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


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_start_4/9,eval_start_5/9,eval_start_6/9,eval_start_7/9,eval_start_bb2_in/9,eval_start_bb3_in/9]
1. recursive  : [eval_start_10/8,eval_start_11/8,eval_start_12/8,eval_start_9/8,eval_start__critedge_in/8,eval_start_bb4_in/8]
2. recursive  : [eval_start_13/17,eval_start_14/17,eval_start__critedge3_in/17,eval_start__critedge_in_loop_cont/18,eval_start_bb1_in/17,eval_start_bb2_in_loop_cont/18,eval_start_bb6_in/17]
3. non_recursive  : [eval_start_stop/11]
4. non_recursive  : [eval_start_bb5_in/11]
5. non_recursive  : [exit_location/1]
6. non_recursive  : [eval_start_bb1_in_loop_cont/12]
7. non_recursive  : [eval_start_16/11]
8. non_recursive  : [eval_start_15/11]
9. non_recursive  : [eval_start_bb7_in/11]
10. non_recursive  : [eval_start_2/11]
11. non_recursive  : [eval_start_1/11]
12. non_recursive  : [eval_start_0/11]
13. non_recursive  : [eval_start_bb0_in/11]
14. non_recursive  : [eval_start_start/11]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_start_bb2_in/9
1. SCC is partially evaluated into eval_start__critedge_in/8
2. SCC is partially evaluated into eval_start_bb1_in/17
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_start_bb1_in_loop_cont/12
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 partially evaluated into eval_start_2/11
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 partially evaluated into eval_start_start/11

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

### Specialization of cost equations eval_start_bb2_in/9 
* CE 13 is refined into CE [19] 
* CE 11 is refined into CE [20] 
* CE 14 is refined into CE [21] 
* CE 12 is refined into CE [22] 


### Cost equations --> "Loop" of eval_start_bb2_in/9 
* CEs [22] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [20] --> Loop 19 
* CEs [21] --> Loop 20 

### Ranking functions of CR eval_start_bb2_in(V__01,V__1,V__12,V_1,V_3,B,C,D,E) 
* RF of phase [17]: [V__01-V__1-1]

#### Partial ranking functions of CR eval_start_bb2_in(V__01,V__1,V__12,V_1,V_3,B,C,D,E) 
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    V__01-V__1-1


### Specialization of cost equations eval_start__critedge_in/8 
* CE 18 is refined into CE [23] 
* CE 17 is refined into CE [24] 
* CE 15 is refined into CE [25] 
* CE 16 is refined into CE [26] 


### Cost equations --> "Loop" of eval_start__critedge_in/8 
* CEs [26] --> Loop 21 
* CEs [23] --> Loop 22 
* CEs [24] --> Loop 23 
* CEs [25] --> Loop 24 

### Ranking functions of CR eval_start__critedge_in(V__12,V_1,V_5,V_7,B,C,D,E) 
* RF of phase [21]: [V__12-V_1-1]

#### Partial ranking functions of CR eval_start__critedge_in(V__12,V_1,V_5,V_7,B,C,D,E) 
* Partial RF of phase [21]:
  - RF of loop [21:1]:
    V__12-V_1-1


### Specialization of cost equations eval_start_bb1_in/17 
* CE 4 is refined into CE [27,28,29,30,31,32] 
* CE 6 is refined into CE [33,34,35,36,37,38] 
* CE 7 is refined into CE [39,40] 
* CE 8 is refined into CE [41] 
* CE 5 is refined into CE [42,43,44,45] 


### Cost equations --> "Loop" of eval_start_bb1_in/17 
* CEs [45] --> Loop 25 
* CEs [44] --> Loop 26 
* CEs [43] --> Loop 27 
* CEs [42] --> Loop 28 
* CEs [32] --> Loop 29 
* CEs [31] --> Loop 30 
* CEs [28] --> Loop 31 
* CEs [30] --> Loop 32 
* CEs [29] --> Loop 33 
* CEs [27] --> Loop 34 
* CEs [38] --> Loop 35 
* CEs [36,37] --> Loop 36 
* CEs [34,35,40] --> Loop 37 
* CEs [39,41] --> Loop 38 
* CEs [33] --> Loop 39 

