/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^2))  

Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. non_recursive  : [eval_realheapsort_step2_stop/6]
1. non_recursive  : [eval_realheapsort_step2_bb12_in/6]
2. recursive  : [eval_realheapsort_step2_bb10_in/7,eval_realheapsort_step2_bb4_in/7,eval_realheapsort_step2_bb5_in/7,eval_realheapsort_step2_bb6_in/7,eval_realheapsort_step2_bb7_in/7,eval_realheapsort_step2_bb8_in/7,eval_realheapsort_step2_bb9_in/7]
3. recursive  : [eval_realheapsort_step2_58/10,eval_realheapsort_step2_59/10,eval_realheapsort_step2_bb11_in/10,eval_realheapsort_step2_bb2_in/10,eval_realheapsort_step2_bb3_in/10,eval_realheapsort_step2_bb4_in_loop_cont/11]
4. non_recursive  : [exit_location/1]
5. non_recursive  : [eval_realheapsort_step2_bb2_in_loop_cont/7]
6. non_recursive  : [eval_realheapsort_step2_12/6]
7. non_recursive  : [eval_realheapsort_step2_11/6]
8. non_recursive  : [eval_realheapsort_step2_10/6]
9. non_recursive  : [eval_realheapsort_step2_9/6]
10. non_recursive  : [eval_realheapsort_step2_8/6]
11. non_recursive  : [eval_realheapsort_step2_7/6]
12. non_recursive  : [eval_realheapsort_step2_6/6]
13. non_recursive  : [eval_realheapsort_step2_5/6]
14. non_recursive  : [eval_realheapsort_step2_4/6]
15. non_recursive  : [eval_realheapsort_step2_3/6]
16. non_recursive  : [eval_realheapsort_step2_bb1_in/6]
17. non_recursive  : [eval_realheapsort_step2_2/6]
18. non_recursive  : [eval_realheapsort_step2_1/6]
19. non_recursive  : [eval_realheapsort_step2_0/6]
20. non_recursive  : [eval_realheapsort_step2_bb0_in/6]
21. non_recursive  : [eval_realheapsort_step2_start/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is completely evaluated into other SCCs
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into eval_realheapsort_step2_bb4_in/7
3. SCC is partially evaluated into eval_realheapsort_step2_bb2_in/10
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval_realheapsort_step2_bb2_in_loop_cont/7
6. SCC is partially evaluated into eval_realheapsort_step2_12/6
7. SCC is completely evaluated into other SCCs
8. SCC is completely evaluated into other SCCs
9. SCC is completely evaluated into other SCCs
10. SCC is completely evaluated into other SCCs
11. SCC is completely evaluated into other SCCs
12. SCC is completely evaluated into other SCCs
13. SCC is completely evaluated into other SCCs
14. SCC is completely evaluated into other SCCs
15. SCC is completely evaluated into other SCCs
16. SCC is completely evaluated into other SCCs
17. SCC is partially evaluated into eval_realheapsort_step2_2/6
18. SCC is completely evaluated into other SCCs
19. SCC is completely evaluated into other SCCs
20. SCC is completely evaluated into other SCCs
21. SCC is partially evaluated into eval_realheapsort_step2_start/6

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations eval_realheapsort_step2_bb4_in/7 
* CE 18 is refined into CE [19] 
* CE 17 is refined into CE [20] 
* CE 12 is refined into CE [21] 
* CE 14 is refined into CE [22] 
* CE 13 is refined into CE [23] 
* CE 15 is refined into CE [24] 
* CE 11 is refined into CE [25] 
* CE 16 is refined into CE [26] 


### Cost equations --> "Loop" of eval_realheapsort_step2_bb4_in/7 
* CEs [21] --> Loop 19 
* CEs [22] --> Loop 20 
* CEs [23] --> Loop 21 
* CEs [24] --> Loop 22 
* CEs [25] --> Loop 23 
* CEs [26] --> Loop 24 
* CEs [19] --> Loop 25 
* CEs [20] --> Loop 26 

### Ranking functions of CR eval_realheapsort_step2_bb4_in(V_N,V_j_0,V_k_0,V_m_0,B,C,D) 
* RF of phase [22,24]: [V_N/2-V_j_0-3/2,V_N/2-V_j_0-V_k_0/2-3/2]

#### Partial ranking functions of CR eval_realheapsort_step2_bb4_in(V_N,V_j_0,V_k_0,V_m_0,B,C,D) 
* Partial RF of phase [22,24]:
  - RF of loop [22:1,24:1]:
    V_N/2-V_j_0-3/2
    V_N/2-V_j_0-V_k_0/2-3/2


### Specialization of cost equations eval_realheapsort_step2_bb2_in/10 
* CE 7 is refined into CE [27] 
* CE 5 is refined into CE [28,29,30,31,32] 
* CE 8 is refined into CE [33] 
* CE 6 is refined into CE [34,35,36,37,38,39,40,41,42,43] 


