,39},8->{13,26,39},9->{13
,26,39},10->{40},11->{40},12->{40},13->{5,6},26->{5,6},39->{5,6},40->{3,4},41->{}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C)
(< 1,0,A>, A) (< 1,0,B>, 1) (< 1,0,C>, C)
(< 2,0,A>, A) (< 2,0,B>, B) (< 2,0,C>, C)
(< 3,0,A>, A) (< 3,0,B>, A) (< 3,0,C>, ?)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,C>, ?)
(< 5,0,A>, A) (< 5,0,B>, ?) (< 5,0,C>, ?)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,C>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,C>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
+ Applied Processor:
ChainProcessor False [0,1,2,3,4,5,6,7,8,9,10,11,12,13,26,39,40,41]
+ Details:
We chained rule 0 to obtain the rules [42,43] .
* Step 5: UnreachableRules WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
1. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (?,1)
2. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (?,1)
3. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [A >= 1 + B] (?,1)
4. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [B >= A] (?,1)
5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= C] (?,1)
6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [C >= 1] (?,1)
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[1->{3,4},2->{41},3->{5,6},4->{41},5->{40},6->{7,8,9,10,11,12},7->{13,26,39},8->{13,26,39},9->{13,26,39}
,10->{40},11->{40},12->{40},13->{5,6},26->{5,6},39->{5,6},40->{3,4},41->{},42->{3,4},43->{41}]
Sizebounds:
(< 1,0,A>, A) (< 1,0,B>, 1) (< 1,0,C>, C)
(< 2,0,A>, A) (< 2,0,B>, B) (< 2,0,C>, C)
(< 3,0,A>, A) (< 3,0,B>, A) (< 3,0,C>, ?)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,C>, ?)
(< 5,0,A>, A) (< 5,0,B>, ?) (< 5,0,C>, ?)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,C>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,C>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [1,2]
* Step 6: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
3. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [A >= 1 + B] (?,1)
4. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [B >= A] (?,1)
5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= C] (?,1)
6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [C >= 1] (?,1)
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[3->{5,6},4->{41},5->{40},6->{7,8,9,10,11,12},7->{13,26,39},8->{13,26,39},9->{13,26,39},10->{40},11->{40}
,12->{40},13->{5,6},26->{5,6},39->{5,6},40->{3,4},41->{},42->{3,4},43->{41}]
Sizebounds:
(< 3,0,A>, A) (< 3,0,B>, A) (< 3,0,C>, ?)
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,C>, ?)
(< 5,0,A>, A) (< 5,0,B>, ?) (< 5,0,C>, ?)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,C>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,C>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
+ Applied Processor:
ChainProcessor False [3,4,5,6,7,8,9,10,11,12,13,26,39,40,41,42,43]
+ Details:
We chained rule 3 to obtain the rules [44,45] .
* Step 7: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
4. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [B >= A] (?,1)
5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= C] (?,1)
6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [C >= 1] (?,1)
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[4->{41},5->{40},6->{7,8,9,10,11,12},7->{13,26,39},8->{13,26,39},9->{13,26,39},10->{40},11->{40},12->{40}
,13->{5,6},26->{5,6},39->{5,6},40->{4,44,45},41->{},42->{4,44,45},43->{41},44->{40},45->{7,8,9,10,11,12}]
Sizebounds:
(< 4,0,A>, A) (< 4,0,B>, ?) (< 4,0,C>, ?)
(< 5,0,A>, A) (< 5,0,B>, ?) (< 5,0,C>, ?)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,C>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,C>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
+ Applied Processor:
ChainProcessor False [4,5,6,7,8,9,10,11,12,13,26,39,40,41,42,43,44,45]
+ Details:
We chained rule 4 to obtain the rules [46] .
* Step 8: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= C] (?,1)
6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [C >= 1] (?,1)
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[5->{40},6->{7,8,9,10,11,12},7->{13,26,39},8->{13,26,39},9->{13,26,39},10->{40},11->{40},12->{40},13->{5
,6},26->{5,6},39->{5,6},40->{44,45,46},41->{},42->{44,45,46},43->{41},44->{40},45->{7,8,9,10,11,12},46->{}]
Sizebounds:
(< 5,0,A>, A) (< 5,0,B>, ?) (< 5,0,C>, ?)
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,C>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,C>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
+ Applied Processor:
ChainProcessor False [5,6,7,8,9,10,11,12,13,26,39,40,41,42,43,44,45,46]
+ Details:
We chained rule 5 to obtain the rules [47] .
* Step 9: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [C >= 1] (?,1)
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[6->{7,8,9,10,11,12},7->{13,26,39},8->{13,26,39},9->{13,26,39},10->{40},11->{40},12->{40},13->{6,47}
,26->{6,47},39->{6,47},40->{44,45,46},41->{},42->{44,45,46},43->{41},44->{40},45->{7,8,9,10,11,12},46->{}
,47->{44,45,46}]
Sizebounds:
(< 6,0,A>, A) (< 6,0,B>, ?) (< 6,0,C>, ?)
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,C>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
+ Applied Processor:
ChainProcessor False [6,7,8,9,10,11,12,13,26,39,40,41,42,43,44,45,46,47]
+ Details:
We chained rule 6 to obtain the rules [48,49,50,51,52,53] .
* Step 10: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [1 + C = 0] (?,1)
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[7->{13,26,39},8->{13,26,39},9->{13,26,39},10->{40},11->{40},12->{40},13->{47,48,49,50,51,52,53},26->{47
,48,49,50,51,52,53},39->{47,48,49,50,51,52,53},40->{44,45,46},41->{},42->{44,45,46},43->{41},44->{40},45->{7
,8,9,10,11,12},46->{},47->{44,45,46},48->{13,26,39},49->{13,26,39},50->{13,26,39},51->{40},52->{40}
,53->{40}]
Sizebounds:
(< 7,0,A>, A) (< 7,0,B>, ?) (< 7,0,C>, 0)
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
+ Applied Processor:
ChainProcessor False [7,8,9,10,11,12,13,26,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]
+ Details:
We chained rule 7 to obtain the rules [54,55,56] .
* Step 11: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[8->{13,26,39},9->{13,26,39},10->{40},11->{40},12->{40},13->{47,48,49,50,51,52,53},26->{47,48,49,50,51,52
,53},39->{47,48,49,50,51,52,53},40->{44,45,46},41->{},42->{44,45,46},43->{41},44->{40},45->{8,9,10,11,12,54
,55,56},46->{},47->{44,45,46},48->{13,26,39},49->{13,26,39},50->{13,26,39},51->{40},52->{40},53->{40}
,54->{47,48,49,50,51,52,53},55->{47,48,49,50,51,52,53},56->{47,48,49,50,51,52,53}]
Sizebounds:
(< 8,0,A>, A) (< 8,0,B>, ?) (< 8,0,C>, ?)
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
+ Applied Processor:
ChainProcessor False [8,9,10,11,12,13,26,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56]
+ Details:
We chained rule 8 to obtain the rules [57,58,59] .
* Step 12: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
9. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[9->{13,26,39},10->{40},11->{40},12->{40},13->{47,48,49,50,51,52,53},26->{47,48,49,50,51,52,53},39->{47,48
,49,50,51,52,53},40->{44,45,46},41->{},42->{44,45,46},43->{41},44->{40},45->{9,10,11,12,54,55,56,57,58,59}
,46->{},47->{44,45,46},48->{13,26,39},49->{13,26,39},50->{13,26,39},51->{40},52->{40},53->{40},54->{47,48,49
,50,51,52,53},55->{47,48,49,50,51,52,53},56->{47,48,49,50,51,52,53},57->{47,48,49,50,51,52,53},58->{47,48,49
,50,51,52,53},59->{47,48,49,50,51,52,53}]
Sizebounds:
(< 9,0,A>, A) (< 9,0,B>, ?) (< 9,0,C>, 0)
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
+ Applied Processor:
ChainProcessor False [9,10,11,12,13,26,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59]
+ Details:
We chained rule 9 to obtain the rules [60,61,62] .
* Step 13: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
10. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [1 + C = 0] (?,1)
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
60. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D && 1 + C = 0] (?,2)
61. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
62. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[10->{40},11->{40},12->{40},13->{47,48,49,50,51,52,53},26->{47,48,49,50,51,52,53},39->{47,48,49,50,51,52
,53},40->{44,45,46},41->{},42->{44,45,46},43->{41},44->{40},45->{10,11,12,54,55,56,57,58,59,60,61,62},46->{}
,47->{44,45,46},48->{13,26,39},49->{13,26,39},50->{13,26,39},51->{40},52->{40},53->{40},54->{47,48,49,50,51
,52,53},55->{47,48,49,50,51,52,53},56->{47,48,49,50,51,52,53},57->{47,48,49,50,51,52,53},58->{47,48,49,50,51
,52,53},59->{47,48,49,50,51,52,53},60->{47,48,49,50,51,52,53},61->{47,48,49,50,51,52,53},62->{47,48,49,50,51
,52,53}]
Sizebounds:
(<10,0,A>, A) (<10,0,B>, ?) (<10,0,C>, ?)
