/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. recursive  : [eval_nestedLoop_10/9,eval_nestedLoop_11/9,eval_nestedLoop_bb4_in/9,eval_nestedLoop_bb5_in/9]
1. recursive  : [eval_nestedLoop_6/15,eval_nestedLoop_7/15,eval_nestedLoop_bb2_in/15,eval_nestedLoop_bb3_in/15,eval_nestedLoop_bb4_in_loop_cont/16]
2. recursive  : [eval_nestedLoop_15/22,eval_nestedLoop_16/22,eval_nestedLoop_4/22,eval_nestedLoop_5/22,eval_nestedLoop_bb1_in/22,eval_nestedLoop_bb2_in_loop_cont/23,eval_nestedLoop_bb6_in/22]
3. non_recursive  : [eval_nestedLoop_stop/13]
4. non_recursive  : [eval_nestedLoop_bb7_in/13]
5. non_recursive  : [exit_location/1]
6. non_recursive  : [eval_nestedLoop_bb1_in_loop_cont/14]
7. non_recursive  : [eval_nestedLoop_3/13]
8. non_recursive  : [eval_nestedLoop_2/13]
9. non_recursive  : [eval_nestedLoop_1/13]
10. non_recursive  : [eval_nestedLoop_0/13]
11. non_recursive  : [eval_nestedLoop_bb0_in/13]
12. non_recursive  : [eval_nestedLoop_start/13]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_nestedLoop_bb4_in/9
1. SCC is partially evaluated into eval_nestedLoop_bb2_in/15
2. SCC is partially evaluated into eval_nestedLoop_bb1_in/22
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into eval_nestedLoop_bb1_in_loop_cont/14
7. SCC is partially evaluated into eval_nestedLoop_3/13
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 partially evaluated into eval_nestedLoop_start/13

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

### Specialization of cost equations eval_nestedLoop_bb4_in/9 
* CE 21 is refined into CE [22] 
* CE 18 is refined into CE [23] 
* CE 19 is refined into CE [24] 
* CE 20 is refined into CE [25] 


### Cost equations --> "Loop" of eval_nestedLoop_bb4_in/9 
* CEs [25] --> Loop 22 
* CEs [22] --> Loop 23 
* CEs [23] --> Loop 24 
* CEs [24] --> Loop 25 

### Ranking functions of CR eval_nestedLoop_bb4_in(V_10,V_N,V_i_1,V_j_0,V_k_0,B,C,D,E) 
* RF of phase [22]: [V_N-V_k_0]

#### Partial ranking functions of CR eval_nestedLoop_bb4_in(V_10,V_N,V_i_1,V_j_0,V_k_0,B,C,D,E) 
* Partial RF of phase [22]:
  - RF of loop [22:1]:
    V_N-V_k_0


### Specialization of cost equations eval_nestedLoop_bb2_in/15 
* CE 13 is refined into CE [26] 
* CE 14 is refined into CE [27] 
* CE 16 is refined into CE [28,29] 
* CE 17 is refined into CE [30] 
* CE 15 is refined into CE [31,32,33,34] 


### Cost equations --> "Loop" of eval_nestedLoop_bb2_in/15 
* CEs [34] --> Loop 26 
* CEs [33] --> Loop 27 
* CEs [32] --> Loop 28 
* CEs [31] --> Loop 29 
* CEs [27] --> Loop 30 
* CEs [26] --> Loop 31 
* CEs [28] --> Loop 32 
* CEs [30] --> Loop 33 
* CEs [29] --> Loop 34 

### Ranking functions of CR eval_nestedLoop_bb2_in(V_10,V_6,V_9,V_N,V_i_1,V_j_0,V_k_0,V_m,B,C,D,E,F,G,H) 
* RF of phase [26,27,28,29]: [-V_j_0+V_m]

#### Partial ranking functions of CR eval_nestedLoop_bb2_in(V_10,V_6,V_9,V_N,V_i_1,V_j_0,V_k_0,V_m,B,C,D,E,F,G,H) 
* Partial RF of phase [26,27,28,29]:
  - RF of loop [26:1,27:1,28:1,29:1]:
    -V_j_0+V_m
  - RF of loop [26:1,29:1]:
    V_N-V_i_1


### Specialization of cost equations eval_nestedLoop_bb1_in/22 
* CE 6 is refined into CE [35] 
* CE 7 is refined into CE [36] 
* CE 9 is refined into CE [37,38,39,40,41] 
* CE 10 is refined into CE [42] 
* CE 8 is refined into CE [43,44,45,46] 


### Cost equations --> "Loop" of eval_nestedLoop_bb1_in/22 
* CEs [46] --> Loop 35 
* CEs [45] --> Loop 36 
* CEs [44] --> Loop 37 
* CEs [43] --> Loop 38 
* CEs [35] --> Loop 39 
* CEs [36] --> Loop 40 
* CEs [41] --> Loop 41 
* CEs [38] --> Loop 42 
* CEs [40] --> Loop 43 
* CEs [37] --> Loop 44 
* CEs [39] --> Loop 45 
* CEs [42] --> Loop 46 