### Cost equations --> "Loop" of eval_realheapsort_step2_bb2_in/10 
* CEs [43] --> Loop 27 
* CEs [39] --> Loop 28 
* CEs [42] --> Loop 29 
* CEs [41] --> Loop 30 
* CEs [40] --> Loop 31 
* CEs [37] --> Loop 32 
* CEs [38] --> Loop 33 
* CEs [35] --> Loop 34 
* CEs [34] --> Loop 35 
* CEs [36] --> Loop 36 
* CEs [27] --> Loop 37 
* CEs [31] --> Loop 38 
* CEs [30] --> Loop 39 
* CEs [32] --> Loop 40 
* CEs [29] --> Loop 41 
* CEs [33] --> Loop 42 
* CEs [28] --> Loop 43 

### Ranking functions of CR eval_realheapsort_step2_bb2_in(V_57,V_N,V_j_0,V_k_0,V_m_0,B,C,D,E,F) 
* RF of phase [27,28,29,30,31,32,33]: [V_N-V_k_0-3]

#### Partial ranking functions of CR eval_realheapsort_step2_bb2_in(V_57,V_N,V_j_0,V_k_0,V_m_0,B,C,D,E,F) 
* Partial RF of phase [27,28,29,30,31,32,33]:
  - RF of loop [27:1,28:1]:
    V_N-V_k_0-4
  - RF of loop [29:1,32:1,33:1]:
    V_N-V_k_0-3
  - RF of loop [30:1,31:1]:
    V_N-V_k_0-5


### Specialization of cost equations eval_realheapsort_step2_bb2_in_loop_cont/7 
* CE 9 is refined into CE [44] 
* CE 10 is refined into CE [45] 


### Cost equations --> "Loop" of eval_realheapsort_step2_bb2_in_loop_cont/7 
* CEs [44] --> Loop 44 
* CEs [45] --> Loop 45 

### Ranking functions of CR eval_realheapsort_step2_bb2_in_loop_cont(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR eval_realheapsort_step2_bb2_in_loop_cont(A,B,C,D,E,F,G) 


### Specialization of cost equations eval_realheapsort_step2_12/6 
* CE 4 is refined into CE [46,47,48,49,50,51,52,53,54,55] 


### Cost equations --> "Loop" of eval_realheapsort_step2_12/6 
* CEs [53] --> Loop 46 
* CEs [52] --> Loop 47 
* CEs [51] --> Loop 48 
* CEs [50,55] --> Loop 49 
* CEs [48,49] --> Loop 50 
* CEs [46,47,54] --> Loop 51 

### Ranking functions of CR eval_realheapsort_step2_12(V_57,V_N,V_j_0,V_k_0,V_m_0,B) 

#### Partial ranking functions of CR eval_realheapsort_step2_12(V_57,V_N,V_j_0,V_k_0,V_m_0,B) 


### Specialization of cost equations eval_realheapsort_step2_2/6 
* CE 2 is refined into CE [56,57,58,59,60,61] 
* CE 3 is refined into CE [62] 


### Cost equations --> "Loop" of eval_realheapsort_step2_2/6 
* CEs [61] --> Loop 52 
* CEs [60] --> Loop 53 
* CEs [59] --> Loop 54 
* CEs [58] --> Loop 55 
* CEs [57] --> Loop 56 
* CEs [62] --> Loop 57 
* CEs [56] --> Loop 58 

### Ranking functions of CR eval_realheapsort_step2_2(V_57,V_N,V_j_0,V_k_0,V_m_0,B) 

#### Partial ranking functions of CR eval_realheapsort_step2_2(V_57,V_N,V_j_0,V_k_0,V_m_0,B) 


### Specialization of cost equations eval_realheapsort_step2_start/6 
* CE 1 is refined into CE [63,64,65,66,67,68,69] 


### Cost equations --> "Loop" of eval_realheapsort_step2_start/6 
* CEs [69] --> Loop 59 
* CEs [68] --> Loop 60 
* CEs [67] --> Loop 61 
* CEs [66] --> Loop 62 
* CEs [65] --> Loop 63 
* CEs [64] --> Loop 64 
* CEs [63] --> Loop 65 