### Ranking functions of CR eval_start_bb1_in(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,B,C,D,E,F,G,H,I,J) 
* RF of phase [25,26,27,28]: [-V__0/2+V__01/2-1]

#### Partial ranking functions of CR eval_start_bb1_in(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,B,C,D,E,F,G,H,I,J) 
* Partial RF of phase [25,26,27,28]:
  - RF of loop [25:1]:
    -V__0/4+V__01/4-1
  - RF of loop [26:1,27:1]:
    -V__0/3+V__01/3-1
  - RF of loop [28:1]:
    -V__0/2+V__01/2-1


### Specialization of cost equations eval_start_bb1_in_loop_cont/12 
* CE 9 is refined into CE [46] 
* CE 10 is refined into CE [47] 


### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/12 
* CEs [46] --> Loop 40 
* CEs [47] --> Loop 41 

### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 

#### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 


### Specialization of cost equations eval_start_2/11 
* CE 3 is refined into CE [48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66] 
* CE 2 is refined into CE [67] 


### Cost equations --> "Loop" of eval_start_2/11 
* CEs [54,66] --> Loop 42 
* CEs [53,63,65] --> Loop 43 
* CEs [52,60,61,64] --> Loop 44 
* CEs [51,58,59,62] --> Loop 45 
* CEs [50,57] --> Loop 46 
* CEs [49] --> Loop 47 
* CEs [67] --> Loop 48 
* CEs [55] --> Loop 49 
* CEs [48,56] --> Loop 50 

### Ranking functions of CR eval_start_2(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,V_h,V_l,B) 

#### Partial ranking functions of CR eval_start_2(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,V_h,V_l,B) 


### Specialization of cost equations eval_start_start/11 
* CE 1 is refined into CE [68,69,70,71,72,73,74,75,76] 


### Cost equations --> "Loop" of eval_start_start/11 
* CEs [76] --> Loop 51 
* CEs [75] --> Loop 52 
* CEs [74] --> Loop 53 
* CEs [73] --> Loop 54 
* CEs [72] --> Loop 55 
* CEs [71] --> Loop 56 
* CEs [70] --> Loop 57 
* CEs [68] --> Loop 58 
* CEs [69] --> Loop 59 

### Ranking functions of CR eval_start_start(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,V_h,V_l,B) 

#### Partial ranking functions of CR eval_start_start(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,V_h,V_l,B) 


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

#### Cost of chains of eval_start_bb2_in(V__01,V__1,V__12,V_1,V_3,B,C,D,E):
* Chain [[17],20]: 1*it(17)+0
  Such that:it(17) =< V__01-V__1

  with precondition: [B=3,V__01>=V__1+2] 

* Chain [[17],19]: 1*it(17)+0
  Such that:it(17) =< V__01-V__1

  with precondition: [B=4,V__01=C+1,V__01=D,E>=1,V__01>=V__1+2] 

* Chain [[17],18]: 1*it(17)+0
  Such that:it(17) =< -V__1+D

  with precondition: [B=4,C+1=D,0>=E,C>=V__1+1,V__01>=C+2] 

* Chain [20]: 0
  with precondition: [B=3,V__01>=V__1+1] 

* Chain [19]: 0
  with precondition: [B=4,V__01=V__1+1,E=V_3,V__01=C+1,V__01=D] 

* Chain [18]: 0
  with precondition: [B=4,V__1=C,V__1+1=D,0>=E,V__01>=V__1+2] 


#### Cost of chains of eval_start__critedge_in(V__12,V_1,V_5,V_7,B,C,D,E):
* Chain [[21],24]: 1*it(21)+0
  Such that:it(21) =< V__12-C

  with precondition: [B=2,V_1+1=C,V_1=D,E>=1,V__12>=V_1+2] 