### Ranking functions of CR eval_nestedLoop_bb1_in(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B,C,D,E,F,G,H,I,J,K) 
* RF of phase [35,36,37,38]: [-V_i_0+V_n]

#### Partial ranking functions of CR eval_nestedLoop_bb1_in(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B,C,D,E,F,G,H,I,J,K) 
* Partial RF of phase [35,36,37,38]:
  - RF of loop [35:1,36:1,37:1,38:1]:
    -V_i_0+V_n


### Specialization of cost equations eval_nestedLoop_bb1_in_loop_cont/14 
* CE 11 is refined into CE [47] 
* CE 12 is refined into CE [48] 


### Cost equations --> "Loop" of eval_nestedLoop_bb1_in_loop_cont/14 
* CEs [47] --> Loop 47 
* CEs [48] --> Loop 48 

### Ranking functions of CR eval_nestedLoop_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 

#### Partial ranking functions of CR eval_nestedLoop_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 


### Specialization of cost equations eval_nestedLoop_3/13 
* CE 5 is refined into CE [49,50,51,52,53,54,55,56,57,58,59,60,61,62,63] 
* CE 2 is refined into CE [64] 
* CE 3 is refined into CE [65] 
* CE 4 is refined into CE [66] 


### Cost equations --> "Loop" of eval_nestedLoop_3/13 
* CEs [59] --> Loop 49 
* CEs [57] --> Loop 50 
* CEs [58] --> Loop 51 
* CEs [56] --> Loop 52 
* CEs [55] --> Loop 53 
* CEs [54] --> Loop 54 
* CEs [53] --> Loop 55 
* CEs [52] --> Loop 56 
* CEs [51] --> Loop 57 
* CEs [50,62,63] --> Loop 58 
* CEs [49,60] --> Loop 59 
* CEs [64] --> Loop 60 
* CEs [65] --> Loop 61 
* CEs [66] --> Loop 62 
* CEs [61] --> Loop 63 

### Ranking functions of CR eval_nestedLoop_3(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B) 

#### Partial ranking functions of CR eval_nestedLoop_3(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B) 


### Specialization of cost equations eval_nestedLoop_start/13 
* CE 1 is refined into CE [67,68,69,70,71,72,73,74,75,76,77,78,79,80,81] 


### Cost equations --> "Loop" of eval_nestedLoop_start/13 
* CEs [81] --> Loop 64 
* CEs [80] --> Loop 65 
* CEs [79] --> Loop 66 
* CEs [78] --> Loop 67 
* CEs [77] --> Loop 68 
* CEs [76] --> Loop 69 
* CEs [75] --> Loop 70 
* CEs [74] --> Loop 71 
* CEs [73] --> Loop 72 
* CEs [72] --> Loop 73 
* CEs [71] --> Loop 74 
* CEs [70] --> Loop 75 
* CEs [69] --> Loop 76 
* CEs [68] --> Loop 77 
* CEs [67] --> Loop 78 

### Ranking functions of CR eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B) 

#### Partial ranking functions of CR eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B) 


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

#### Cost of chains of eval_nestedLoop_bb4_in(V_10,V_N,V_i_1,V_j_0,V_k_0,B,C,D,E):
* Chain [[22],25]: 1*it(22)+0
  Such that:it(22) =< -V_k_0+D

  with precondition: [B=2,D=E,0>=C,V_N>=0,V_j_0>=0,V_k_0>=V_i_1,D>=V_k_0+1,V_N>=D] 

* Chain [[22],24]: 1*it(22)+0
  Such that:it(22) =< -V_k_0+E

  with precondition: [B=2,V_N=D,V_N=E,V_N>=0,V_j_0>=0,V_k_0>=V_i_1,V_N>=V_k_0+1] 

* Chain [[22],23]: 1*it(22)+0
  Such that:it(22) =< V_N-V_k_0

  with precondition: [B=3,V_N>=0,V_j_0>=0,V_k_0>=V_i_1,V_N>=V_k_0+1] 

* Chain [25]: 0
  with precondition: [B=2,V_k_0=D,V_k_0=E,0>=C,V_N>=0,V_j_0>=0,V_k_0>=V_i_1] 

* Chain [24]: 0
  with precondition: [B=2,V_k_0=D,V_k_0=E,V_N>=0,V_j_0>=0,V_k_0>=V_N,V_k_0>=V_i_1] 

* Chain [23]: 0
  with precondition: [B=3,V_N>=0,V_j_0>=0,V_k_0>=V_i_1] 


#### Cost of chains of eval_nestedLoop_bb2_in(V_10,V_6,V_9,V_N,V_i_1,V_j_0,V_k_0,V_m,B,C,D,E,F,G,H):
* Chain [[26,27,28,29],34]: 2*it(26)+2*it(27)+3*s(1)+0
  Such that:aux(5) =< V_N-V_i_1
aux(6) =< -V_j_0+V_m
s(1) =< aux(5)
it(26) =< aux(5)
it(26) =< aux(6)
it(27) =< aux(6)

  with precondition: [B=3,V_N>=0,V_j_0>=0,V_N>=V_i_1+1,V_m>=V_j_0+2] 