### Ranking functions of CR eval_realheapsort_step2_start(V_57,V_N,V_j_0,V_k_0,V_m_0,B) 

#### Partial ranking functions of CR eval_realheapsort_step2_start(V_57,V_N,V_j_0,V_k_0,V_m_0,B) 


Computing Bounds
=====================================

#### Cost of chains of eval_realheapsort_step2_bb4_in(V_N,V_j_0,V_k_0,V_m_0,B,C,D):
* Chain [[22,24],26]: 2*it(22)+0
  Such that:aux(1) =< V_N/2-V_j_0
aux(2) =< V_N/2-V_j_0-V_k_0/2
aux(5) =< -V_j_0+C
it(22) =< aux(1)
it(22) =< aux(2)
it(22) =< aux(5)

  with precondition: [B=2,C=D,V_j_0>=0,V_k_0>=0,C>=2*V_j_0+1,V_N>=2*V_j_0+V_k_0+4,V_k_0+2*C+2>=V_N,V_N>=V_k_0+C+2] 

* Chain [[22,24],25]: 2*it(22)+0
  Such that:aux(1) =< V_N/2-V_j_0
aux(2) =< V_N/2-V_j_0-V_k_0/2
aux(6) =< V_N-V_j_0-V_k_0
it(22) =< aux(1)
it(22) =< aux(2)
it(22) =< aux(6)

  with precondition: [B=3,V_j_0>=0,V_k_0>=0,V_N>=2*V_j_0+V_k_0+4] 

* Chain [[22,24],23,26]: 2*it(22)+1
  Such that:aux(1) =< -V_j_0+V_k_0/2+C/2+1
aux(2) =< -V_j_0+C/2+1
aux(7) =< -V_j_0+C/2
it(22) =< aux(1)
it(22) =< aux(2)
it(22) =< aux(7)

  with precondition: [B=2,V_N=V_k_0+C+2,V_N=V_k_0+D+2,V_j_0>=0,V_k_0>=0,V_N>=4*V_j_0+V_k_0+5] 

* Chain [[22,24],23,25]: 2*it(22)+1
  Such that:aux(1) =< V_N/2-V_j_0
aux(8) =< V_N/2-V_j_0-V_k_0/2
it(22) =< aux(1)
it(22) =< aux(8)

  with precondition: [B=3,V_j_0>=0,V_k_0>=0,V_N>=4*V_j_0+V_k_0+5] 

* Chain [[22,24],21,26]: 2*it(22)+1
  Such that:aux(2) =< -V_j_0-V_k_0/2+C/2
aux(1) =< -V_j_0+C/2
aux(9) =< -V_j_0+D/2
it(22) =< aux(1)
it(22) =< aux(2)
it(22) =< aux(9)

  with precondition: [B=2,V_N=C,V_j_0>=0,V_k_0>=0,D>=4*V_j_0+4,V_N>=V_k_0+D+2] 

* Chain [[22,24],21,25]: 2*it(22)+1
  Such that:aux(1) =< V_N/2-V_j_0
aux(10) =< V_N/2-V_j_0-V_k_0/2
it(22) =< aux(1)
it(22) =< aux(10)

  with precondition: [B=3,V_j_0>=0,V_k_0>=0,V_N>=4*V_j_0+V_k_0+6] 

* Chain [[22,24],20,26]: 2*it(22)+1
  Such that:aux(2) =< -V_j_0-V_k_0/2+C/2
aux(1) =< -V_j_0+C/2
aux(11) =< -V_j_0+D/2
it(22) =< aux(1)
it(22) =< aux(2)
it(22) =< aux(11)

  with precondition: [B=2,V_N=C,V_j_0>=0,V_k_0>=0,D>=4*V_j_0+3,V_N>=V_k_0+D+3] 

* Chain [[22,24],20,25]: 2*it(22)+1
  Such that:aux(1) =< V_N/2-V_j_0
aux(12) =< V_N/2-V_j_0-V_k_0/2
it(22) =< aux(1)
it(22) =< aux(12)

  with precondition: [B=3,V_j_0>=0,V_k_0>=0,V_N>=4*V_j_0+V_k_0+6] 

* Chain [[22,24],19,26]: 2*it(22)+1
  Such that:aux(1) =< -V_j_0+C/2
aux(2) =< -V_j_0+D/2+1
aux(13) =< -V_j_0+D/2
it(22) =< aux(1)
it(22) =< aux(2)
it(22) =< aux(13)

  with precondition: [B=2,V_N=C,V_N=V_k_0+D+2,V_j_0>=0,V_k_0>=0,V_N>=4*V_j_0+V_k_0+5] 

* Chain [[22,24],19,25]: 2*it(22)+1
  Such that:aux(1) =< V_N/2-V_j_0
aux(14) =< V_N/2-V_j_0-V_k_0/2
it(22) =< aux(1)
it(22) =< aux(14)

  with precondition: [B=3,V_j_0>=0,V_k_0>=0,V_N>=4*V_j_0+V_k_0+5] 

* Chain [26]: 0
  with precondition: [B=2,D=V_m_0,V_j_0=C,V_N>=3,V_k_0>=0,V_N>=V_j_0,V_N>=V_k_0+2,4*V_N>=3*V_k_0+V_j_0+9,V_k_0+2*V_j_0+2>=V_N] 