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
(<60,0,A>, A) (<60,0,B>, ?) (<60,0,C>, 1)
(<61,0,A>, A) (<61,0,B>, ?) (<61,0,C>, 0)
(<62,0,A>, A) (<62,0,B>, ?) (<62,0,C>, 0)
+ Applied Processor:
ChainProcessor False [10,11,12,13,26,39,40,41,42,43,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62]
+ Details:
We chained rule 10 to obtain the rules [63] .
* Step 14: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
11. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,1)
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
60. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D && 1 + C = 0] (?,2)
61. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
62. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
63. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [1 + C = 0] (?,2)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[11->{40},12->{40},13->{47,48,49,50,51,52,53},26->{47,48,49,50,51,52,53},39->{47,48,49,50,51,52,53}
,40->{44,45,46},41->{},42->{44,45,46},43->{41},44->{40},45->{11,12,54,55,56,57,58,59,60,61,62,63},46->{}
,47->{44,45,46},48->{13,26,39},49->{13,26,39},50->{13,26,39},51->{40},52->{40},53->{40},54->{47,48,49,50,51
,52,53},55->{47,48,49,50,51,52,53},56->{47,48,49,50,51,52,53},57->{47,48,49,50,51,52,53},58->{47,48,49,50,51
,52,53},59->{47,48,49,50,51,52,53},60->{47,48,49,50,51,52,53},61->{47,48,49,50,51,52,53},62->{47,48,49,50,51
,52,53},63->{44,45,46}]
Sizebounds:
(<11,0,A>, A) (<11,0,B>, ?) (<11,0,C>, ?)
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
(<60,0,A>, A) (<60,0,B>, ?) (<60,0,C>, 1)
(<61,0,A>, A) (<61,0,B>, ?) (<61,0,C>, 0)
(<62,0,A>, A) (<62,0,B>, ?) (<62,0,C>, 0)
(<63,0,A>, A) (<63,0,B>, ?) (<63,0,C>, ?)
+ Applied Processor:
ChainProcessor False [11,12,13,26,39,40,41,42,43,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63]
+ Details:
We chained rule 11 to obtain the rules [64] .
* Step 15: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
12. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,1)
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
60. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D && 1 + C = 0] (?,2)
61. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
62. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
63. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [1 + C = 0] (?,2)
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[12->{40},13->{47,48,49,50,51,52,53},26->{47,48,49,50,51,52,53},39->{47,48,49,50,51,52,53},40->{44,45,46}
,41->{},42->{44,45,46},43->{41},44->{40},45->{12,54,55,56,57,58,59,60,61,62,63,64},46->{},47->{44,45,46}
,48->{13,26,39},49->{13,26,39},50->{13,26,39},51->{40},52->{40},53->{40},54->{47,48,49,50,51,52,53},55->{47
,48,49,50,51,52,53},56->{47,48,49,50,51,52,53},57->{47,48,49,50,51,52,53},58->{47,48,49,50,51,52,53},59->{47
,48,49,50,51,52,53},60->{47,48,49,50,51,52,53},61->{47,48,49,50,51,52,53},62->{47,48,49,50,51,52,53},63->{44
,45,46},64->{44,45,46}]
Sizebounds:
(<12,0,A>, A) (<12,0,B>, ?) (<12,0,C>, ?)
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
(<60,0,A>, A) (<60,0,B>, ?) (<60,0,C>, 1)
(<61,0,A>, A) (<61,0,B>, ?) (<61,0,C>, 0)
(<62,0,A>, A) (<62,0,B>, ?) (<62,0,C>, 0)
(<63,0,A>, A) (<63,0,B>, ?) (<63,0,C>, ?)
(<64,0,A>, A) (<64,0,B>, ?) (<64,0,C>, ?)
+ Applied Processor:
ChainProcessor False [12,13,26,39,40,41,42,43,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64]
+ Details:
We chained rule 12 to obtain the rules [65] .
* Step 16: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
13. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0] (?,1)
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
60. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D && 1 + C = 0] (?,2)
61. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
62. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
63. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [1 + C = 0] (?,2)
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
65. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,2)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[13->{47,48,49,50,51,52,53},26->{47,48,49,50,51,52,53},39->{47,48,49,50,51,52,53},40->{44,45,46},41->{}
,42->{44,45,46},43->{41},44->{40},45->{54,55,56,57,58,59,60,61,62,63,64,65},46->{},47->{44,45,46},48->{13,26
,39},49->{13,26,39},50->{13,26,39},51->{40},52->{40},53->{40},54->{47,48,49,50,51,52,53},55->{47,48,49,50,51
,52,53},56->{47,48,49,50,51,52,53},57->{47,48,49,50,51,52,53},58->{47,48,49,50,51,52,53},59->{47,48,49,50,51
,52,53},60->{47,48,49,50,51,52,53},61->{47,48,49,50,51,52,53},62->{47,48,49,50,51,52,53},63->{44,45,46}
,64->{44,45,46},65->{44,45,46}]
Sizebounds:
(<13,0,A>, A) (<13,0,B>, ?) (<13,0,C>, 1)
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
(<60,0,A>, A) (<60,0,B>, ?) (<60,0,C>, 1)
(<61,0,A>, A) (<61,0,B>, ?) (<61,0,C>, 0)
(<62,0,A>, A) (<62,0,B>, ?) (<62,0,C>, 0)
(<63,0,A>, A) (<63,0,B>, ?) (<63,0,C>, ?)
(<64,0,A>, A) (<64,0,B>, ?) (<64,0,C>, ?)
(<65,0,A>, A) (<65,0,B>, ?) (<65,0,C>, ?)
+ Applied Processor:
ChainProcessor False [13,26,39,40,41,42,43,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]
+ Details:
We chained rule 13 to obtain the rules [66,67,68,69,70,71,72] .
* Step 17: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
26. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [C >= 0 (?,1)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C]
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
60. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D && 1 + C = 0] (?,2)
61. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
62. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
63. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [1 + C = 0] (?,2)
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
65. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,2)
66. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1) [1 + C = 0 && 0 >= -1] (?,3)
67. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
68. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
69. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
70. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
71. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
72. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[26->{47,48,49,50,51,52,53},39->{47,48,49,50,51,52,53},40->{44,45,46},41->{},42->{44,45,46},43->{41}
,44->{40},45->{54,55,56,57,58,59,60,61,62,63,64,65},46->{},47->{44,45,46},48->{26,39,66,67,68,69,70,71,72}
,49->{26,39,66,67,68,69,70,71,72},50->{26,39,66,67,68,69,70,71,72},51->{40},52->{40},53->{40},54->{47,48,49
,50,51,52,53},55->{47,48,49,50,51,52,53},56->{47,48,49,50,51,52,53},57->{47,48,49,50,51,52,53},58->{47,48,49
,50,51,52,53},59->{47,48,49,50,51,52,53},60->{47,48,49,50,51,52,53},61->{47,48,49,50,51,52,53},62->{47,48,49
,50,51,52,53},63->{44,45,46},64->{44,45,46},65->{44,45,46},66->{44,45,46},67->{26,39,66,67,68,69,70,71,72}
,68->{26,39,66,67,68,69,70,71,72},69->{26,39,66,67,68,69,70,71,72},70->{40},71->{40},72->{40}]
Sizebounds:
(<26,0,A>, A) (<26,0,B>, ?) (<26,0,C>, 0)
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
(<60,0,A>, A) (<60,0,B>, ?) (<60,0,C>, 1)
(<61,0,A>, A) (<61,0,B>, ?) (<61,0,C>, 0)
(<62,0,A>, A) (<62,0,B>, ?) (<62,0,C>, 0)
(<63,0,A>, A) (<63,0,B>, ?) (<63,0,C>, ?)
(<64,0,A>, A) (<64,0,B>, ?) (<64,0,C>, ?)
(<65,0,A>, A) (<65,0,B>, ?) (<65,0,C>, ?)
(<66,0,A>, A) (<66,0,B>, ?) (<66,0,C>, ?)
(<67,0,A>, A) (<67,0,B>, ?) (<67,0,C>, 0)
(<68,0,A>, A) (<68,0,B>, ?) (<68,0,C>, ?)
(<69,0,A>, A) (<69,0,B>, ?) (<69,0,C>, 0)
(<70,0,A>, A) (<70,0,B>, ?) (<70,0,C>, ?)
(<71,0,A>, A) (<71,0,B>, ?) (<71,0,C>, ?)
(<72,0,A>, A) (<72,0,B>, ?) (<72,0,C>, ?)
+ Applied Processor:
ChainProcessor False [26,39,40,41,42,43,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72]
+ Details:
We chained rule 26 to obtain the rules [73,74,75,76,77,78,79] .