* Chain [[21],23]: 1*it(21)+0
  Such that:it(21) =< V__12-C

  with precondition: [B=2,C=D+1,0>=E,C>=V_1+2,V__12>=C+1] 

* Chain [[21],22]: 1*it(21)+0
  Such that:it(21) =< V__12-V_1

  with precondition: [B=3,V__12>=V_1+2] 

* Chain [24]: 0
  with precondition: [B=2,E=V_7,V__12=C,V__12=D+1,V_1+1>=V__12] 

* Chain [23]: 0
  with precondition: [B=2,V__12=C,V__12=D+1,0>=E,V__12>=V_1+2] 

* Chain [22]: 0
  with precondition: [B=3] 


#### Cost of chains of eval_start_bb1_in(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,B,C,D,E,F,G,H,I,J):
* Chain [[25,26,27,28],39]: 1*it(25)+2*it(26)+1*it(28)+4*s(9)+0
  Such that:it(25) =< -V__0/4+V__01/4
aux(7) =< -V__0+V__01
aux(8) =< -V__0/2+V__01/2
aux(9) =< -V__0/3+V__01/3
it(26) =< aux(7)
it(28) =< aux(7)
s(9) =< aux(7)
it(25) =< aux(8)
it(26) =< aux(8)
it(28) =< aux(8)
it(26) =< aux(9)

  with precondition: [B=3,V__01>=V__0+3] 

* Chain [[25,26,27,28],38]: 1*it(25)+2*it(26)+1*it(28)+4*s(9)+0
  Such that:it(25) =< -V__0/4+V__01/4
aux(10) =< -V__0+V__01
aux(11) =< -V__0/2+V__01/2
aux(12) =< -V__0/3+V__01/3
it(26) =< aux(10)
it(28) =< aux(10)
s(9) =< aux(10)
it(25) =< aux(11)
it(26) =< aux(11)
it(28) =< aux(11)
it(26) =< aux(12)

  with precondition: [B=3,V__01>=V__0+3] 

* Chain [[25,26,27,28],37]: 1*it(25)+2*it(26)+1*it(28)+6*s(9)+0
  Such that:it(25) =< -V__0/4+V__01/4
aux(14) =< -V__0+V__01
aux(15) =< -V__0/2+V__01/2
aux(16) =< -V__0/3+V__01/3
aux(4) =< aux(14)
aux(6) =< aux(14)
it(25) =< aux(14)
aux(4) =< aux(15)
aux(6) =< aux(16)
s(9) =< aux(14)
it(26) =< aux(14)
it(28) =< aux(14)
it(25) =< aux(15)
it(26) =< aux(15)
it(28) =< aux(15)
it(25) =< aux(4)
it(26) =< aux(4)
it(28) =< aux(4)
it(26) =< aux(16)
it(26) =< aux(6)

  with precondition: [B=3,V__01>=V__0+4] 

* Chain [[25,26,27,28],36]: 1*it(25)+2*it(26)+1*it(28)+6*s(9)+0
  Such that:it(25) =< -V__0/4+V__01/4
aux(18) =< -V__0+V__01
aux(19) =< -V__0/2+V__01/2
aux(20) =< -V__0/3+V__01/3
aux(4) =< aux(18)
aux(6) =< aux(18)
it(25) =< aux(18)
aux(4) =< aux(19)
aux(6) =< aux(20)
s(9) =< aux(18)
it(26) =< aux(18)
it(28) =< aux(18)
it(25) =< aux(19)
it(26) =< aux(19)
it(28) =< aux(19)
it(25) =< aux(4)
it(26) =< aux(4)
it(28) =< aux(4)
it(26) =< aux(20)
it(26) =< aux(6)

  with precondition: [B=3,V__01>=V__0+5] 