* Chain [25]: 0
  with precondition: [B=3,V_N>=3,V_j_0>=0,V_k_0>=0,V_N>=V_j_0,V_N>=V_k_0+2,4*V_N>=3*V_k_0+V_j_0+9] 

* Chain [23,26]: 1
  with precondition: [B=2,C=2*V_j_0+1,C=D,V_k_0+C+2=V_N,C>=1,V_N>=C+2] 

* Chain [23,25]: 1
  with precondition: [B=3,V_k_0+2*V_j_0+3=V_N,V_k_0>=0,V_N>=V_k_0+3] 

* Chain [21,26]: 1
  with precondition: [B=2,V_N=C,2*V_j_0+2=D,V_j_0>=0,V_k_0>=0,V_N>=2*V_j_0+V_k_0+4] 

* Chain [21,25]: 1
  with precondition: [B=3,V_j_0>=0,V_k_0>=0,V_N>=2*V_j_0+V_k_0+4] 

* Chain [20,26]: 1
  with precondition: [B=2,V_N=C,2*V_j_0+1=D,V_j_0>=0,V_k_0>=0,V_N>=2*V_j_0+V_k_0+4] 

* Chain [20,25]: 1
  with precondition: [B=3,V_j_0>=0,V_k_0>=0,V_N>=2*V_j_0+V_k_0+4] 

* Chain [19,26]: 1
  with precondition: [B=2,D=2*V_j_0+1,V_N=C,V_N=V_k_0+D+2,D>=1,V_N>=D+2] 

* Chain [19,25]: 1
  with precondition: [B=3,V_k_0+2*V_j_0+3=V_N,V_k_0>=0,V_N>=V_k_0+3] 


#### Cost of chains of eval_realheapsort_step2_bb2_in(V_57,V_N,V_j_0,V_k_0,V_m_0,B,C,D,E,F):
* Chain [[27,28,29,30,31,32,33],43]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+1
  Such that:aux(22) =< V_N/2
aux(21) =< V_N/2-V_k_0/2
aux(36) =< V_N-V_k_0
it(27) =< aux(36)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],42]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+0
  Such that:aux(22) =< V_N/2
aux(21) =< V_N/2-V_k_0/2
aux(37) =< V_N-V_k_0
it(27) =< aux(37)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],41]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+0
  Such that:aux(22) =< V_N/2
aux(21) =< V_N/2-V_k_0/2
aux(38) =< V_N-V_k_0
it(27) =< aux(38)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],40]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+2*s(76)+1
  Such that:aux(39) =< V_N-V_k_0
aux(40) =< V_N/2
aux(41) =< V_N/2-V_k_0/2
s(75) =< aux(39)
s(75) =< aux(41)
s(76) =< aux(40)
s(76) =< s(75)
s(76) =< aux(39)
it(27) =< aux(39)
aux(33) =< aux(41)-3/2
aux(24) =< aux(40)
aux(23) =< aux(41)
aux(30) =< aux(41)-1
aux(27) =< aux(41)*2-2
s(57) =< it(27)*aux(40)
s(56) =< it(27)*aux(41)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+5] 

* Chain [[27,28,29,30,31,32,33],39]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+4*s(79)+1
  Such that:aux(42) =< V_N-V_k_0
aux(43) =< V_N/2
aux(44) =< V_N/2-V_k_0/2
s(78) =< aux(42)
s(78) =< aux(44)
s(79) =< aux(43)
s(79) =< s(78)
it(27) =< aux(42)
aux(33) =< aux(44)-3/2
aux(24) =< aux(43)
aux(23) =< aux(44)
aux(30) =< aux(44)-1
aux(27) =< aux(44)*2-2
s(57) =< it(27)*aux(43)
s(56) =< it(27)*aux(44)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+6] 

* Chain [[27,28,29,30,31,32,33],38]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+4*s(82)+1
  Such that:aux(45) =< V_N-V_k_0
aux(46) =< V_N/2
aux(47) =< V_N/2-V_k_0/2
s(81) =< aux(45)
s(81) =< aux(47)
s(82) =< aux(46)
s(82) =< s(81)
it(27) =< aux(45)
aux(33) =< aux(47)-3/2
aux(24) =< aux(46)
aux(23) =< aux(47)
aux(30) =< aux(47)-1
aux(27) =< aux(47)*2-2
s(57) =< it(27)*aux(46)
s(56) =< it(27)*aux(47)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+7] 