* Step 18: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
39. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [0 >= 2 + C (?,1)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D]
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
60. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D && 1 + C = 0] (?,2)
61. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
62. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
63. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [1 + C = 0] (?,2)
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
65. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,2)
66. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1) [1 + C = 0 && 0 >= -1] (?,3)
67. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
68. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
69. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
70. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
71. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
72. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
74. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& D = 0]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
76. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
77. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& D = 0]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
79. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[39->{47,48,49,50,51,52,53},40->{44,45,46},41->{},42->{44,45,46},43->{41},44->{40},45->{54,55,56,57,58,59
,60,61,62,63,64,65},46->{},47->{44,45,46},48->{39,66,67,68,69,70,71,72,73,74,75,76,77,78,79},49->{39,66,67
,68,69,70,71,72,73,74,75,76,77,78,79},50->{39,66,67,68,69,70,71,72,73,74,75,76,77,78,79},51->{40},52->{40}
,53->{40},54->{47,48,49,50,51,52,53},55->{47,48,49,50,51,52,53},56->{47,48,49,50,51,52,53},57->{47,48,49,50
,51,52,53},58->{47,48,49,50,51,52,53},59->{47,48,49,50,51,52,53},60->{47,48,49,50,51,52,53},61->{47,48,49,50
,51,52,53},62->{47,48,49,50,51,52,53},63->{44,45,46},64->{44,45,46},65->{44,45,46},66->{44,45,46},67->{39,66
,67,68,69,70,71,72,73,74,75,76,77,78,79},68->{39,66,67,68,69,70,71,72,73,74,75,76,77,78,79},69->{39,66,67,68
,69,70,71,72,73,74,75,76,77,78,79},70->{40},71->{40},72->{40},73->{44,45,46},74->{39,66,67,68,69,70,71,72,73
,74,75,76,77,78,79},75->{39,66,67,68,69,70,71,72,73,74,75,76,77,78,79},76->{39,66,67,68,69,70,71,72,73,74,75
,76,77,78,79},77->{40},78->{40},79->{40}]
Sizebounds:
(<39,0,A>, A) (<39,0,B>, ?) (<39,0,C>, 0)
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
(<60,0,A>, A) (<60,0,B>, ?) (<60,0,C>, 1)
(<61,0,A>, A) (<61,0,B>, ?) (<61,0,C>, 0)
(<62,0,A>, A) (<62,0,B>, ?) (<62,0,C>, 0)
(<63,0,A>, A) (<63,0,B>, ?) (<63,0,C>, ?)
(<64,0,A>, A) (<64,0,B>, ?) (<64,0,C>, ?)
(<65,0,A>, A) (<65,0,B>, ?) (<65,0,C>, ?)
(<66,0,A>, A) (<66,0,B>, ?) (<66,0,C>, ?)
(<67,0,A>, A) (<67,0,B>, ?) (<67,0,C>, 0)
(<68,0,A>, A) (<68,0,B>, ?) (<68,0,C>, ?)
(<69,0,A>, A) (<69,0,B>, ?) (<69,0,C>, 0)
(<70,0,A>, A) (<70,0,B>, ?) (<70,0,C>, ?)
(<71,0,A>, A) (<71,0,B>, ?) (<71,0,C>, ?)
(<72,0,A>, A) (<72,0,B>, ?) (<72,0,C>, ?)
(<73,0,A>, A) (<73,0,B>, ?) (<73,0,C>, ?)
(<74,0,A>, A) (<74,0,B>, ?) (<74,0,C>, 0)
(<75,0,A>, A) (<75,0,B>, ?) (<75,0,C>, ?)
(<76,0,A>, A) (<76,0,B>, ?) (<76,0,C>, 0)
(<77,0,A>, A) (<77,0,B>, ?) (<77,0,C>, ?)
(<78,0,A>, A) (<78,0,B>, ?) (<78,0,C>, ?)
(<79,0,A>, A) (<79,0,B>, ?) (<79,0,C>, ?)
+ Applied Processor:
ChainProcessor False [39,40,41,42,43,44,46,47,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,70,71,72,73,77,78,79]
+ Details:
We chained rule 39 to obtain the rules [80,81,82,83,84,85,86] .
* Step 19: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
40. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) True (?,1)
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
60. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D && 1 + C = 0] (?,2)
61. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
62. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
63. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [1 + C = 0] (?,2)
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
65. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,2)
66. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1) [1 + C = 0 && 0 >= -1] (?,3)
67. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
68. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
69. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
70. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
71. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
72. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
74. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& D = 0]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
76. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
77. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& D = 0]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
79. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
80. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= -1 + D]
81. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& D = 0]
82. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
83. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
84. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& D = 0]
85. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
86. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[40->{44,45,46},41->{},42->{44,45,46},43->{41},44->{40},45->{54,55,56,57,58,59,60,61,62,63,64,65},46->{}
,47->{44,45,46},48->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},49->{66,67,68,69,70,71
,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},50->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84
,85,86},51->{40},52->{40},53->{40},54->{47,48,49,50,51,52,53},55->{47,48,49,50,51,52,53},56->{47,48,49,50,51
,52,53},57->{47,48,49,50,51,52,53},58->{47,48,49,50,51,52,53},59->{47,48,49,50,51,52,53},60->{47,48,49,50,51
,52,53},61->{47,48,49,50,51,52,53},62->{47,48,49,50,51,52,53},63->{44,45,46},64->{44,45,46},65->{44,45,46}
,66->{44,45,46},67->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},68->{66,67,68,69,70,71
,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},69->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84
,85,86},70->{40},71->{40},72->{40},73->{44,45,46},74->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83
,84,85,86},75->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},76->{66,67,68,69,70,71,72,73
,74,75,76,77,78,79,80,81,82,83,84,85,86},77->{40},78->{40},79->{40},80->{44,45,46},81->{66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86},82->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85
,86},83->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},84->{40},85->{40},86->{40}]
Sizebounds:
(<40,0,A>, A) (<40,0,B>, ?) (<40,0,C>, ?)
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
(<60,0,A>, A) (<60,0,B>, ?) (<60,0,C>, 1)
(<61,0,A>, A) (<61,0,B>, ?) (<61,0,C>, 0)
(<62,0,A>, A) (<62,0,B>, ?) (<62,0,C>, 0)
(<63,0,A>, A) (<63,0,B>, ?) (<63,0,C>, ?)
(<64,0,A>, A) (<64,0,B>, ?) (<64,0,C>, ?)
(<65,0,A>, A) (<65,0,B>, ?) (<65,0,C>, ?)
(<66,0,A>, A) (<66,0,B>, ?) (<66,0,C>, ?)
(<67,0,A>, A) (<67,0,B>, ?) (<67,0,C>, 0)
(<68,0,A>, A) (<68,0,B>, ?) (<68,0,C>, ?)
(<69,0,A>, A) (<69,0,B>, ?) (<69,0,C>, 0)
(<70,0,A>, A) (<70,0,B>, ?) (<70,0,C>, ?)
(<71,0,A>, A) (<71,0,B>, ?) (<71,0,C>, ?)
(<72,0,A>, A) (<72,0,B>, ?) (<72,0,C>, ?)
(<73,0,A>, A) (<73,0,B>, ?) (<73,0,C>, ?)
(<74,0,A>, A) (<74,0,B>, ?) (<74,0,C>, 0)
(<75,0,A>, A) (<75,0,B>, ?) (<75,0,C>, ?)
(<76,0,A>, A) (<76,0,B>, ?) (<76,0,C>, 0)
(<77,0,A>, A) (<77,0,B>, ?) (<77,0,C>, ?)
(<78,0,A>, A) (<78,0,B>, ?) (<78,0,C>, ?)
(<79,0,A>, A) (<79,0,B>, ?) (<79,0,C>, ?)
(<80,0,A>, A) (<80,0,B>, ?) (<80,0,C>, ?)
(<81,0,A>, A) (<81,0,B>, ?) (<81,0,C>, 0)
(<82,0,A>, A) (<82,0,B>, ?) (<82,0,C>, ?)
(<83,0,A>, A) (<83,0,B>, ?) (<83,0,C>, 0)
(<84,0,A>, A) (<84,0,B>, ?) (<84,0,C>, ?)
(<85,0,A>, A) (<85,0,B>, ?) (<85,0,C>, ?)
(<86,0,A>, A) (<86,0,B>, ?) (<86,0,C>, ?)
+ Applied Processor:
ChainProcessor False [40,41,42,43,44,46,47,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,70,71,72,73,77,78,79,80,84,85,86]
+ Details:
We chained rule 40 to obtain the rules [87,88,89] .