* Chain [[26,27,28,29],33]: 2*it(26)+2*it(27)+2*s(6)+0
  Such that:aux(1) =< V_N-V_i_1
aux(7) =< -V_j_0+V_m
it(26) =< aux(1)
s(6) =< aux(1)
it(26) =< aux(7)
it(27) =< aux(7)

  with precondition: [B=3,V_N>=0,V_j_0>=0,V_m>=V_j_0+1] 

* Chain [[26,27,28,29],32]: 2*it(26)+2*it(27)+2*s(6)+0
  Such that:aux(1) =< V_N-V_i_1
aux(8) =< -V_j_0+V_m
it(26) =< aux(1)
s(6) =< aux(1)
it(26) =< aux(8)
it(27) =< aux(8)

  with precondition: [B=3,V_N>=0,V_j_0>=0,V_m>=V_j_0+2] 

* Chain [[26,27,28,29],31]: 2*it(26)+2*it(27)+2*s(6)+0
  Such that:aux(1) =< V_N-V_i_1
aux(2) =< -V_i_1+H
aux(9) =< -V_j_0+V_m
it(26) =< aux(1)
s(6) =< aux(1)
it(26) =< aux(2)
s(6) =< aux(2)
it(26) =< aux(9)
it(27) =< aux(9)

  with precondition: [B=4,V_m=E,V_m=G,F=H,V_N>=0,V_j_0>=0,F>=V_i_1,V_m>=V_j_0+1] 

* Chain [[26,27,28,29],30]: 2*it(26)+2*it(27)+2*s(6)+0
  Such that:aux(1) =< V_N-V_i_1
aux(2) =< -V_i_1+H
aux(3) =< -V_j_0+V_m
aux(4) =< -V_j_0+E
it(26) =< aux(1)
s(6) =< aux(1)
it(26) =< aux(2)
s(6) =< aux(2)
it(26) =< aux(3)
it(27) =< aux(3)
it(26) =< aux(4)
it(27) =< aux(4)

  with precondition: [B=4,E=G,F=H,0>=D,V_N>=0,V_j_0>=0,F>=V_i_1,E>=V_j_0+1,V_m>=E] 

* Chain [34]: 1*s(1)+0
  Such that:s(1) =< V_N-V_i_1

  with precondition: [B=3,V_N>=0,V_j_0>=0,V_N>=V_i_1+1,V_m>=V_j_0+1] 

* Chain [33]: 0
  with precondition: [B=3,V_N>=0,V_j_0>=0,V_m>=V_j_0] 

* Chain [32]: 0
  with precondition: [B=3,V_N>=0,V_j_0>=0,V_m>=V_j_0+1] 

* Chain [31]: 0
  with precondition: [B=4,C=V_10,E=V_9,F=V_i_1,V_m=V_j_0,H=V_k_0,V_m=G,V_N>=0,V_m>=0] 

* Chain [30]: 0
  with precondition: [B=4,C=V_10,E=V_9,F=V_i_1,H=V_k_0,V_j_0=G,0>=D,V_N>=0,V_j_0>=0,V_m>=V_j_0] 


#### Cost of chains of eval_nestedLoop_bb1_in(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B,C,D,E,F,G,H,I,J,K):
* Chain [[35,36,37,38],46]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+0
  Such that:aux(10) =< V_N
aux(12) =< V_N-V_i_0
aux(19) =< -V_i_0+V_n
aux(13) =< V_m
it(35) =< aux(19)
aux(14) =< aux(13)
aux(15) =< aux(12)
s(42) =< it(35)*aux(13)
s(45) =< it(35)*aux(12)
s(45) =< it(35)*aux(10)
s(43) =< it(35)*aux(14)
s(51) =< it(35)*aux(15)
s(46) =< s(51)
s(47) =< s(51)
s(46) =< s(43)
s(48) =< s(43)
s(39) =< s(45)
s(40) =< s(45)
s(39) =< s(43)
s(41) =< s(43)
s(39) =< s(42)
s(41) =< s(42)

  with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=0,V_n>=V_i_0+1] 

* Chain [[35,36,37,38],45]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+0
  Such that:aux(10) =< V_N
aux(12) =< V_N-V_i_0
aux(13) =< V_m
aux(21) =< -V_i_0+V_n
it(35) =< aux(21)
aux(14) =< aux(13)
aux(15) =< aux(12)
s(42) =< it(35)*aux(13)
s(45) =< it(35)*aux(12)
s(45) =< it(35)*aux(10)
s(43) =< it(35)*aux(14)
s(51) =< it(35)*aux(15)
s(46) =< s(51)
s(47) =< s(51)
s(46) =< s(43)
s(48) =< s(43)
s(39) =< s(45)
s(40) =< s(45)
s(39) =< s(43)
s(41) =< s(43)
s(39) =< s(42)
s(41) =< s(42)

  with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=0,V_n>=V_i_0+2] 