* Chain [[25,26,27,28],35]: 1*it(25)+2*it(26)+1*it(28)+6*s(9)+0
  Such that:it(25) =< -V__0/4+V__01/4
aux(22) =< -V__0+V__01
aux(23) =< -V__0/2+V__01/2
aux(24) =< -V__0/3+V__01/3
aux(4) =< aux(22)
aux(6) =< aux(22)
it(25) =< aux(22)
aux(4) =< aux(23)
aux(6) =< aux(24)
s(9) =< aux(22)
it(26) =< aux(22)
it(28) =< aux(22)
it(25) =< aux(23)
it(26) =< aux(23)
it(28) =< aux(23)
it(25) =< aux(4)
it(26) =< aux(4)
it(28) =< aux(4)
it(26) =< aux(24)
it(26) =< aux(6)

  with precondition: [B=3,V__01>=V__0+6] 

* Chain [[25,26,27,28],34]: 1*it(25)+2*it(26)+1*it(28)+4*s(9)+0
  Such that:it(25) =< -V__0/4+V__01/4
aux(25) =< -V__0+V__01
aux(26) =< -V__0/2+V__01/2
aux(27) =< -V__0/3+V__01/3
it(26) =< aux(25)
it(28) =< aux(25)
s(9) =< aux(25)
it(25) =< aux(26)
it(26) =< aux(26)
it(28) =< aux(26)
it(26) =< aux(27)

  with precondition: [B=5,C+1=D,C=E,C+1=F,C+1=G,C=I,0>=H,0>=J,C>=V__0+1,V__01>=C+2] 

* Chain [[25,26,27,28],33]: 1*it(25)+2*it(26)+1*it(28)+4*s(9)+0
  Such that:it(25) =< -V__0/4+V__01/4
aux(28) =< -V__0+V__01
aux(29) =< -V__0/2+V__01/2
aux(30) =< -V__0/3+V__01/3
it(26) =< aux(28)
it(28) =< aux(28)
s(9) =< aux(28)
it(25) =< aux(29)
it(26) =< aux(29)
it(28) =< aux(29)
it(26) =< aux(30)

  with precondition: [B=5,C+2=D,C=E,C+2=F,C+1=G,C+1=I,0>=H,0>=J,C>=V__0+1,V__01>=C+3] 

* Chain [[25,26,27,28],32]: 1*it(25)+2*it(26)+1*it(28)+4*s(9)+1*s(19)+0
  Such that:aux(1) =< -V__0+V__01
aux(2) =< -V__0+V__01+C-D
aux(3) =< -V__0/2+V__01/2
aux(4) =< -V__0/2+V__01/2+C/2-D/2
aux(5) =< -V__0/3+V__01/3
aux(6) =< -V__0/3+V__01/3+C/3-D/3
it(25) =< -V__0/4+V__01/4+C/4-D/4
s(19) =< -C+D
it(26) =< aux(1)
it(28) =< aux(1)
s(9) =< aux(1)
it(26) =< aux(2)
it(28) =< aux(2)
s(9) =< aux(2)
it(25) =< aux(3)
it(26) =< aux(3)
it(28) =< aux(3)
it(25) =< aux(4)
it(26) =< aux(4)
it(28) =< aux(4)
it(26) =< aux(5)
it(26) =< aux(6)

  with precondition: [B=5,C=E,C+2=F,C+1=G,C+1=I,0>=H,J>=1,C>=V__0+1,D>=C+3,V__01>=D+1] 

* Chain [[25,26,27,28],31]: 1*it(25)+2*it(26)+1*it(28)+4*s(9)+1*s(20)+0
  Such that:aux(1) =< -V__0+V__01
aux(2) =< -V__0+V__01+C-E
aux(3) =< -V__0/2+V__01/2
aux(4) =< -V__0/2+V__01/2+C/2-E/2
aux(5) =< -V__0/3+V__01/3
aux(6) =< -V__0/3+V__01/3+C/3-E/3
it(25) =< -V__0/4+V__01/4+C/4-E/4
s(20) =< -C+E+1
it(26) =< aux(1)
it(28) =< aux(1)
s(9) =< aux(1)
it(26) =< aux(2)
it(28) =< aux(2)
s(9) =< aux(2)
it(25) =< aux(3)
it(26) =< aux(3)
it(28) =< aux(3)
it(25) =< aux(4)
it(26) =< aux(4)
it(28) =< aux(4)
it(26) =< aux(5)
it(26) =< aux(6)

  with precondition: [B=5,D=E+1,D=F,D=G,D=I+1,0>=J,H>=1,C>=V__0+1,D>=C+2,V__01>=D+1] 