* Chain [[27,28,29,30,31,32,33],35,42]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+2
  Such that:aux(22) =< V_N/2
aux(21) =< V_N/2-V_k_0/2
aux(48) =< V_N-V_k_0
it(27) =< aux(48)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],35,41]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+2
  Such that:aux(22) =< V_N/2
aux(21) =< V_N/2-V_k_0/2
aux(49) =< V_N-V_k_0
it(27) =< aux(49)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],35,36,42]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+3
  Such that:aux(22) =< V_N/2
aux(21) =< V_N/2-V_k_0/2
aux(50) =< V_N-V_k_0
it(27) =< aux(50)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],35,36,37]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+3
  Such that:aux(35) =< -V_k_0+C
aux(34) =< -V_k_0+C+1
aux(21) =< -V_k_0/2+C/2+1/2
aux(22) =< C/2+1/2
it(27) =< aux(34)
it(27) =< aux(35)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=4,D=0,F=1,V_N=C+1,V_N=E+1,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],34,42]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+2
  Such that:aux(22) =< V_N/2
aux(21) =< V_N/2-V_k_0/2
aux(51) =< V_N-V_k_0
it(27) =< aux(51)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],34,41]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+2
  Such that:aux(22) =< V_N/2
aux(21) =< V_N/2-V_k_0/2
aux(52) =< V_N-V_k_0
it(27) =< aux(52)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],34,36,42]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+3
  Such that:aux(22) =< V_N/2
aux(21) =< V_N/2-V_k_0/2
aux(53) =< V_N-V_k_0
it(27) =< aux(53)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [[27,28,29,30,31,32,33],34,36,37]: 13*it(27)+2*s(55)+2*s(58)+2*s(61)+2*s(65)+2*s(69)+3
  Such that:aux(35) =< -V_k_0+C
aux(34) =< -V_k_0+C+1
aux(21) =< -V_k_0/2+C/2+1/2
aux(22) =< C/2+1/2
it(27) =< aux(34)
it(27) =< aux(35)
aux(33) =< aux(21)-3/2
aux(24) =< aux(22)
aux(23) =< aux(21)
aux(30) =< aux(21)-1
aux(27) =< aux(21)*2-2
s(57) =< it(27)*aux(22)
s(56) =< it(27)*aux(21)
s(70) =< it(27)*aux(33)
s(60) =< it(27)*aux(24)
s(59) =< it(27)*aux(23)
s(66) =< it(27)*aux(30)
s(62) =< it(27)*aux(27)
s(69) =< s(60)
s(69) =< s(59)
s(69) =< s(70)
s(65) =< s(60)
s(65) =< s(59)
s(65) =< s(66)
s(61) =< s(60)
s(61) =< s(59)
s(61) =< s(62)
s(58) =< s(60)
s(58) =< s(59)
s(55) =< s(57)
s(55) =< s(56)

  with precondition: [B=4,D=0,F=1,V_N=C+1,V_N=E+1,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [43]: 1
  with precondition: [B=3,V_k_0+3=V_N,V_k_0>=0] 

* Chain [42]: 0
  with precondition: [B=3,V_N>=3,V_k_0>=0,V_N>=V_k_0+1] 

* Chain [41]: 0
  with precondition: [B=3,V_N>=3,V_k_0>=0,V_N>=V_k_0+2] 

* Chain [40]: 2*s(76)+1
  Such that:s(73) =< V_N-V_k_0
s(74) =< V_N/2
s(75) =< V_N/2-V_k_0/2
s(76) =< s(74)
s(76) =< s(75)
s(76) =< s(73)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] 

* Chain [39]: 4*s(79)+1
  Such that:s(77) =< V_N/2
s(78) =< V_N/2-V_k_0/2
s(79) =< s(77)
s(79) =< s(78)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+5] 

* Chain [38]: 4*s(82)+1
  Such that:s(80) =< V_N/2
s(81) =< V_N/2-V_k_0/2
s(82) =< s(80)
s(82) =< s(81)

  with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+6] 

* Chain [35,42]: 2
  with precondition: [B=3,V_N=V_k_0+3,V_N>=3] 

* Chain [35,41]: 2
  with precondition: [B=3,V_N=V_k_0+3,V_N>=3] 

* Chain [35,36,42]: 3
  with precondition: [B=3,V_N=V_k_0+3,V_N>=3] 

* Chain [35,36,37]: 3
  with precondition: [B=4,D=0,F=1,C+1=V_N,C=V_k_0+2,C=E,C>=2] 

* Chain [34,42]: 2
  with precondition: [B=3,V_N=V_k_0+3,V_N>=3] 

* Chain [34,41]: 2
  with precondition: [B=3,V_N=V_k_0+3,V_N>=3] 

* Chain [34,36,42]: 3
  with precondition: [B=3,V_N=V_k_0+3,V_N>=3] 

* Chain [34,36,37]: 3
  with precondition: [B=4,D=0,F=1,C+1=V_N,C=V_k_0+2,C=E,C>=2] 