* Chain [[35,36,37,38],44]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+1*s(52)+0
  Such that:aux(10) =< V_N
aux(19) =< -V_i_0+V_n
aux(13) =< V_m
aux(22) =< V_N-V_i_0
s(52) =< aux(22)
it(35) =< aux(19)
it(35) =< aux(22)
aux(14) =< aux(13)
aux(15) =< aux(22)
s(42) =< it(35)*aux(13)
s(45) =< it(35)*aux(22)
s(45) =< it(35)*aux(10)
s(43) =< it(35)*aux(14)
s(51) =< it(35)*aux(15)
s(46) =< s(51)
s(47) =< s(51)
s(46) =< s(43)
s(48) =< s(43)
s(39) =< s(45)
s(40) =< s(45)
s(39) =< s(43)
s(41) =< s(43)
s(39) =< s(42)
s(41) =< s(42)

  with precondition: [B=3,V_i_0>=0,V_m>=1,V_N>=V_i_0+2,V_n>=V_i_0+2] 

* Chain [[35,36,37,38],43]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+2*s(55)+2*s(56)+2*s(57)+0
  Such that:aux(10) =< V_N
aux(23) =< V_N-V_i_0
aux(24) =< -V_i_0+V_n
aux(25) =< V_m
s(55) =< aux(23)
s(56) =< aux(23)
s(55) =< aux(25)
s(57) =< aux(25)
it(35) =< aux(24)
aux(14) =< aux(25)
aux(15) =< aux(23)
s(42) =< it(35)*aux(25)
s(45) =< it(35)*aux(23)
s(45) =< it(35)*aux(10)
s(43) =< it(35)*aux(14)
s(51) =< it(35)*aux(15)
s(46) =< s(51)
s(47) =< s(51)
s(46) =< s(43)
s(48) =< s(43)
s(39) =< s(45)
s(40) =< s(45)
s(39) =< s(43)
s(41) =< s(43)
s(39) =< s(42)
s(41) =< s(42)

  with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=1,V_n>=V_i_0+2] 

* Chain [[35,36,37,38],42]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+3*s(60)+2*s(61)+2*s(62)+0
  Such that:aux(10) =< V_N
aux(26) =< V_N-V_i_0
aux(27) =< -V_i_0+V_n
aux(28) =< V_m
aux(20) =< aux(26)
aux(20) =< aux(27)
s(60) =< aux(26)
s(61) =< aux(26)
s(61) =< aux(28)
s(62) =< aux(28)
it(35) =< aux(27)
it(35) =< aux(20)
aux(14) =< aux(28)
aux(15) =< aux(26)
s(42) =< it(35)*aux(28)
s(45) =< it(35)*aux(26)
s(45) =< it(35)*aux(10)
s(43) =< it(35)*aux(14)
s(51) =< it(35)*aux(15)
s(46) =< s(51)
s(47) =< s(51)
s(46) =< s(43)
s(48) =< s(43)
s(39) =< s(45)
s(40) =< s(45)
s(39) =< s(43)
s(41) =< s(43)
s(39) =< s(42)
s(41) =< s(42)

  with precondition: [B=3,V_i_0>=0,V_m>=2,V_N>=V_i_0+2,V_n>=V_i_0+2] 

* Chain [[35,36,37,38],41]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+2*s(65)+2*s(66)+2*s(67)+0
  Such that:aux(10) =< V_N
aux(29) =< V_N-V_i_0
aux(30) =< -V_i_0+V_n
aux(31) =< V_m
s(65) =< aux(29)
s(66) =< aux(29)
s(65) =< aux(31)
s(67) =< aux(31)
it(35) =< aux(30)
aux(14) =< aux(31)
aux(15) =< aux(29)
s(42) =< it(35)*aux(31)
s(45) =< it(35)*aux(29)
s(45) =< it(35)*aux(10)
s(43) =< it(35)*aux(14)
s(51) =< it(35)*aux(15)
s(46) =< s(51)
s(47) =< s(51)
s(46) =< s(43)
s(48) =< s(43)
s(39) =< s(45)
s(40) =< s(45)
s(39) =< s(43)
s(41) =< s(43)
s(39) =< s(42)
s(41) =< s(42)

  with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=2,V_n>=V_i_0+2] 

* Chain [[35,36,37,38],40]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+0
  Such that:aux(10) =< V_N
aux(12) =< V_N-V_i_0
aux(19) =< -V_i_0+V_n
aux(20) =< -V_i_0+I+1
aux(13) =< V_m
it(35) =< aux(19)
it(35) =< aux(20)
aux(14) =< aux(13)
aux(15) =< aux(12)
s(42) =< it(35)*aux(13)
s(45) =< it(35)*aux(12)
s(45) =< it(35)*aux(10)
s(43) =< it(35)*aux(14)
s(51) =< it(35)*aux(15)
s(46) =< s(51)
s(47) =< s(51)
s(46) =< s(43)
s(48) =< s(43)
s(39) =< s(45)
s(40) =< s(45)
s(39) =< s(43)
s(41) =< s(43)
s(39) =< s(42)
s(41) =< s(42)

  with precondition: [B=5,I+1=D,I+1=H,0>=E,V_N>=0,V_i_0>=0,J>=0,V_n>=V_i_0+1,I>=V_i_0,V_m>=J] 