* Step 20: UnsatPaths WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
60. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D && 1 + C = 0] (?,2)
61. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
62. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
63. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [1 + C = 0] (?,2)
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
65. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,2)
66. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1) [1 + C = 0 && 0 >= -1] (?,3)
67. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
68. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
69. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
70. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
71. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
72. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
74. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& D = 0]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
76. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
77. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& D = 0]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
79. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
80. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= -1 + D]
81. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& D = 0]
82. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
83. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
84. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& D = 0]
85. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
86. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (?,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (?,3)
89. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1stop(A,1 + B,C) [1 + B >= A] (?,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[41->{},42->{44,45,46},43->{41},44->{87,88,89},45->{54,55,56,57,58,59,60,61,62,63,64,65},46->{},47->{44,45
,46},48->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},49->{66,67,68,69,70,71,72,73,74,75
,76,77,78,79,80,81,82,83,84,85,86},50->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86}
,51->{87,88,89},52->{87,88,89},53->{87,88,89},54->{47,48,49,50,51,52,53},55->{47,48,49,50,51,52,53},56->{47
,48,49,50,51,52,53},57->{47,48,49,50,51,52,53},58->{47,48,49,50,51,52,53},59->{47,48,49,50,51,52,53},60->{47
,48,49,50,51,52,53},61->{47,48,49,50,51,52,53},62->{47,48,49,50,51,52,53},63->{44,45,46},64->{44,45,46}
,65->{44,45,46},66->{44,45,46},67->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},68->{66
,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},69->{66,67,68,69,70,71,72,73,74,75,76,77,78,79
,80,81,82,83,84,85,86},70->{87,88,89},71->{87,88,89},72->{87,88,89},73->{44,45,46},74->{66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86},75->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85
,86},76->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},77->{87,88,89},78->{87,88,89}
,79->{87,88,89},80->{44,45,46},81->{66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},82->{66
,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86},83->{66,67,68,69,70,71,72,73,74,75,76,77,78,79
,80,81,82,83,84,85,86},84->{87,88,89},85->{87,88,89},86->{87,88,89},87->{87,88,89},88->{54,55,56,57,58,59,60
,61,62,63,64,65},89->{}]
Sizebounds:
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
(<60,0,A>, A) (<60,0,B>, ?) (<60,0,C>, 1)
(<61,0,A>, A) (<61,0,B>, ?) (<61,0,C>, 0)
(<62,0,A>, A) (<62,0,B>, ?) (<62,0,C>, 0)
(<63,0,A>, A) (<63,0,B>, ?) (<63,0,C>, ?)
(<64,0,A>, A) (<64,0,B>, ?) (<64,0,C>, ?)
(<65,0,A>, A) (<65,0,B>, ?) (<65,0,C>, ?)
(<66,0,A>, A) (<66,0,B>, ?) (<66,0,C>, ?)
(<67,0,A>, A) (<67,0,B>, ?) (<67,0,C>, 0)
(<68,0,A>, A) (<68,0,B>, ?) (<68,0,C>, ?)
(<69,0,A>, A) (<69,0,B>, ?) (<69,0,C>, 0)
(<70,0,A>, A) (<70,0,B>, ?) (<70,0,C>, ?)
(<71,0,A>, A) (<71,0,B>, ?) (<71,0,C>, ?)
(<72,0,A>, A) (<72,0,B>, ?) (<72,0,C>, ?)
(<73,0,A>, A) (<73,0,B>, ?) (<73,0,C>, ?)
(<74,0,A>, A) (<74,0,B>, ?) (<74,0,C>, 0)
(<75,0,A>, A) (<75,0,B>, ?) (<75,0,C>, ?)
(<76,0,A>, A) (<76,0,B>, ?) (<76,0,C>, 0)
(<77,0,A>, A) (<77,0,B>, ?) (<77,0,C>, ?)
(<78,0,A>, A) (<78,0,B>, ?) (<78,0,C>, ?)
(<79,0,A>, A) (<79,0,B>, ?) (<79,0,C>, ?)
(<80,0,A>, A) (<80,0,B>, ?) (<80,0,C>, ?)
(<81,0,A>, A) (<81,0,B>, ?) (<81,0,C>, 0)
(<82,0,A>, A) (<82,0,B>, ?) (<82,0,C>, ?)
(<83,0,A>, A) (<83,0,B>, ?) (<83,0,C>, 0)
(<84,0,A>, A) (<84,0,B>, ?) (<84,0,C>, ?)
(<85,0,A>, A) (<85,0,B>, ?) (<85,0,C>, ?)
(<86,0,A>, A) (<86,0,B>, ?) (<86,0,C>, ?)
(<87,0,A>, A) (<87,0,B>, ?) (<87,0,C>, ?)
(<88,0,A>, A) (<88,0,B>, ?) (<88,0,C>, ?)
(<89,0,A>, A) (<89,0,B>, ?) (<89,0,C>, ?)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(42,44)
,(42,46)
,(45,54)
,(45,55)
,(45,56)
,(45,57)
,(45,59)
,(45,60)
,(45,61)
,(45,62)
,(45,63)
,(45,65)
,(48,66)
,(48,67)
,(48,68)
,(48,69)
,(48,70)
,(48,71)
,(48,72)
,(48,73)
,(48,74)
,(48,75)
,(48,76)
,(48,77)
,(48,78)
,(48,79)
,(48,80)
,(48,81)
,(48,82)
,(48,83)
,(48,84)
,(48,85)
,(48,86)
,(49,66)
,(49,67)
,(49,68)
,(49,69)
,(49,70)
,(49,71)
,(49,72)
,(49,74)
,(49,76)
,(49,77)
,(49,79)
,(49,80)
,(49,81)
,(49,82)
,(49,83)
,(49,84)
,(49,85)
,(49,86)
,(50,66)
,(50,67)
,(50,68)
,(50,69)
,(50,70)
,(50,71)
,(50,72)
,(50,73)
,(50,74)
,(50,75)
,(50,76)
,(50,77)
,(50,78)
,(50,79)
,(50,80)
,(50,81)
,(50,82)
,(50,83)
,(50,84)
,(50,85)
,(50,86)
,(51,87)
,(51,88)
,(51,89)
,(53,87)
,(53,88)
,(53,89)
,(54,48)
,(54,49)
,(54,50)
,(54,51)
,(54,52)
,(54,53)
,(55,47)
,(55,48)
,(55,49)
,(55,50)
,(55,51)
,(55,52)
,(55,53)
,(56,47)
,(56,48)
,(56,49)
,(56,50)
,(56,51)
,(56,52)
,(56,53)
,(57,47)
,(57,48)
,(57,49)
,(57,50)
,(57,51)
,(57,52)
,(57,53)
,(58,48)
,(58,50)
,(58,51)
,(58,53)
,(59,47)
,(59,48)
,(59,49)
,(59,50)
,(59,51)
,(59,52)
,(59,53)
,(60,47)
,(60,48)
,(60,49)
,(60,50)
,(60,51)
,(60,52)
,(60,53)
,(61,47)
,(61,48)
,(61,49)
,(61,50)
,(61,51)
,(61,52)
,(61,53)
,(62,48)
,(62,49)
,(62,50)
,(62,51)
,(62,52)
,(62,53)
,(67,66)
,(67,67)
,(67,68)
,(67,69)
,(67,70)
,(67,71)
,(67,72)
,(67,73)
,(67,74)
,(67,75)
,(67,76)
,(67,77)
,(67,78)
,(67,79)
,(67,80)
,(67,81)
,(67,82)
,(67,83)
,(67,84)
,(67,85)
,(67,86)
,(68,66)
,(68,67)
,(68,68)
,(68,69)
,(68,70)
,(68,71)
,(68,72)
,(68,73)
,(68,74)
,(68,75)
,(68,76)
,(68,77)
,(68,78)
,(68,79)
,(68,80)
,(68,81)
,(68,82)
,(68,83)
,(68,84)
,(68,85)
,(68,86)
,(69,66)
,(69,67)
,(69,68)
,(69,69)
,(69,70)
,(69,71)
,(69,72)
,(69,73)
,(69,74)
,(69,75)
,(69,76)
,(69,77)
,(69,78)
,(69,79)
,(69,80)
,(69,81)
,(69,82)
,(69,83)
,(69,84)
,(69,85)
,(69,86)
,(70,87)
,(70,88)
,(70,89)
,(71,87)
,(71,88)
,(71,89)
,(72,87)
,(72,88)
,(72,89)
,(74,66)
,(74,67)
,(74,68)
,(74,69)
,(74,70)
,(74,71)
,(74,72)
,(74,73)
,(74,74)
,(74,75)
,(74,76)
,(74,77)
,(74,78)
,(74,79)
,(74,80)
,(74,81)
,(74,82)
,(74,83)
,(74,84)
,(74,85)
,(74,86)
,(75,66)
,(75,67)
,(75,68)
,(75,69)
,(75,70)
,(75,71)
,(75,72)
,(75,74)
,(75,76)
,(75,77)
,(75,79)
,(75,80)
,(75,81)
,(75,82)
,(75,83)
,(75,84)
,(75,85)
,(75,86)
,(76,66)
,(76,67)
,(76,68)
,(76,69)
,(76,70)
,(76,71)
,(76,72)
,(76,73)
,(76,74)
,(76,75)
,(76,76)
,(76,77)
,(76,78)
,(76,79)
,(76,80)
,(76,81)
,(76,82)
,(76,83)
,(76,84)
,(76,85)
,(76,86)
,(77,87)
,(77,88)
,(77,89)
,(79,87)
,(79,88)
,(79,89)
,(81,66)
,(81,67)
,(81,68)
,(81,69)
,(81,70)
,(81,71)
,(81,72)
,(81,73)
,(81,74)
,(81,75)
,(81,76)
,(81,77)
,(81,78)
,(81,79)
,(81,80)
,(81,81)
,(81,82)