* Chain [[25,26,27,28],30]: 1*it(25)+2*it(26)+1*it(28)+4*s(9)+1*s(21)+0
  Such that:aux(1) =< -V__0+V__01
aux(2) =< -V__0+V__01+C-D
aux(3) =< -V__0/2+V__01/2
aux(4) =< -V__0/2+V__01/2+C/2-D/2
aux(5) =< -V__0/3+V__01/3
aux(6) =< -V__0/3+V__01/3+C/3-D/3
it(25) =< -V__0/4+V__01/4+C/4-D/4
s(21) =< -C+D
it(26) =< aux(1)
it(28) =< aux(1)
s(9) =< aux(1)
it(26) =< aux(2)
it(28) =< aux(2)
s(9) =< aux(2)
it(25) =< aux(3)
it(26) =< aux(3)
it(28) =< aux(3)
it(25) =< aux(4)
it(26) =< aux(4)
it(28) =< aux(4)
it(26) =< aux(5)
it(26) =< aux(6)

  with precondition: [B=5,D=E+2,D=F,D=G+1,D=I+1,0>=H,0>=J,C>=V__0+1,D>=C+3,V__01>=D+1] 

* Chain [[25,26,27,28],29]: 1*it(25)+2*it(26)+1*it(28)+4*s(9)+2*s(22)+0
  Such that:aux(1) =< -V__0+V__01
aux(2) =< -V__0+V__01+C-D
aux(3) =< -V__0/2+V__01/2
aux(4) =< -V__0/2+V__01/2+C/2-D/2
aux(5) =< -V__0/3+V__01/3
aux(6) =< -V__0/3+V__01/3+C/3-D/3
it(25) =< -V__0/4+V__01/4+C/4-D/4
aux(31) =< -C+D
s(22) =< aux(31)
it(26) =< aux(1)
it(28) =< aux(1)
s(9) =< aux(1)
it(26) =< aux(2)
it(28) =< aux(2)
s(9) =< aux(2)
it(25) =< aux(3)
it(26) =< aux(3)
it(28) =< aux(3)
it(25) =< aux(4)
it(26) =< aux(4)
it(28) =< aux(4)
it(26) =< aux(5)
it(26) =< aux(6)

  with precondition: [B=5,I=E+1,I+1=F,I=G,0>=H,J>=1,C>=V__0+1,I>=C+2,V__01>=D+1,D>=I+2] 

* Chain [39]: 0
  with precondition: [B=3,V__01=V__0+1] 

* Chain [38]: 0
  with precondition: [B=3,V__01>=V__0+1] 

* Chain [37]: 2*s(13)+0
  Such that:aux(13) =< -V__0+V__01
s(13) =< aux(13)

  with precondition: [B=3,V__01>=V__0+2] 

* Chain [36]: 2*s(15)+0
  Such that:aux(17) =< -V__0+V__01
s(15) =< aux(17)

  with precondition: [B=3,V__01>=V__0+3] 

* Chain [35]: 2*s(17)+0
  Such that:aux(21) =< -V__0+V__01
s(17) =< aux(21)

  with precondition: [B=3,V__01>=V__0+4] 

* Chain [34]: 0
  with precondition: [B=5,V__0+1=V__01,H=V_3,J=V_7,V__0=C,V__0+1=D,V__0=E,V__0+1=F,V__0+1=G,V__0=I] 

* Chain [33]: 0
  with precondition: [B=5,V__0+2=V__01,J=V_7,V__0=C,V__0+2=D,V__0=E,V__0+2=F,V__0+1=G,V__0+1=I,0>=H] 