* Chain [[35,36,37,38],39]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+0
  Such that:aux(10) =< V_N
aux(12) =< V_N-V_i_0
aux(19) =< -V_i_0+V_n
aux(20) =< -V_i_0+D
aux(13) =< V_m
it(35) =< aux(19)
it(35) =< aux(20)
aux(14) =< aux(13)
aux(15) =< aux(12)
s(42) =< it(35)*aux(13)
s(45) =< it(35)*aux(12)
s(45) =< it(35)*aux(10)
s(43) =< it(35)*aux(14)
s(51) =< it(35)*aux(15)
s(46) =< s(51)
s(47) =< s(51)
s(46) =< s(43)
s(48) =< s(43)
s(39) =< s(45)
s(40) =< s(45)
s(39) =< s(43)
s(41) =< s(43)
s(39) =< s(42)
s(41) =< s(42)

  with precondition: [B=5,H=D,H=I+1,V_N>=0,V_i_0>=0,J>=0,V_n>=V_i_0+1,H>=V_n,V_m>=J] 

* Chain [46]: 0
  with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=0,V_n>=0] 

* Chain [45]: 0
  with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=0,V_n>=V_i_0+1] 

* Chain [44]: 1*s(52)+0
  Such that:s(52) =< V_N-V_i_0

  with precondition: [B=3,V_i_0>=0,V_m>=1,V_N>=V_i_0+1,V_n>=V_i_0+1] 

* Chain [43]: 2*s(55)+2*s(56)+2*s(57)+0
  Such that:s(53) =< V_N-V_i_0
s(54) =< V_m
s(55) =< s(53)
s(56) =< s(53)
s(55) =< s(54)
s(57) =< s(54)

  with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=1,V_n>=V_i_0+1] 

* Chain [42]: 3*s(60)+2*s(61)+2*s(62)+0
  Such that:s(58) =< V_N-V_i_0
s(59) =< V_m
s(60) =< s(58)
s(61) =< s(58)
s(61) =< s(59)
s(62) =< s(59)

  with precondition: [B=3,V_i_0>=0,V_m>=2,V_N>=V_i_0+1,V_n>=V_i_0+1] 

* Chain [41]: 2*s(65)+2*s(66)+2*s(67)+0
  Such that:s(63) =< V_N-V_i_0
s(64) =< V_m
s(65) =< s(63)
s(66) =< s(63)
s(65) =< s(64)
s(67) =< s(64)

  with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=2,V_n>=V_i_0+1] 

* Chain [40]: 0
  with precondition: [B=5,C=V_10,D=V_14,F=V_6,G=V_9,I=V_i_1,J=V_j_0,K=V_k_0,V_i_0=H,0>=E,V_N>=0,V_i_0>=0,V_m>=0,V_n>=0] 

* Chain [39]: 0
  with precondition: [B=5,C=V_10,D=V_14,F=V_6,G=V_9,I=V_i_1,J=V_j_0,K=V_k_0,V_i_0=H,V_N>=0,V_m>=0,V_n>=0,V_i_0>=V_n] 


#### Cost of chains of eval_nestedLoop_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N):
* Chain [48]: 0
  with precondition: [A=3,G>=0,L>=0,M>=0] 

* Chain [47]: 0
  with precondition: [A=5,G>=0,L>=0,M>=0] 


#### Cost of chains of eval_nestedLoop_3(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B):
* Chain [63]: 0
  with precondition: [V_n=0,V_N>=0,V_m>=0] 

* Chain [62]: 0
  with precondition: [0>=V_N+1] 

* Chain [61]: 0
  with precondition: [0>=V_m+1] 

* Chain [60]: 0
  with precondition: [0>=V_n+1] 

* Chain [59]: 0
  with precondition: [V_N>=0,V_m>=0,V_n>=0] 

* Chain [58]: 12*s(89)+6*s(96)+6*s(97)+6*s(98)+6*s(99)+6*s(100)+6*s(101)+0
  Such that:aux(35) =< V_N
aux(36) =< V_m
aux(37) =< V_n
s(89) =< aux(37)
s(90) =< aux(36)
s(91) =< aux(35)
s(92) =< s(89)*aux(36)
s(93) =< s(89)*aux(35)
s(94) =< s(89)*s(90)
s(95) =< s(89)*s(91)
s(96) =< s(95)
s(97) =< s(95)
s(96) =< s(94)
s(98) =< s(94)
s(99) =< s(93)
s(100) =< s(93)
s(99) =< s(94)
s(101) =< s(94)
s(99) =< s(92)
s(101) =< s(92)

  with precondition: [V_N>=0,V_m>=0,V_n>=1] 

* Chain [57]: 4*s(142)+2*s(149)+2*s(150)+2*s(151)+2*s(152)+2*s(153)+2*s(154)+0
  Such that:s(140) =< V_m
s(141) =< V_n
aux(38) =< V_N
s(142) =< s(141)
s(143) =< s(140)
s(144) =< aux(38)
s(145) =< s(142)*s(140)
s(146) =< s(142)*aux(38)
s(147) =< s(142)*s(143)
s(148) =< s(142)*s(144)
s(149) =< s(148)
s(150) =< s(148)
s(149) =< s(147)
s(151) =< s(147)
s(152) =< s(146)
s(153) =< s(146)
s(152) =< s(147)
s(154) =< s(147)
s(152) =< s(145)
s(154) =< s(145)

  with precondition: [V_N>=0,V_m>=0,V_n>=2] 