,(81,83)
,(81,84)
,(81,85)
,(81,86)
,(82,66)
,(82,67)
,(82,68)
,(82,69)
,(82,70)
,(82,71)
,(82,72)
,(82,73)
,(82,74)
,(82,75)
,(82,76)
,(82,77)
,(82,78)
,(82,79)
,(82,80)
,(82,81)
,(82,82)
,(82,83)
,(82,84)
,(82,85)
,(82,86)
,(83,66)
,(83,67)
,(83,68)
,(83,69)
,(83,70)
,(83,71)
,(83,72)
,(83,73)
,(83,74)
,(83,75)
,(83,76)
,(83,77)
,(83,78)
,(83,79)
,(83,80)
,(83,81)
,(83,82)
,(83,83)
,(83,84)
,(83,85)
,(83,86)
,(84,87)
,(84,88)
,(84,89)
,(85,87)
,(85,88)
,(85,89)
,(86,87)
,(86,88)
,(86,89)
,(88,54)
,(88,55)
,(88,56)
,(88,57)
,(88,59)
,(88,60)
,(88,61)
,(88,62)
,(88,63)
,(88,65)]
* Step 21: UnreachableRules WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
48. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
50. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
51. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 1 + C = 0] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
53. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && 0 >= 2 + C && 0 >= D$ && 2*D$ >= 1 + C && 2 + C >= 2*D$] (?,2)
54. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [1 + C = 0 && 1 + C = 0] (?,2)
55. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
56. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [1 + C = 0 (?,2)
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
57. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C && 1 + C = 0] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
59. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
60. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D && 1 + C = 0] (?,2)
61. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
62. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [0 >= 2 + C (?,2)
&& 0 >= D
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= 2 + C
&& 0 >= E$
&& 0 >= F$
&& 0 >= D$
&& 2*E$ >= 1 + C
&& 2 + C >= 2*E$
&& 2*F$ >= 1 + C
&& 2 + C >= 2*F$
&& 2*D$ >= 1 + C
&& 2 + C >= 2*D$]
63. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [1 + C = 0] (?,2)
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
65. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= 2 + C && 0 >= D && 2*D >= 1 + C && 2 + C >= 2*D] (?,2)
66. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1) [1 + C = 0 && 0 >= -1] (?,3)
67. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
68. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
69. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
70. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 = 0] (?,3)
71. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && -1 >= 0 && D$$ >= 0 && 0 >= 2*D$$ && 2*D$$ >= -1] (?,3)
72. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1) [1 + C = 0 && -1 >= 1 && 0 >= 1 && 0 >= D$$ && 2*D$$ >= 0 && 1 >= 2*D$$] (?,3)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
74. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& D = 0]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
76. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
77. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& D = 0]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
79. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
80. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& 0 >= -1 + D]
81. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& D = 0]
82. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
83. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
84. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& D = 0]
85. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
86. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [0 >= 2 + C (?,3)
&& 0 >= E
&& 0 >= F
&& 0 >= D
&& 2*E >= 1 + C
&& 2 + C >= 2*E
&& 2*F >= 1 + C
&& 2 + C >= 2*F
&& 2*D >= 1 + C
&& 2 + C >= 2*D
&& -1 + D >= 1
&& 0 >= 1 + D
&& 0 >= D$$
&& 2*D$$ >= D
&& 1 + D >= 2*D$$]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (?,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (?,3)
89. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1stop(A,1 + B,C) [1 + B >= A] (?,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[41->{},42->{45},43->{41},44->{87,88,89},45->{58,64},46->{},47->{44,45,46},48->{},49->{73,75,78},50->{}
,51->{},52->{87,88,89},53->{},54->{47},55->{},56->{},57->{},58->{47,49,52},59->{},60->{},61->{},62->{47}
,63->{44,45,46},64->{44,45,46},65->{44,45,46},66->{44,45,46},67->{},68->{},69->{},70->{},71->{},72->{}
,73->{44,45,46},74->{},75->{73,75,78},76->{},77->{},78->{87,88,89},79->{},80->{44,45,46},81->{},82->{}
,83->{},84->{},85->{},86->{},87->{87,88,89},88->{58,64},89->{}]
Sizebounds:
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<48,0,A>, A) (<48,0,B>, ?) (<48,0,C>, 0)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<50,0,A>, A) (<50,0,B>, ?) (<50,0,C>, 0)
(<51,0,A>, A) (<51,0,B>, ?) (<51,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<53,0,A>, A) (<53,0,B>, ?) (<53,0,C>, ?)
(<54,0,A>, A) (<54,0,B>, ?) (<54,0,C>, 1)
(<55,0,A>, A) (<55,0,B>, ?) (<55,0,C>, 0)
(<56,0,A>, A) (<56,0,B>, ?) (<56,0,C>, 0)
(<57,0,A>, A) (<57,0,B>, ?) (<57,0,C>, 1)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<59,0,A>, A) (<59,0,B>, ?) (<59,0,C>, 0)
(<60,0,A>, A) (<60,0,B>, ?) (<60,0,C>, 1)
(<61,0,A>, A) (<61,0,B>, ?) (<61,0,C>, 0)
(<62,0,A>, A) (<62,0,B>, ?) (<62,0,C>, 0)
(<63,0,A>, A) (<63,0,B>, ?) (<63,0,C>, ?)
(<64,0,A>, A) (<64,0,B>, ?) (<64,0,C>, ?)
(<65,0,A>, A) (<65,0,B>, ?) (<65,0,C>, ?)
(<66,0,A>, A) (<66,0,B>, ?) (<66,0,C>, ?)
(<67,0,A>, A) (<67,0,B>, ?) (<67,0,C>, 0)
(<68,0,A>, A) (<68,0,B>, ?) (<68,0,C>, ?)
(<69,0,A>, A) (<69,0,B>, ?) (<69,0,C>, 0)
(<70,0,A>, A) (<70,0,B>, ?) (<70,0,C>, ?)
(<71,0,A>, A) (<71,0,B>, ?) (<71,0,C>, ?)
(<72,0,A>, A) (<72,0,B>, ?) (<72,0,C>, ?)
(<73,0,A>, A) (<73,0,B>, ?) (<73,0,C>, ?)
(<74,0,A>, A) (<74,0,B>, ?) (<74,0,C>, 0)
(<75,0,A>, A) (<75,0,B>, ?) (<75,0,C>, ?)
(<76,0,A>, A) (<76,0,B>, ?) (<76,0,C>, 0)
(<77,0,A>, A) (<77,0,B>, ?) (<77,0,C>, ?)
(<78,0,A>, A) (<78,0,B>, ?) (<78,0,C>, ?)
(<79,0,A>, A) (<79,0,B>, ?) (<79,0,C>, ?)
(<80,0,A>, A) (<80,0,B>, ?) (<80,0,C>, ?)
(<81,0,A>, A) (<81,0,B>, ?) (<81,0,C>, 0)
(<82,0,A>, A) (<82,0,B>, ?) (<82,0,C>, ?)
(<83,0,A>, A) (<83,0,B>, ?) (<83,0,C>, 0)
(<84,0,A>, A) (<84,0,B>, ?) (<84,0,C>, ?)
(<85,0,A>, A) (<85,0,B>, ?) (<85,0,C>, ?)
(<86,0,A>, A) (<86,0,B>, ?) (<86,0,C>, ?)
(<87,0,A>, A) (<87,0,B>, ?) (<87,0,C>, ?)
(<88,0,A>, A) (<88,0,B>, ?) (<88,0,C>, ?)
(<89,0,A>, A) (<89,0,B>, ?) (<89,0,C>, ?)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [48
,50
,51
,53
,54
,55
,56
,57
,59
,60
,61
,62
,63
,65
,66
,67
,68
,69
,70
,71
,72
,74
,76
,77
,79
,80
,81
,82
,83
,84
,85
,86]
* Step 22: LeafRules WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
41. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1)
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
46. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1stop(A,B,C) [B >= A] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (?,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (?,3)
89. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1stop(A,1 + B,C) [1 + B >= A] (?,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[41->{},42->{45},43->{41},44->{87,88,89},45->{58,64},46->{},47->{44,45,46},49->{73,75,78},52->{87,88,89}
,58->{47,49,52},64->{44,45,46},73->{44,45,46},75->{73,75,78},78->{87,88,89},87->{87,88,89},88->{58,64}
,89->{}]
Sizebounds:
(<41,0,A>, A) (<41,0,B>, ?) (<41,0,C>, ?)