#### Cost of chains of eval_realheapsort_step2_bb2_in_loop_cont(A,B,C,D,E,F,G):
* Chain [45]: 0
  with precondition: [A=3,C>=3] 

* Chain [44]: 0
  with precondition: [A=4,C>=3] 


#### Cost of chains of eval_realheapsort_step2_12(V_57,V_N,V_j_0,V_k_0,V_m_0,B):
* Chain [51]: 3
  with precondition: [V_N=3] 

* Chain [50]: 0
  with precondition: [V_N>=3] 

* Chain [49]: 2*s(375)+143*s(376)+22*s(389)+22*s(390)+22*s(391)+22*s(392)+22*s(393)+3
  Such that:aux(68) =< V_N
aux(69) =< V_N/2
s(376) =< aux(68)
s(377) =< aux(69)-3/2
s(378) =< aux(69)
s(380) =< aux(69)-1
s(381) =< aux(69)*2-2
s(382) =< s(376)*aux(69)
s(384) =< s(376)*s(377)
s(385) =< s(376)*s(378)
s(387) =< s(376)*s(380)
s(388) =< s(376)*s(381)
s(389) =< s(385)
s(389) =< s(384)
s(390) =< s(385)
s(390) =< s(387)
s(391) =< s(385)
s(391) =< s(388)
s(392) =< s(385)
s(393) =< s(382)
s(375) =< aux(69)
s(375) =< aux(68)

  with precondition: [V_N>=4] 

* Chain [48]: 2*s(420)+13*s(421)+2*s(434)+2*s(435)+2*s(436)+2*s(437)+2*s(438)+4*s(439)+1
  Such that:s(416) =< V_N
aux(70) =< V_N/2
s(419) =< s(416)
s(419) =< aux(70)
s(420) =< aux(70)
s(420) =< s(419)
s(420) =< s(416)
s(421) =< s(416)
s(422) =< aux(70)-3/2
s(423) =< aux(70)
s(425) =< aux(70)-1
s(426) =< aux(70)*2-2
s(427) =< s(421)*aux(70)
s(429) =< s(421)*s(422)
s(430) =< s(421)*s(423)
s(432) =< s(421)*s(425)
s(433) =< s(421)*s(426)
s(434) =< s(430)
s(434) =< s(429)
s(435) =< s(430)
s(435) =< s(432)
s(436) =< s(430)
s(436) =< s(433)
s(437) =< s(430)
s(438) =< s(427)
s(439) =< aux(70)

  with precondition: [V_N>=5] 

* Chain [47]: 4*s(444)+13*s(445)+2*s(458)+2*s(459)+2*s(460)+2*s(461)+2*s(462)+4*s(463)+1
  Such that:s(440) =< V_N
aux(71) =< V_N/2
s(443) =< s(440)
s(443) =< aux(71)
s(444) =< aux(71)
s(444) =< s(443)
s(445) =< s(440)
s(446) =< aux(71)-3/2
s(447) =< aux(71)
s(449) =< aux(71)-1
s(450) =< aux(71)*2-2
s(451) =< s(445)*aux(71)
s(453) =< s(445)*s(446)
s(454) =< s(445)*s(447)
s(456) =< s(445)*s(449)
s(457) =< s(445)*s(450)
s(458) =< s(454)
s(458) =< s(453)
s(459) =< s(454)
s(459) =< s(456)
s(460) =< s(454)
s(460) =< s(457)
s(461) =< s(454)
s(462) =< s(451)
s(463) =< aux(71)

  with precondition: [V_N>=6] 

* Chain [46]: 4*s(468)+13*s(469)+2*s(482)+2*s(483)+2*s(484)+2*s(485)+2*s(486)+1
  Such that:s(464) =< V_N
aux(72) =< V_N/2
s(467) =< s(464)
s(467) =< aux(72)
s(468) =< aux(72)
s(468) =< s(467)
s(469) =< s(464)
s(470) =< aux(72)-3/2
s(471) =< aux(72)
s(473) =< aux(72)-1
s(474) =< aux(72)*2-2
s(475) =< s(469)*aux(72)
s(477) =< s(469)*s(470)
s(478) =< s(469)*s(471)
s(480) =< s(469)*s(473)
s(481) =< s(469)*s(474)
s(482) =< s(478)
s(482) =< s(477)
s(483) =< s(478)
s(483) =< s(480)
s(484) =< s(478)
s(484) =< s(481)
s(485) =< s(478)
s(486) =< s(475)

  with precondition: [V_N>=7] 


#### Cost of chains of eval_realheapsort_step2_2(V_57,V_N,V_j_0,V_k_0,V_m_0,B):
* Chain [58]: 3
  with precondition: [V_N=3] 

* Chain [57]: 0
  with precondition: [2>=V_N] 

* Chain [56]: 0
  with precondition: [V_N>=3] 