* Chain [56]: 2*s(157)+2*s(158)+2*s(159)+0
  Such that:s(155) =< V_N
s(156) =< V_m
s(157) =< s(155)
s(158) =< s(155)
s(157) =< s(156)
s(159) =< s(156)

  with precondition: [V_N>=0,V_m>=1,V_n>=1] 

* Chain [55]: 2*s(164)+2*s(165)+2*s(166)+4*s(167)+2*s(174)+2*s(175)+2*s(176)+2*s(177)+2*s(178)+2*s(179)+0
  Such that:s(163) =< V_m
s(162) =< V_n
aux(39) =< V_N
s(164) =< aux(39)
s(165) =< aux(39)
s(164) =< s(163)
s(166) =< s(163)
s(167) =< s(162)
s(168) =< s(163)
s(169) =< aux(39)
s(170) =< s(167)*s(163)
s(171) =< s(167)*aux(39)
s(172) =< s(167)*s(168)
s(173) =< s(167)*s(169)
s(174) =< s(173)
s(175) =< s(173)
s(174) =< s(172)
s(176) =< s(172)
s(177) =< s(171)
s(178) =< s(171)
s(177) =< s(172)
s(179) =< s(172)
s(177) =< s(170)
s(179) =< s(170)

  with precondition: [V_N>=0,V_m>=1,V_n>=2] 

* Chain [54]: 2*s(182)+2*s(183)+2*s(184)+0
  Such that:s(180) =< V_N
s(181) =< V_m
s(182) =< s(180)
s(183) =< s(180)
s(182) =< s(181)
s(184) =< s(181)

  with precondition: [V_N>=0,V_m>=2,V_n>=1] 

* Chain [53]: 2*s(189)+2*s(190)+2*s(191)+4*s(192)+2*s(199)+2*s(200)+2*s(201)+2*s(202)+2*s(203)+2*s(204)+0
  Such that:s(188) =< V_m
s(187) =< V_n
aux(40) =< V_N
s(189) =< aux(40)
s(190) =< aux(40)
s(189) =< s(188)
s(191) =< s(188)
s(192) =< s(187)
s(193) =< s(188)
s(194) =< aux(40)
s(195) =< s(192)*s(188)
s(196) =< s(192)*aux(40)
s(197) =< s(192)*s(193)
s(198) =< s(192)*s(194)
s(199) =< s(198)
s(200) =< s(198)
s(199) =< s(197)
s(201) =< s(197)
s(202) =< s(196)
s(203) =< s(196)
s(202) =< s(197)
s(204) =< s(197)
s(202) =< s(195)
s(204) =< s(195)

  with precondition: [V_N>=0,V_m>=2,V_n>=2] 

* Chain [52]: 1*s(205)+0
  Such that:s(205) =< V_N

  with precondition: [V_N>=1,V_m>=1,V_n>=1] 

* Chain [51]: 3*s(208)+2*s(209)+2*s(210)+0
  Such that:s(206) =< V_N
s(207) =< V_m
s(208) =< s(206)
s(209) =< s(206)
s(209) =< s(207)
s(210) =< s(207)

  with precondition: [V_N>=1,V_m>=2,V_n>=1] 

* Chain [50]: 1*s(215)+4*s(216)+2*s(223)+2*s(224)+2*s(225)+2*s(226)+2*s(227)+2*s(228)+0
  Such that:s(213) =< V_m
s(212) =< V_n
aux(41) =< V_N
s(215) =< aux(41)
s(216) =< s(212)
s(216) =< aux(41)
s(217) =< s(213)
s(218) =< aux(41)
s(219) =< s(216)*s(213)
s(220) =< s(216)*aux(41)
s(221) =< s(216)*s(217)
s(222) =< s(216)*s(218)
s(223) =< s(222)
s(224) =< s(222)
s(223) =< s(221)
s(225) =< s(221)
s(226) =< s(220)
s(227) =< s(220)
s(226) =< s(221)
s(228) =< s(221)
s(226) =< s(219)
s(228) =< s(219)

  with precondition: [V_N>=2,V_m>=1,V_n>=2] 

* Chain [49]: 3*s(234)+2*s(235)+2*s(236)+4*s(237)+2*s(244)+2*s(245)+2*s(246)+2*s(247)+2*s(248)+2*s(249)+0
  Such that:s(232) =< V_m
s(231) =< V_n
aux(42) =< V_N
s(233) =< aux(42)
s(233) =< s(231)
s(234) =< aux(42)
s(235) =< aux(42)
s(235) =< s(232)
s(236) =< s(232)
s(237) =< s(231)
s(237) =< s(233)
s(238) =< s(232)
s(239) =< aux(42)
s(240) =< s(237)*s(232)
s(241) =< s(237)*aux(42)
s(242) =< s(237)*s(238)
s(243) =< s(237)*s(239)
s(244) =< s(243)
s(245) =< s(243)
s(244) =< s(242)
s(246) =< s(242)
s(247) =< s(241)
s(248) =< s(241)
s(247) =< s(242)
s(249) =< s(242)
s(247) =< s(240)
s(249) =< s(240)

  with precondition: [V_N>=2,V_m>=2,V_n>=2] 