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<46,0,A>, A) (<46,0,B>, ?) (<46,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<64,0,A>, A) (<64,0,B>, ?) (<64,0,C>, ?)
(<73,0,A>, A) (<73,0,B>, ?) (<73,0,C>, ?)
(<75,0,A>, A) (<75,0,B>, ?) (<75,0,C>, ?)
(<78,0,A>, A) (<78,0,B>, ?) (<78,0,C>, ?)
(<87,0,A>, A) (<87,0,B>, ?) (<87,0,C>, ?)
(<88,0,A>, A) (<88,0,B>, ?) (<88,0,C>, ?)
(<89,0,A>, A) (<89,0,B>, ?) (<89,0,C>, ?)
+ Applied Processor:
LeafRules
+ Details:
The following transitions are estimated by its predecessors and are removed [41,46,89]
* Step 23: LocalSizeboundsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (?,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (?,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, A) (<45,0,B>, ?) (<45,0,C>, ?)
(<47,0,A>, A) (<47,0,B>, ?) (<47,0,C>, ?)
(<49,0,A>, A) (<49,0,B>, ?) (<49,0,C>, ?)
(<52,0,A>, A) (<52,0,B>, ?) (<52,0,C>, ?)
(<58,0,A>, A) (<58,0,B>, ?) (<58,0,C>, 0)
(<64,0,A>, A) (<64,0,B>, ?) (<64,0,C>, ?)
(<73,0,A>, A) (<73,0,B>, ?) (<73,0,C>, ?)
(<75,0,A>, A) (<75,0,B>, ?) (<75,0,C>, ?)
(<78,0,A>, A) (<78,0,B>, ?) (<78,0,C>, ?)
(<87,0,A>, A) (<87,0,B>, ?) (<87,0,C>, ?)
(<88,0,A>, A) (<88,0,B>, ?) (<88,0,C>, ?)
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(<42,0,A>, A, .= 0) (<42,0,B>, 1, .= 1) (<42,0,C>, C, .= 0)
(<43,0,A>, A, .= 0) (<43,0,B>, B, .= 0) (<43,0,C>, C, .= 0)
(<44,0,A>, A, .= 0) (<44,0,B>, B, .= 0) (<44,0,C>, B, .= 0)
(<45,0,A>, A, .= 0) (<45,0,B>, B, .= 0) (<45,0,C>, B, .= 0)
(<47,0,A>, A, .= 0) (<47,0,B>, 1 + B, .+ 1) (<47,0,C>, C, .= 0)
(<49,0,A>, A, .= 0) (<49,0,B>, B, .= 0) (<49,0,C>, C, .= 0)
(<52,0,A>, A, .= 0) (<52,0,B>, B, .= 0) (<52,0,C>, C, .= 0)
(<58,0,A>, A, .= 0) (<58,0,B>, B, .= 0) (<58,0,C>, 1 + C, .+ 1)
(<64,0,A>, A, .= 0) (<64,0,B>, 1 + B, .+ 1) (<64,0,C>, C, .= 0)
(<73,0,A>, A, .= 0) (<73,0,B>, 1 + B, .+ 1) (<73,0,C>, 1, .= 1)
(<75,0,A>, A, .= 0) (<75,0,B>, B, .= 0) (<75,0,C>, C, .= 0)
(<78,0,A>, A, .= 0) (<78,0,B>, B, .= 0) (<78,0,C>, C, .= 0)
(<87,0,A>, A, .= 0) (<87,0,B>, 1 + A + B, .* 1) (<87,0,C>, 1 + A + B, .* 1)
(<88,0,A>, A, .= 0) (<88,0,B>, 1 + A + B, .* 1) (<88,0,C>, 1 + A + B, .* 1)
* Step 24: SizeboundsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (?,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (?,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, ?) (<42,0,B>, ?) (<42,0,C>, ?)
(<43,0,A>, ?) (<43,0,B>, ?) (<43,0,C>, ?)
(<44,0,A>, ?) (<44,0,B>, ?) (<44,0,C>, ?)
(<45,0,A>, ?) (<45,0,B>, ?) (<45,0,C>, ?)
(<47,0,A>, ?) (<47,0,B>, ?) (<47,0,C>, ?)
(<49,0,A>, ?) (<49,0,B>, ?) (<49,0,C>, ?)
(<52,0,A>, ?) (<52,0,B>, ?) (<52,0,C>, ?)
(<58,0,A>, ?) (<58,0,B>, ?) (<58,0,C>, ?)
(<64,0,A>, ?) (<64,0,B>, ?) (<64,0,C>, ?)
(<73,0,A>, ?) (<73,0,B>, ?) (<73,0,C>, ?)
(<75,0,A>, ?) (<75,0,B>, ?) (<75,0,C>, ?)
(<78,0,A>, ?) (<78,0,B>, ?) (<78,0,C>, ?)
(<87,0,A>, ?) (<87,0,B>, ?) (<87,0,C>, ?)
(<88,0,A>, ?) (<88,0,B>, ?) (<88,0,C>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
* Step 25: LocationConstraintsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (?,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (?,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
LocationConstraintsProc
+ Details:
We computed the location constraints 42 : True 43 : True 44 : True 45 : True 47 : [False] 49 : [False] 52 : [False] 58 : [A >= 1 + B] 64 : [A >= 1 + B] 73 : [C >= 1] 75 : [C >= 1] 78 : [C >= 1] 87 : True 88 : True .
* Step 26: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (?,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (?,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalrealheapsortstep1bb2in) = -1 + x1 + -1*x2
p(evalrealheapsortstep1bb3in) = -1 + x1 + -1*x2
p(evalrealheapsortstep1bb4in) = -1 + x1 + -1*x2
p(evalrealheapsortstep1bb5in) = -1 + x1 + -1*x2
p(evalrealheapsortstep1bb6in) = x1 + -1*x2
p(evalrealheapsortstep1returnin) = x1
p(evalrealheapsortstep1start) = x1
The following rules are strictly oriented:
[A >= 3] ==>
evalrealheapsortstep1start(A,B,C) = A
> -1 + A
= evalrealheapsortstep1bb6in(A,1,C)
[A >= 2 + B && 1 + B >= 1] ==>
evalrealheapsortstep1bb5in(A,B,C) = -1 + A + -1*B
> -2 + A + -1*B
= evalrealheapsortstep1bb4in(A,1 + B,1 + B)
The following rules are weakly oriented:
[2 >= A] ==>
evalrealheapsortstep1start(A,B,C) = A
>= A
= evalrealheapsortstep1returnin(A,B,C)
[A >= 1 + B && 0 >= B] ==>
evalrealheapsortstep1bb6in(A,B,C) = A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb5in(A,B,B)
[A >= 1 + B && B >= 1] ==>
evalrealheapsortstep1bb6in(A,B,C) = A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb4in(A,B,B)
[0 >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = -1 + A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = -1 + A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb2in(A,B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = -1 + A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb5in(A,B,C)
[C >= 0 ==>
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
evalrealheapsortstep1bb4in(A,B,C) = -1 + A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb3in(A,B,-1 + D$)
[C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] ==>
evalrealheapsortstep1bb4in(A,B,C) = -1 + A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = -1 + A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = -1 + A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb2in(A,B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = -1 + A + -1*B
>= -1 + A + -1*B
= evalrealheapsortstep1bb5in(A,B,-1 + D)
[A >= 2 + B && 0 >= 1 + B] ==>
evalrealheapsortstep1bb5in(A,B,C) = -1 + A + -1*B
>= -2 + A + -1*B
= evalrealheapsortstep1bb5in(A,1 + B,1 + B)
* Step 27: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (?,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (A,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalrealheapsortstep1bb2in) = -1*x2
p(evalrealheapsortstep1bb3in) = -1*x2
p(evalrealheapsortstep1bb4in) = -1*x2
p(evalrealheapsortstep1bb5in) = -1*x2
p(evalrealheapsortstep1bb6in) = -1*x2
p(evalrealheapsortstep1returnin) = 1
p(evalrealheapsortstep1start) = 1
The following rules are strictly oriented:
[A >= 3] ==>
evalrealheapsortstep1start(A,B,C) = 1
> -1
= evalrealheapsortstep1bb6in(A,1,C)
[A >= 2 + B && 0 >= 1 + B] ==>
evalrealheapsortstep1bb5in(A,B,C) = -1*B
> -1 + -1*B
= evalrealheapsortstep1bb5in(A,1 + B,1 + B)
The following rules are weakly oriented:
[2 >= A] ==>
evalrealheapsortstep1start(A,B,C) = 1
>= 1
= evalrealheapsortstep1returnin(A,B,C)
[A >= 1 + B && 0 >= B] ==>
evalrealheapsortstep1bb6in(A,B,C) = -1*B
>= -1*B
= evalrealheapsortstep1bb5in(A,B,B)
[A >= 1 + B && B >= 1] ==>
evalrealheapsortstep1bb6in(A,B,C) = -1*B
>= -1*B
= evalrealheapsortstep1bb4in(A,B,B)
[0 >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = -1*B
>= -1 + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = -1*B
>= -1*B
= evalrealheapsortstep1bb2in(A,B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = -1*B
>= -1*B
= evalrealheapsortstep1bb5in(A,B,C)
[C >= 0 ==>
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
evalrealheapsortstep1bb4in(A,B,C) = -1*B
>= -1*B
= evalrealheapsortstep1bb3in(A,B,-1 + D$)
[C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] ==>
evalrealheapsortstep1bb4in(A,B,C) = -1*B
>= -1 + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = -1*B
>= -1 + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = -1*B
>= -1*B
= evalrealheapsortstep1bb2in(A,B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = -1*B
>= -1*B
= evalrealheapsortstep1bb5in(A,B,-1 + D)
[A >= 2 + B && 1 + B >= 1] ==>
evalrealheapsortstep1bb5in(A,B,C) = -1*B
>= -1 + -1*B
= evalrealheapsortstep1bb4in(A,1 + B,1 + B)
* Step 28: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (?,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (1,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (A,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalrealheapsortstep1bb2in) = 1 + -1*x2
p(evalrealheapsortstep1bb3in) = 1 + -1*x2
p(evalrealheapsortstep1bb4in) = 2 + -1*x2
p(evalrealheapsortstep1bb5in) = 1 + -1*x2
p(evalrealheapsortstep1bb6in) = 2 + -1*x2
p(evalrealheapsortstep1returnin) = 1
p(evalrealheapsortstep1start) = 1
The following rules are strictly oriented:
[A >= 1 + B && 0 >= B] ==>
evalrealheapsortstep1bb6in(A,B,C) = 2 + -1*B
> 1 + -1*B
= evalrealheapsortstep1bb5in(A,B,B)
[A >= 2 + B && 0 >= 1 + B] ==>
evalrealheapsortstep1bb5in(A,B,C) = 1 + -1*B
> -1*B
= evalrealheapsortstep1bb5in(A,1 + B,1 + B)
The following rules are weakly oriented:
[A >= 3] ==>
evalrealheapsortstep1start(A,B,C) = 1
>= 1
= evalrealheapsortstep1bb6in(A,1,C)
[2 >= A] ==>
evalrealheapsortstep1start(A,B,C) = 1
>= 1
= evalrealheapsortstep1returnin(A,B,C)
[A >= 1 + B && B >= 1] ==>
evalrealheapsortstep1bb6in(A,B,C) = 2 + -1*B
>= 2 + -1*B
= evalrealheapsortstep1bb4in(A,B,B)
[0 >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1 + -1*B
>= 1 + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1 + -1*B
>= 1 + -1*B
= evalrealheapsortstep1bb2in(A,B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1 + -1*B
>= 1 + -1*B
= evalrealheapsortstep1bb5in(A,B,C)
[C >= 0 ==>
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
evalrealheapsortstep1bb4in(A,B,C) = 2 + -1*B
>= 1 + -1*B
= evalrealheapsortstep1bb3in(A,B,-1 + D$)
[C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] ==>
evalrealheapsortstep1bb4in(A,B,C) = 2 + -1*B
>= 1 + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1 + -1*B
>= 1 + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1 + -1*B
>= 1 + -1*B
= evalrealheapsortstep1bb2in(A,B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1 + -1*B
>= 1 + -1*B
= evalrealheapsortstep1bb5in(A,B,-1 + D)
[A >= 2 + B && 1 + B >= 1] ==>
evalrealheapsortstep1bb5in(A,B,C) = 1 + -1*B
>= 1 + -1*B
= evalrealheapsortstep1bb4in(A,1 + B,1 + B)
* Step 29: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (1,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (?,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (1,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (A,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalrealheapsortstep1bb2in) = 1 + x1 + -1*x2
p(evalrealheapsortstep1bb3in) = 1 + x1 + -1*x2
p(evalrealheapsortstep1bb4in) = 1 + x1 + -1*x2
p(evalrealheapsortstep1bb5in) = x1 + -1*x2
p(evalrealheapsortstep1bb6in) = 2 + x1 + -1*x2
p(evalrealheapsortstep1returnin) = 1 + x1
p(evalrealheapsortstep1start) = 1 + x1
The following rules are strictly oriented:
[A >= 1 + B && 0 >= B] ==>
evalrealheapsortstep1bb6in(A,B,C) = 2 + A + -1*B
> A + -1*B
= evalrealheapsortstep1bb5in(A,B,B)
[A >= 1 + B && B >= 1] ==>
evalrealheapsortstep1bb6in(A,B,C) = 2 + A + -1*B
> 1 + A + -1*B
= evalrealheapsortstep1bb4in(A,B,B)
[A >= 2 + B && 0 >= 1 + B] ==>
evalrealheapsortstep1bb5in(A,B,C) = A + -1*B
> -1 + A + -1*B
= evalrealheapsortstep1bb5in(A,1 + B,1 + B)
The following rules are weakly oriented:
[A >= 3] ==>
evalrealheapsortstep1start(A,B,C) = 1 + A
>= 1 + A
= evalrealheapsortstep1bb6in(A,1,C)
[2 >= A] ==>
evalrealheapsortstep1start(A,B,C) = 1 + A
>= 1 + A
= evalrealheapsortstep1returnin(A,B,C)
[0 >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1 + A + -1*B
>= 1 + A + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1 + A + -1*B
>= 1 + A + -1*B
= evalrealheapsortstep1bb2in(A,B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1 + A + -1*B
>= A + -1*B
= evalrealheapsortstep1bb5in(A,B,C)
[C >= 0 ==>
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
evalrealheapsortstep1bb4in(A,B,C) = 1 + A + -1*B
>= 1 + A + -1*B
= evalrealheapsortstep1bb3in(A,B,-1 + D$)
[C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] ==>
evalrealheapsortstep1bb4in(A,B,C) = 1 + A + -1*B
>= 1 + A + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1 + A + -1*B
>= 1 + A + -1*B
= evalrealheapsortstep1bb6in(A,1 + B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1 + A + -1*B
>= 1 + A + -1*B
= evalrealheapsortstep1bb2in(A,B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1 + A + -1*B
>= A + -1*B
= evalrealheapsortstep1bb5in(A,B,-1 + D)
[A >= 2 + B && 1 + B >= 1] ==>
evalrealheapsortstep1bb5in(A,B,C) = A + -1*B
>= A + -1*B
= evalrealheapsortstep1bb4in(A,1 + B,1 + B)
* Step 30: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (1,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (1 + A,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (1,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (A,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [45,47,58,44,64,73,49,75,52,78,87], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalrealheapsortstep1bb2in) = 9
p(evalrealheapsortstep1bb3in) = 9
p(evalrealheapsortstep1bb4in) = 9
p(evalrealheapsortstep1bb5in) = 8
p(evalrealheapsortstep1bb6in) = 9
The following rules are strictly oriented:
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 9
> 8
= evalrealheapsortstep1bb5in(A,B,C)
The following rules are weakly oriented:
[A >= 1 + B && 0 >= B] ==>
evalrealheapsortstep1bb6in(A,B,C) = 9
>= 8
= evalrealheapsortstep1bb5in(A,B,B)
[A >= 1 + B && B >= 1] ==>
evalrealheapsortstep1bb6in(A,B,C) = 9
>= 9
= evalrealheapsortstep1bb4in(A,B,B)
[0 >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 9
>= 9
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 9
>= 9
= evalrealheapsortstep1bb2in(A,B,C)
[C >= 0 ==>
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
evalrealheapsortstep1bb4in(A,B,C) = 9
>= 9
= evalrealheapsortstep1bb3in(A,B,-1 + D$)
[C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] ==>
evalrealheapsortstep1bb4in(A,B,C) = 9
>= 9
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 9
>= 9
= evalrealheapsortstep1bb6in(A,1 + B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 9
>= 9
= evalrealheapsortstep1bb2in(A,B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 9
>= 8
= evalrealheapsortstep1bb5in(A,B,-1 + D)
[A >= 2 + B && 0 >= 1 + B] ==>
evalrealheapsortstep1bb5in(A,B,C) = 8
>= 8
= evalrealheapsortstep1bb5in(A,1 + B,1 + B)
We use the following global sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
* Step 31: KnowledgePropagation WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (1,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (1 + A,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (?,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (?,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (9 + 9*A,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (?,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (?,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (1,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (A,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 32: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (1,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (1 + A,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (1 + 2*A,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (1 + 2*A,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (9 + 9*A,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (1 + 2*A,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (1 + 2*A,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (1,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (A,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [45,47,88,44,64,73,49,75,52,78,87], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalrealheapsortstep1bb2in) = 1
p(evalrealheapsortstep1bb3in) = 1
p(evalrealheapsortstep1bb4in) = 0
p(evalrealheapsortstep1bb5in) = 0
p(evalrealheapsortstep1bb6in) = 0
The following rules are strictly oriented:
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1
> 0
= evalrealheapsortstep1bb5in(A,B,C)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1
> 0
= evalrealheapsortstep1bb6in(A,1 + B,-1 + D)
The following rules are weakly oriented:
[A >= 1 + B && 0 >= B] ==>
evalrealheapsortstep1bb6in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb5in(A,B,B)
[A >= 1 + B && B >= 1] ==>
evalrealheapsortstep1bb6in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb4in(A,B,B)
[0 >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1
>= 0
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1
>= 1
= evalrealheapsortstep1bb2in(A,B,C)
[C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] ==>
evalrealheapsortstep1bb4in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1
>= 1
= evalrealheapsortstep1bb2in(A,B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1
>= 0
= evalrealheapsortstep1bb5in(A,B,-1 + D)