* Chain [32]: 1*s(19)+0
  Such that:s(19) =< -V__0+V__01

  with precondition: [B=5,V__0=C,V__01=D,V__0=E,V__0+2=F,V__0+1=G,V__0+1=I,0>=H,J>=1,V__01>=V__0+3] 

* Chain [31]: 1*s(20)+0
  Such that:s(20) =< -V__0+V__01

  with precondition: [B=5,J=V_7,V__0=C,V__01=D,V__01=E+1,V__01=F,V__01=G,V__01=I+1,H>=1,V__01>=V__0+2] 

* Chain [30]: 1*s(21)+0
  Such that:s(21) =< -V__0+V__01

  with precondition: [B=5,J=V_7,V__0=C,V__01=D,V__01=E+2,V__01=F,V__01=G+1,V__01=I+1,0>=H,V__01>=V__0+3] 

* Chain [29]: 2*s(22)+0
  Such that:aux(31) =< -V__0+V__01
s(22) =< aux(31)

  with precondition: [B=5,V__0=C,V__01=D,I=E+1,I+1=F,I=G,0>=H,J>=1,I>=V__0+2,V__01>=I+2] 


#### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L):
* Chain [41]: 0
  with precondition: [A=3,J>=K+1] 

* Chain [40]: 0
  with precondition: [A=5,J>=K+1] 


#### Cost of chains of eval_start_2(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,V_h,V_l,B):
* Chain [50]: 0
  with precondition: [V_l+1=V_h] 

* Chain [49]: 0
  with precondition: [V_l+2=V_h] 

* Chain [48]: 0
  with precondition: [V_l>=V_h] 

* Chain [47]: 0
  with precondition: [V_h>=V_l+1] 

* Chain [46]: 3*s(52)+0
  Such that:aux(37) =< V_h-V_l
s(52) =< aux(37)

  with precondition: [V_h>=V_l+2] 

* Chain [45]: 3*s(58)+16*s(59)+6*s(60)+3*s(61)+0
  Such that:aux(38) =< V_h-V_l
aux(39) =< V_h/2-V_l/2
aux(40) =< V_h/3-V_l/3
aux(41) =< V_h/4-V_l/4
s(59) =< aux(38)
s(58) =< aux(41)
s(60) =< aux(38)
s(61) =< aux(38)
s(58) =< aux(39)
s(60) =< aux(39)
s(61) =< aux(39)
s(60) =< aux(40)

  with precondition: [V_h>=V_l+3] 

* Chain [44]: 1*s(73)+14*s(75)+2*s(78)+1*s(79)+1*s(82)+2*s(86)+1*s(87)+1*s(95)+1*s(96)+2*s(97)+1*s(98)+4*s(99)+0
  Such that:aux(43) =< V_h-V_l+1
aux(46) =< V_h-V_l
aux(47) =< V_h/2-V_l/2
aux(48) =< V_h/3-V_l/3
aux(49) =< V_h/4-V_l/4
s(73) =< aux(49)
s(82) =< aux(49)
s(95) =< aux(49)
s(75) =< aux(46)
s(76) =< aux(46)
s(77) =< aux(46)
s(73) =< aux(46)
s(76) =< aux(47)
s(77) =< aux(48)
s(78) =< aux(46)
s(79) =< aux(46)
s(73) =< aux(47)
s(78) =< aux(47)
s(79) =< aux(47)
s(73) =< s(76)
s(78) =< s(76)
s(79) =< s(76)
s(78) =< aux(48)
s(78) =< s(77)
s(86) =< aux(46)
s(87) =< aux(46)
s(82) =< aux(47)
s(86) =< aux(47)
s(87) =< aux(47)
s(86) =< aux(48)
s(90) =< aux(46)
s(90) =< aux(43)
s(92) =< aux(43)
s(94) =< aux(43)
s(95) =< aux(43)
s(96) =< aux(43)
s(92) =< aux(47)
s(94) =< aux(48)
s(97) =< aux(46)
s(98) =< aux(46)
s(99) =< aux(46)
s(97) =< s(90)
s(98) =< s(90)
s(99) =< s(90)
s(95) =< aux(47)
s(97) =< aux(47)
s(98) =< aux(47)
s(95) =< s(92)
s(97) =< s(92)
s(98) =< s(92)
s(97) =< aux(48)
s(97) =< s(94)

  with precondition: [V_h>=V_l+4] 