* Chain [55]: 143*s(489)+22*s(499)+22*s(500)+22*s(501)+22*s(502)+22*s(503)+2*s(504)+3
  Such that:s(487) =< V_N
s(488) =< V_N/2
s(489) =< s(487)
s(490) =< s(488)-3/2
s(491) =< s(488)
s(492) =< s(488)-1
s(493) =< s(488)*2-2
s(494) =< s(489)*s(488)
s(495) =< s(489)*s(490)
s(496) =< s(489)*s(491)
s(497) =< s(489)*s(492)
s(498) =< s(489)*s(493)
s(499) =< s(496)
s(499) =< s(495)
s(500) =< s(496)
s(500) =< s(497)
s(501) =< s(496)
s(501) =< s(498)
s(502) =< s(496)
s(503) =< s(494)
s(504) =< s(488)
s(504) =< s(487)

  with precondition: [V_N>=4] 

* Chain [54]: 2*s(508)+13*s(509)+2*s(519)+2*s(520)+2*s(521)+2*s(522)+2*s(523)+4*s(524)+1
  Such that:s(505) =< V_N
s(506) =< V_N/2
s(507) =< s(505)
s(507) =< s(506)
s(508) =< s(506)
s(508) =< s(507)
s(508) =< s(505)
s(509) =< s(505)
s(510) =< s(506)-3/2
s(511) =< s(506)
s(512) =< s(506)-1
s(513) =< s(506)*2-2
s(514) =< s(509)*s(506)
s(515) =< s(509)*s(510)
s(516) =< s(509)*s(511)
s(517) =< s(509)*s(512)
s(518) =< s(509)*s(513)
s(519) =< s(516)
s(519) =< s(515)
s(520) =< s(516)
s(520) =< s(517)
s(521) =< s(516)
s(521) =< s(518)
s(522) =< s(516)
s(523) =< s(514)
s(524) =< s(506)

  with precondition: [V_N>=5] 

* Chain [53]: 4*s(528)+13*s(529)+2*s(539)+2*s(540)+2*s(541)+2*s(542)+2*s(543)+4*s(544)+1
  Such that:s(525) =< V_N
s(526) =< V_N/2
s(527) =< s(525)
s(527) =< s(526)
s(528) =< s(526)
s(528) =< s(527)
s(529) =< s(525)
s(530) =< s(526)-3/2
s(531) =< s(526)
s(532) =< s(526)-1
s(533) =< s(526)*2-2
s(534) =< s(529)*s(526)
s(535) =< s(529)*s(530)
s(536) =< s(529)*s(531)
s(537) =< s(529)*s(532)
s(538) =< s(529)*s(533)
s(539) =< s(536)
s(539) =< s(535)
s(540) =< s(536)
s(540) =< s(537)
s(541) =< s(536)
s(541) =< s(538)
s(542) =< s(536)
s(543) =< s(534)
s(544) =< s(526)

  with precondition: [V_N>=6] 

* Chain [52]: 4*s(548)+13*s(549)+2*s(559)+2*s(560)+2*s(561)+2*s(562)+2*s(563)+1
  Such that:s(545) =< V_N
s(546) =< V_N/2
s(547) =< s(545)
s(547) =< s(546)
s(548) =< s(546)
s(548) =< s(547)
s(549) =< s(545)
s(550) =< s(546)-3/2
s(551) =< s(546)
s(552) =< s(546)-1
s(553) =< s(546)*2-2
s(554) =< s(549)*s(546)
s(555) =< s(549)*s(550)
s(556) =< s(549)*s(551)
s(557) =< s(549)*s(552)
s(558) =< s(549)*s(553)
s(559) =< s(556)
s(559) =< s(555)
s(560) =< s(556)
s(560) =< s(557)
s(561) =< s(556)
s(561) =< s(558)
s(562) =< s(556)
s(563) =< s(554)

  with precondition: [V_N>=7] 


#### Cost of chains of eval_realheapsort_step2_start(V_57,V_N,V_j_0,V_k_0,V_m_0,B):
* Chain [65]: 3
  with precondition: [V_N=3] 

* Chain [64]: 0
  with precondition: [2>=V_N] 

* Chain [63]: 0
  with precondition: [V_N>=3] 

* Chain [62]: 143*s(566)+22*s(576)+22*s(577)+22*s(578)+22*s(579)+22*s(580)+2*s(581)+3
  Such that:s(564) =< V_N
s(565) =< V_N/2
s(566) =< s(564)
s(567) =< s(565)-3/2
s(568) =< s(565)
s(569) =< s(565)-1
s(570) =< s(565)*2-2
s(571) =< s(566)*s(565)
s(572) =< s(566)*s(567)
s(573) =< s(566)*s(568)
s(574) =< s(566)*s(569)
s(575) =< s(566)*s(570)
s(576) =< s(573)
s(576) =< s(572)
s(577) =< s(573)
s(577) =< s(574)
s(578) =< s(573)
s(578) =< s(575)
s(579) =< s(573)
s(580) =< s(571)
s(581) =< s(565)
s(581) =< s(564)

  with precondition: [V_N>=4] 