[A >= 2 + B && 0 >= 1 + B] ==>
evalrealheapsortstep1bb5in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb5in(A,1 + B,1 + B)
[A >= 2 + B && 1 + B >= 1] ==>
evalrealheapsortstep1bb5in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb4in(A,1 + B,1 + B)
We use the following global sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
* Step 33: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (1,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (1 + A,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (1 + 2*A,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (1 + 2*A,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (1 + 2*A,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (1 + 2*A,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (1 + 2*A,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (1 + 2*A,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (1,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (A,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [45,47,88,44,64,73,49,75,52,78,87], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalrealheapsortstep1bb2in) = 1
p(evalrealheapsortstep1bb3in) = 1
p(evalrealheapsortstep1bb4in) = 0
p(evalrealheapsortstep1bb5in) = 0
p(evalrealheapsortstep1bb6in) = 0
The following rules are strictly oriented:
[0 >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1
> 0
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1
> 0
= evalrealheapsortstep1bb5in(A,B,C)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1
> 0
= evalrealheapsortstep1bb6in(A,1 + B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1
> 0
= evalrealheapsortstep1bb5in(A,B,-1 + D)
The following rules are weakly oriented:
[A >= 1 + B && 0 >= B] ==>
evalrealheapsortstep1bb6in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb5in(A,B,B)
[A >= 1 + B && B >= 1] ==>
evalrealheapsortstep1bb6in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb4in(A,B,B)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 1
>= 1
= evalrealheapsortstep1bb2in(A,B,C)
[C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] ==>
evalrealheapsortstep1bb4in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1
>= 1
= evalrealheapsortstep1bb2in(A,B,-1 + D)
[A >= 2 + B && 0 >= 1 + B] ==>
evalrealheapsortstep1bb5in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb5in(A,1 + B,1 + B)
[A >= 2 + B && 1 + B >= 1] ==>
evalrealheapsortstep1bb5in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb4in(A,1 + B,1 + B)
We use the following global sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
* Step 34: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (1,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (1 + A,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (1 + 2*A,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (1 + 2*A,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (1 + 2*A,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (1 + 2*A,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (1 + 2*A,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (1 + 2*A,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (?,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (1 + 2*A,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (1,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (A,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [45,47,58,88,44,64,73,75,52,78,87], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalrealheapsortstep1bb2in) = 1 + x3
p(evalrealheapsortstep1bb3in) = 0
p(evalrealheapsortstep1bb4in) = 0
p(evalrealheapsortstep1bb5in) = 0
p(evalrealheapsortstep1bb6in) = 0
The following rules are strictly oriented:
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1 + C
> 0
= evalrealheapsortstep1bb6in(A,1 + B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1 + C
> D
= evalrealheapsortstep1bb2in(A,B,-1 + D)
[C >= 0 ==>
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
evalrealheapsortstep1bb2in(A,B,C) = 1 + C
> 0
= evalrealheapsortstep1bb5in(A,B,-1 + D)
The following rules are weakly oriented:
[A >= 1 + B && 0 >= B] ==>
evalrealheapsortstep1bb6in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb5in(A,B,B)
[A >= 1 + B && B >= 1] ==>
evalrealheapsortstep1bb6in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb4in(A,B,B)
[0 >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb6in(A,1 + B,C)
[C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] ==>
evalrealheapsortstep1bb3in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb5in(A,B,C)
[C >= 0 ==>
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
evalrealheapsortstep1bb4in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb3in(A,B,-1 + D$)
[C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] ==>
evalrealheapsortstep1bb4in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb6in(A,1 + B,C)
[A >= 2 + B && 0 >= 1 + B] ==>
evalrealheapsortstep1bb5in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb5in(A,1 + B,1 + B)
[A >= 2 + B && 1 + B >= 1] ==>
evalrealheapsortstep1bb5in(A,B,C) = 0
>= 0
= evalrealheapsortstep1bb4in(A,1 + B,1 + B)
We use the following global sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
* Step 35: KnowledgePropagation WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
42. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,2)
43. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (1,2)
44. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,B) [A >= 1 + B && 0 >= B] (1,2)
45. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,B) [A >= 1 + B && B >= 1] (1 + A,2)
47. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [0 >= C] (1 + 2*A,2)
49. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (1 + 2*A,2)
52. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [C >= 1 && C >= 0 && D$ >= 0 && 1 + C >= 2*D$ && 2*D$ >= C] (1 + 2*A,2)
58. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D$) [C >= 0 (1 + 2*A,2)
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& C >= 0
&& E$ >= 0
&& 1 + C >= 2*E$
&& 2*E$ >= C
&& F$ >= 0
&& 1 + C >= 2*F$
&& 2*F$ >= C
&& D$ >= 0
&& 1 + C >= 2*D$
&& 2*D$ >= C]
64. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] (1 + 2*A,2)
73. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,-1 + D) [C >= 0 (1 + 2*A,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& 0 >= -1 + D]
75. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,-1 + D) [C >= 0 (3 + 7*A + 2*A^2,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
78. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,-1 + D) [C >= 0 (1 + 2*A,3)
&& E >= 0
&& 1 + C >= 2*E
&& 2*E >= C
&& F >= 0
&& 1 + C >= 2*F
&& 2*F >= C
&& D >= 0
&& 1 + C >= 2*D
&& 2*D >= C
&& -1 + D >= 1
&& -1 + D >= 0
&& D$$ >= 0
&& D >= 2*D$$
&& 2*D$$ >= -1 + D]
87. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb5in(A,1 + B,1 + B) [A >= 2 + B && 0 >= 1 + B] (1,3)
88. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb4in(A,1 + B,1 + B) [A >= 2 + B && 1 + B >= 1] (A,3)
Signature:
{(evalrealheapsortstep1bb2in,3)
;(evalrealheapsortstep1bb3in,3)
;(evalrealheapsortstep1bb4in,3)
;(evalrealheapsortstep1bb5in,3)
;(evalrealheapsortstep1bb6in,3)
;(evalrealheapsortstep1entryin,3)
;(evalrealheapsortstep1returnin,3)
;(evalrealheapsortstep1start,3)
;(evalrealheapsortstep1stop,3)}
Flow Graph:
[42->{45},43->{},44->{87,88},45->{58,64},47->{44,45},49->{73,75,78},52->{87,88},58->{47,49,52},64->{44,45}
,73->{44,45},75->{73,75,78},78->{87,88},87->{87,88},88->{58,64}]
Sizebounds:
(<42,0,A>, A) (<42,0,B>, 1) (<42,0,C>, C)
(<43,0,A>, A) (<43,0,B>, B) (<43,0,C>, C)
(<44,0,A>, A) (<44,0,B>, A) (<44,0,C>, A)
(<45,0,A>, A) (<45,0,B>, A) (<45,0,C>, 1 + A)
(<47,0,A>, A) (<47,0,B>, A) (<47,0,C>, 2 + A)
(<49,0,A>, A) (<49,0,B>, A) (<49,0,C>, 2 + A)
(<52,0,A>, A) (<52,0,B>, A) (<52,0,C>, 2 + A)
(<58,0,A>, A) (<58,0,B>, A) (<58,0,C>, 2 + A)
(<64,0,A>, A) (<64,0,B>, A) (<64,0,C>, 1 + A)
(<73,0,A>, A) (<73,0,B>, A) (<73,0,C>, 1)
(<75,0,A>, A) (<75,0,B>, A) (<75,0,C>, 0)
(<78,0,A>, A) (<78,0,B>, A) (<78,0,C>, 2 + A)
(<87,0,A>, A) (<87,0,B>, A) (<87,0,C>, A)
(<88,0,A>, A) (<88,0,B>, A) (<88,0,C>, A)
+ Applied Processor:
KnowledgePropagation
+ Details:
The problem is already solved.
WORST_CASE(?,O(n^2))