* Chain [43]: 3*s(100)+16*s(106)+6*s(107)+3*s(108)+0
  Such that:aux(56) =< V_h-V_l
aux(57) =< V_h/2-V_l/2
aux(58) =< V_h/3-V_l/3
aux(59) =< V_h/4-V_l/4
s(100) =< aux(59)
s(104) =< aux(56)
s(105) =< aux(56)
s(100) =< aux(56)
s(104) =< aux(57)
s(105) =< aux(58)
s(106) =< aux(56)
s(107) =< aux(56)
s(108) =< aux(56)
s(100) =< aux(57)
s(107) =< aux(57)
s(108) =< aux(57)
s(100) =< s(104)
s(107) =< s(104)
s(108) =< s(104)
s(107) =< aux(58)
s(107) =< s(105)

  with precondition: [V_h>=V_l+5] 

* Chain [42]: 2*s(131)+12*s(137)+4*s(138)+2*s(139)+0
  Such that:aux(63) =< V_h-V_l
aux(64) =< V_h/2-V_l/2
aux(65) =< V_h/3-V_l/3
aux(66) =< V_h/4-V_l/4
s(131) =< aux(66)
s(135) =< aux(63)
s(136) =< aux(63)
s(131) =< aux(63)
s(135) =< aux(64)
s(136) =< aux(65)
s(137) =< aux(63)
s(138) =< aux(63)
s(139) =< aux(63)
s(131) =< aux(64)
s(138) =< aux(64)
s(139) =< aux(64)
s(131) =< s(135)
s(138) =< s(135)
s(139) =< s(135)
s(138) =< aux(65)
s(138) =< s(136)

  with precondition: [V_h>=V_l+6] 


#### Cost of chains of eval_start_start(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,V_h,V_l,B):
* Chain [59]: 0
  with precondition: [V_l+1=V_h] 

* Chain [58]: 0
  with precondition: [V_l+2=V_h] 

* Chain [57]: 0
  with precondition: [V_l>=V_h] 

* Chain [56]: 0
  with precondition: [V_h>=V_l+1] 

* Chain [55]: 3*s(153)+0
  Such that:s(152) =< V_h-V_l
s(153) =< s(152)

  with precondition: [V_h>=V_l+2] 

* Chain [54]: 16*s(158)+3*s(159)+6*s(160)+3*s(161)+0
  Such that:s(154) =< V_h-V_l
s(155) =< V_h/2-V_l/2
s(156) =< V_h/3-V_l/3
s(157) =< V_h/4-V_l/4
s(158) =< s(154)
s(159) =< s(157)
s(160) =< s(154)
s(161) =< s(154)
s(159) =< s(155)
s(160) =< s(155)
s(161) =< s(155)
s(160) =< s(156)

  with precondition: [V_h>=V_l+3] 

* Chain [53]: 1*s(167)+1*s(168)+1*s(169)+14*s(170)+2*s(173)+1*s(174)+2*s(175)+1*s(176)+1*s(180)+2*s(181)+1*s(182)+4*s(183)+0
  Such that:s(163) =< V_h-V_l
s(162) =< V_h-V_l+1
s(164) =< V_h/2-V_l/2
s(165) =< V_h/3-V_l/3
s(166) =< V_h/4-V_l/4
s(167) =< s(166)
s(168) =< s(166)
s(169) =< s(166)
s(170) =< s(163)
s(171) =< s(163)
s(172) =< s(163)
s(167) =< s(163)
s(171) =< s(164)
s(172) =< s(165)
s(173) =< s(163)
s(174) =< s(163)
s(167) =< s(164)
s(173) =< s(164)
s(174) =< s(164)
s(167) =< s(171)
s(173) =< s(171)
s(174) =< s(171)
s(173) =< s(165)
s(173) =< s(172)
s(175) =< s(163)
s(176) =< s(163)
s(168) =< s(164)
s(175) =< s(164)
s(176) =< s(164)
s(175) =< s(165)
s(177) =< s(163)
s(177) =< s(162)
s(178) =< s(162)
s(179) =< s(162)
s(169) =< s(162)
s(180) =< s(162)
s(178) =< s(164)
s(179) =< s(165)
s(181) =< s(163)
s(182) =< s(163)
s(183) =< s(163)
s(181) =< s(177)
s(182) =< s(177)
s(183) =< s(177)
s(169) =< s(164)
s(181) =< s(164)
s(182) =< s(164)
s(169) =< s(178)
s(181) =< s(178)
s(182) =< s(178)
s(181) =< s(165)
s(181) =< s(179)