* Chain [61]: 2*s(585)+13*s(586)+2*s(596)+2*s(597)+2*s(598)+2*s(599)+2*s(600)+4*s(601)+1
  Such that:s(582) =< V_N
s(583) =< V_N/2
s(584) =< s(582)
s(584) =< s(583)
s(585) =< s(583)
s(585) =< s(584)
s(585) =< s(582)
s(586) =< s(582)
s(587) =< s(583)-3/2
s(588) =< s(583)
s(589) =< s(583)-1
s(590) =< s(583)*2-2
s(591) =< s(586)*s(583)
s(592) =< s(586)*s(587)
s(593) =< s(586)*s(588)
s(594) =< s(586)*s(589)
s(595) =< s(586)*s(590)
s(596) =< s(593)
s(596) =< s(592)
s(597) =< s(593)
s(597) =< s(594)
s(598) =< s(593)
s(598) =< s(595)
s(599) =< s(593)
s(600) =< s(591)
s(601) =< s(583)

  with precondition: [V_N>=5] 

* Chain [60]: 4*s(605)+13*s(606)+2*s(616)+2*s(617)+2*s(618)+2*s(619)+2*s(620)+4*s(621)+1
  Such that:s(602) =< V_N
s(603) =< V_N/2
s(604) =< s(602)
s(604) =< s(603)
s(605) =< s(603)
s(605) =< s(604)
s(606) =< s(602)
s(607) =< s(603)-3/2
s(608) =< s(603)
s(609) =< s(603)-1
s(610) =< s(603)*2-2
s(611) =< s(606)*s(603)
s(612) =< s(606)*s(607)
s(613) =< s(606)*s(608)
s(614) =< s(606)*s(609)
s(615) =< s(606)*s(610)
s(616) =< s(613)
s(616) =< s(612)
s(617) =< s(613)
s(617) =< s(614)
s(618) =< s(613)
s(618) =< s(615)
s(619) =< s(613)
s(620) =< s(611)
s(621) =< s(603)

  with precondition: [V_N>=6] 

* Chain [59]: 4*s(625)+13*s(626)+2*s(636)+2*s(637)+2*s(638)+2*s(639)+2*s(640)+1
  Such that:s(622) =< V_N
s(623) =< V_N/2
s(624) =< s(622)
s(624) =< s(623)
s(625) =< s(623)
s(625) =< s(624)
s(626) =< s(622)
s(627) =< s(623)-3/2
s(628) =< s(623)
s(629) =< s(623)-1
s(630) =< s(623)*2-2
s(631) =< s(626)*s(623)
s(632) =< s(626)*s(627)
s(633) =< s(626)*s(628)
s(634) =< s(626)*s(629)
s(635) =< s(626)*s(630)
s(636) =< s(633)
s(636) =< s(632)
s(637) =< s(633)
s(637) =< s(634)
s(638) =< s(633)
s(638) =< s(635)
s(639) =< s(633)
s(640) =< s(631)

  with precondition: [V_N>=7] 


Closed-form bounds of eval_realheapsort_step2_start(V_57,V_N,V_j_0,V_k_0,V_m_0,B): 
-------------------------------------
* Chain [65] with precondition: [V_N=3] 
    - Upper bound: 3 
    - Complexity: constant 
* Chain [64] with precondition: [2>=V_N] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [63] with precondition: [V_N>=3] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [62] with precondition: [V_N>=4] 
    - Upper bound: 143*V_N+3+V_N/2*(110*V_N)+V_N 
    - Complexity: n^2 
* Chain [61] with precondition: [V_N>=5] 
    - Upper bound: 13*V_N+1+V_N/2*(10*V_N)+3*V_N 
    - Complexity: n^2 
* Chain [60] with precondition: [V_N>=6] 
    - Upper bound: 13*V_N+1+V_N/2*(10*V_N)+4*V_N 
    - Complexity: n^2 
* Chain [59] with precondition: [V_N>=7] 
    - Upper bound: 13*V_N+1+V_N/2*(10*V_N)+2*V_N 
    - Complexity: n^2 

### Maximum cost of eval_realheapsort_step2_start(V_57,V_N,V_j_0,V_k_0,V_m_0,B): max([2,nat(V_N)*10*nat(V_N/2)+nat(V_N)*13+nat(V_N/2)*2+max([nat(V_N/2)*6,nat(V_N)*130+2+nat(V_N)*100*nat(V_N/2)])])+1 
Asymptotic class: n^2 
* Total analysis performed in 2085 ms.