#### Cost of chains of eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B):
* Chain [78]: 0
  with precondition: [V_n=0,V_N>=0,V_m>=0] 

* Chain [77]: 0
  with precondition: [0>=V_N+1] 

* Chain [76]: 0
  with precondition: [0>=V_m+1] 

* Chain [75]: 0
  with precondition: [0>=V_n+1] 

* Chain [74]: 0
  with precondition: [V_N>=0,V_m>=0,V_n>=0] 

* Chain [73]: 12*s(253)+6*s(260)+6*s(261)+6*s(262)+6*s(263)+6*s(264)+6*s(265)+0
  Such that:s(250) =< V_N
s(251) =< V_m
s(252) =< V_n
s(253) =< s(252)
s(254) =< s(251)
s(255) =< s(250)
s(256) =< s(253)*s(251)
s(257) =< s(253)*s(250)
s(258) =< s(253)*s(254)
s(259) =< s(253)*s(255)
s(260) =< s(259)
s(261) =< s(259)
s(260) =< s(258)
s(262) =< s(258)
s(263) =< s(257)
s(264) =< s(257)
s(263) =< s(258)
s(265) =< s(258)
s(263) =< s(256)
s(265) =< s(256)

  with precondition: [V_N>=0,V_m>=0,V_n>=1] 

* Chain [72]: 4*s(269)+2*s(276)+2*s(277)+2*s(278)+2*s(279)+2*s(280)+2*s(281)+0
  Such that:s(268) =< V_N
s(266) =< V_m
s(267) =< V_n
s(269) =< s(267)
s(270) =< s(266)
s(271) =< s(268)
s(272) =< s(269)*s(266)
s(273) =< s(269)*s(268)
s(274) =< s(269)*s(270)
s(275) =< s(269)*s(271)
s(276) =< s(275)
s(277) =< s(275)
s(276) =< s(274)
s(278) =< s(274)
s(279) =< s(273)
s(280) =< s(273)
s(279) =< s(274)
s(281) =< s(274)
s(279) =< s(272)
s(281) =< s(272)

  with precondition: [V_N>=0,V_m>=0,V_n>=2] 

* Chain [71]: 2*s(284)+2*s(285)+2*s(286)+0
  Such that:s(282) =< V_N
s(283) =< V_m
s(284) =< s(282)
s(285) =< s(282)
s(284) =< s(283)
s(286) =< s(283)

  with precondition: [V_N>=0,V_m>=1,V_n>=1] 

* Chain [70]: 2*s(290)+2*s(291)+2*s(292)+4*s(293)+2*s(300)+2*s(301)+2*s(302)+2*s(303)+2*s(304)+2*s(305)+0
  Such that:s(289) =< V_N
s(287) =< V_m
s(288) =< V_n
s(290) =< s(289)
s(291) =< s(289)
s(290) =< s(287)
s(292) =< s(287)
s(293) =< s(288)
s(294) =< s(287)
s(295) =< s(289)
s(296) =< s(293)*s(287)
s(297) =< s(293)*s(289)
s(298) =< s(293)*s(294)
s(299) =< s(293)*s(295)
s(300) =< s(299)
s(301) =< s(299)
s(300) =< s(298)
s(302) =< s(298)
s(303) =< s(297)
s(304) =< s(297)
s(303) =< s(298)
s(305) =< s(298)
s(303) =< s(296)
s(305) =< s(296)

  with precondition: [V_N>=0,V_m>=1,V_n>=2] 

* Chain [69]: 2*s(308)+2*s(309)+2*s(310)+0
  Such that:s(306) =< V_N
s(307) =< V_m
s(308) =< s(306)
s(309) =< s(306)
s(308) =< s(307)
s(310) =< s(307)

  with precondition: [V_N>=0,V_m>=2,V_n>=1] 

* Chain [68]: 2*s(314)+2*s(315)+2*s(316)+4*s(317)+2*s(324)+2*s(325)+2*s(326)+2*s(327)+2*s(328)+2*s(329)+0
  Such that:s(313) =< V_N
s(311) =< V_m
s(312) =< V_n
s(314) =< s(313)
s(315) =< s(313)
s(314) =< s(311)
s(316) =< s(311)
s(317) =< s(312)
s(318) =< s(311)
s(319) =< s(313)
s(320) =< s(317)*s(311)
s(321) =< s(317)*s(313)
s(322) =< s(317)*s(318)
s(323) =< s(317)*s(319)
s(324) =< s(323)
s(325) =< s(323)
s(324) =< s(322)
s(326) =< s(322)
s(327) =< s(321)
s(328) =< s(321)
s(327) =< s(322)
s(329) =< s(322)
s(327) =< s(320)
s(329) =< s(320)

  with precondition: [V_N>=0,V_m>=2,V_n>=2] 

* Chain [67]: 1*s(330)+0
  Such that:s(330) =< V_N

  with precondition: [V_N>=1,V_m>=1,V_n>=1] 