  with precondition: [V_h>=V_l+4] 

* Chain [52]: 3*s(188)+16*s(191)+6*s(192)+3*s(193)+0
  Such that:s(184) =< V_h-V_l
s(185) =< V_h/2-V_l/2
s(186) =< V_h/3-V_l/3
s(187) =< V_h/4-V_l/4
s(188) =< s(187)
s(189) =< s(184)
s(190) =< s(184)
s(188) =< s(184)
s(189) =< s(185)
s(190) =< s(186)
s(191) =< s(184)
s(192) =< s(184)
s(193) =< s(184)
s(188) =< s(185)
s(192) =< s(185)
s(193) =< s(185)
s(188) =< s(189)
s(192) =< s(189)
s(193) =< s(189)
s(192) =< s(186)
s(192) =< s(190)

  with precondition: [V_h>=V_l+5] 

* Chain [51]: 2*s(198)+12*s(201)+4*s(202)+2*s(203)+0
  Such that:s(194) =< V_h-V_l
s(195) =< V_h/2-V_l/2
s(196) =< V_h/3-V_l/3
s(197) =< V_h/4-V_l/4
s(198) =< s(197)
s(199) =< s(194)
s(200) =< s(194)
s(198) =< s(194)
s(199) =< s(195)
s(200) =< s(196)
s(201) =< s(194)
s(202) =< s(194)
s(203) =< s(194)
s(198) =< s(195)
s(202) =< s(195)
s(203) =< s(195)
s(198) =< s(199)
s(202) =< s(199)
s(203) =< s(199)
s(202) =< s(196)
s(202) =< s(200)

  with precondition: [V_h>=V_l+6] 


Closed-form bounds of eval_start_start(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,V_h,V_l,B): 
-------------------------------------
* Chain [59] with precondition: [V_l+1=V_h] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [58] with precondition: [V_l+2=V_h] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [57] with precondition: [V_l>=V_h] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [56] with precondition: [V_h>=V_l+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [55] with precondition: [V_h>=V_l+2] 
    - Upper bound: 3*V_h-3*V_l 
    - Complexity: n 
* Chain [54] with precondition: [V_h>=V_l+3] 
    - Upper bound: 103/4*V_h-103/4*V_l 
    - Complexity: n 
* Chain [53] with precondition: [V_h>=V_l+4] 
    - Upper bound: 115/4*V_h-115/4*V_l+1 
    - Complexity: n 
* Chain [52] with precondition: [V_h>=V_l+5] 
    - Upper bound: 103/4*V_h-103/4*V_l 
    - Complexity: n 
* Chain [51] with precondition: [V_h>=V_l+6] 
    - Upper bound: 37/2*V_h-37/2*V_l 
    - Complexity: n 

### Maximum cost of eval_start_start(V__0,V__01,V__1,V__12,V_1,V_3,V_5,V_7,V_h,V_l,B): nat(V_h-V_l)*7+nat(V_h/4-V_l/4)+(nat(V_h-V_l)*2+nat(V_h-V_l+1))+(nat(V_h/4-V_l/4)*2+nat(V_h-V_l)*15)+nat(V_h-V_l)*3 
Asymptotic class: n 
* Total analysis performed in 1674 ms.