* Chain [66]: 3*s(333)+2*s(334)+2*s(335)+0
  Such that:s(331) =< V_N
s(332) =< V_m
s(333) =< s(331)
s(334) =< s(331)
s(334) =< s(332)
s(335) =< s(332)

  with precondition: [V_N>=1,V_m>=2,V_n>=1] 

* Chain [65]: 1*s(339)+4*s(340)+2*s(347)+2*s(348)+2*s(349)+2*s(350)+2*s(351)+2*s(352)+0
  Such that:s(338) =< V_N
s(336) =< V_m
s(337) =< V_n
s(339) =< s(338)
s(340) =< s(337)
s(340) =< s(338)
s(341) =< s(336)
s(342) =< s(338)
s(343) =< s(340)*s(336)
s(344) =< s(340)*s(338)
s(345) =< s(340)*s(341)
s(346) =< s(340)*s(342)
s(347) =< s(346)
s(348) =< s(346)
s(347) =< s(345)
s(349) =< s(345)
s(350) =< s(344)
s(351) =< s(344)
s(350) =< s(345)
s(352) =< s(345)
s(350) =< s(343)
s(352) =< s(343)

  with precondition: [V_N>=2,V_m>=1,V_n>=2] 

* Chain [64]: 3*s(357)+2*s(358)+2*s(359)+4*s(360)+2*s(367)+2*s(368)+2*s(369)+2*s(370)+2*s(371)+2*s(372)+0
  Such that:s(355) =< V_N
s(353) =< V_m
s(354) =< V_n
s(356) =< s(355)
s(356) =< s(354)
s(357) =< s(355)
s(358) =< s(355)
s(358) =< s(353)
s(359) =< s(353)
s(360) =< s(354)
s(360) =< s(356)
s(361) =< s(353)
s(362) =< s(355)
s(363) =< s(360)*s(353)
s(364) =< s(360)*s(355)
s(365) =< s(360)*s(361)
s(366) =< s(360)*s(362)
s(367) =< s(366)
s(368) =< s(366)
s(367) =< s(365)
s(369) =< s(365)
s(370) =< s(364)
s(371) =< s(364)
s(370) =< s(365)
s(372) =< s(365)
s(370) =< s(363)
s(372) =< s(363)

  with precondition: [V_N>=2,V_m>=2,V_n>=2] 


Closed-form bounds of eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B): 
-------------------------------------
* Chain [78] with precondition: [V_n=0,V_N>=0,V_m>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [77] with precondition: [0>=V_N+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [76] with precondition: [0>=V_m+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [75] with precondition: [0>=V_n+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [74] with precondition: [V_N>=0,V_m>=0,V_n>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [73] with precondition: [V_N>=0,V_m>=0,V_n>=1] 
    - Upper bound: 24*V_N*V_n+12*V_m*V_n+12*V_n 
    - Complexity: n^2 
* Chain [72] with precondition: [V_N>=0,V_m>=0,V_n>=2] 
    - Upper bound: 8*V_N*V_n+4*V_m*V_n+4*V_n 
    - Complexity: n^2 
* Chain [71] with precondition: [V_N>=0,V_m>=1,V_n>=1] 
    - Upper bound: 4*V_N+2*V_m 
    - Complexity: n 
* Chain [70] with precondition: [V_N>=0,V_m>=1,V_n>=2] 
    - Upper bound: 8*V_N*V_n+4*V_N+2*V_m+4*V_m*V_n+4*V_n 
    - Complexity: n^2 
* Chain [69] with precondition: [V_N>=0,V_m>=2,V_n>=1] 
    - Upper bound: 4*V_N+2*V_m 
    - Complexity: n 
* Chain [68] with precondition: [V_N>=0,V_m>=2,V_n>=2] 
    - Upper bound: 8*V_N*V_n+4*V_N+2*V_m+4*V_m*V_n+4*V_n 
    - Complexity: n^2 
* Chain [67] with precondition: [V_N>=1,V_m>=1,V_n>=1] 
    - Upper bound: V_N 
    - Complexity: n 
* Chain [66] with precondition: [V_N>=1,V_m>=2,V_n>=1] 
    - Upper bound: 5*V_N+2*V_m 
    - Complexity: n 
* Chain [65] with precondition: [V_N>=2,V_m>=1,V_n>=2] 
    - Upper bound: 8*V_N*V_n+V_N+4*V_m*V_n+4*V_n 
    - Complexity: n^2 
* Chain [64] with precondition: [V_N>=2,V_m>=2,V_n>=2] 
    - Upper bound: 8*V_N*V_n+5*V_N+2*V_m+4*V_m*V_n+4*V_n 
    - Complexity: n^2 

### Maximum cost of eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B): max([nat(V_m)*8*nat(V_n)+nat(V_N)*16*nat(V_n)+nat(V_n)*8+(nat(V_m)*4*nat(V_n)+nat(V_N)*8*nat(V_n)+nat(V_n)*4),nat(V_m)*4*nat(V_n)+nat(V_N)*8*nat(V_n)+nat(V_n)*4+nat(V_N)+(nat(V_m)*2+nat(V_N)*4)]) 
Asymptotic class: n^2 
* Total analysis performed in 2086 ms.