/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_bb1_in/7,eval_start_bb2_in/7]
1. recursive  : [eval_start_bb3_in/4,eval_start_bb4_in/4]
2. recursive  : [eval_start_bb5_in/3,eval_start_bb6_in/3]
3. non_recursive  : [eval_start_stop/7]
4. non_recursive  : [eval_start_bb7_in/7]
5. non_recursive  : [exit_location/1]
6. non_recursive  : [eval_start_bb5_in_loop_cont/8]
7. non_recursive  : [eval_start_bb3_in_loop_cont/8]
8. non_recursive  : [eval_start_bb1_in_loop_cont/8]
9. non_recursive  : [eval_start_5/7]
10. non_recursive  : [eval_start_4/7]
11. non_recursive  : [eval_start_3/7]
12. non_recursive  : [eval_start_2/7]
13. non_recursive  : [eval_start_1/7]
14. non_recursive  : [eval_start_0/7]
15. non_recursive  : [eval_start_bb0_in/7]
16. non_recursive  : [eval_start_start/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_start_bb1_in/7
1. SCC is partially evaluated into eval_start_bb3_in/4
2. SCC is partially evaluated into eval_start_bb5_in/3
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_bb5_in_loop_cont/8
7. SCC is partially evaluated into eval_start_bb3_in_loop_cont/8
8. SCC is partially evaluated into eval_start_bb1_in_loop_cont/8
9. SCC is partially evaluated into eval_start_5/7
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 partially evaluated into eval_start_start/7

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

### Specialization of cost equations eval_start_bb1_in/7 
* CE 4 is refined into CE [18] 
* CE 5 is refined into CE [19] 
* CE 3 is refined into CE [20] 


### Cost equations --> "Loop" of eval_start_bb1_in/7 
* CEs [20] --> Loop 18 
* CEs [18] --> Loop 19 
* CEs [19] --> Loop 20 

### Ranking functions of CR eval_start_bb1_in(V__0,V__01,V__12,B,C,D,E) 
* RF of phase [18]: [V__0-V__01]

#### Partial ranking functions of CR eval_start_bb1_in(V__0,V__01,V__12,B,C,D,E) 
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    V__0-V__01


### Specialization of cost equations eval_start_bb3_in/4 
* CE 9 is refined into CE [21] 
* CE 10 is refined into CE [22] 
* CE 8 is refined into CE [23] 


### Cost equations --> "Loop" of eval_start_bb3_in/4 
* CEs [23] --> Loop 21 
* CEs [21] --> Loop 22 
* CEs [22] --> Loop 23 

### Ranking functions of CR eval_start_bb3_in(V__1,V__12,B,C) 
* RF of phase [21]: [V__12]

#### Partial ranking functions of CR eval_start_bb3_in(V__1,V__12,B,C) 
* Partial RF of phase [21]:
  - RF of loop [21:1]:
    V__12


### Specialization of cost equations eval_start_bb5_in/3 
* CE 15 is refined into CE [24] 
* CE 14 is refined into CE [25] 
* CE 13 is refined into CE [26] 


### Cost equations --> "Loop" of eval_start_bb5_in/3 
* CEs [26] --> Loop 24 
* CEs [24] --> Loop 25 
* CEs [25] --> Loop 26 

### Ranking functions of CR eval_start_bb5_in(V__1,B,C) 
* RF of phase [24]: [-V__1]

#### Partial ranking functions of CR eval_start_bb5_in(V__1,B,C) 
* Partial RF of phase [24]:
  - RF of loop [24:1]:
    -V__1


### Specialization of cost equations eval_start_bb5_in_loop_cont/8 
* CE 17 is refined into CE [27] 
* CE 16 is refined into CE [28] 


### Cost equations --> "Loop" of eval_start_bb5_in_loop_cont/8 
* CEs [27] --> Loop 27 
* CEs [28] --> Loop 28 

### Ranking functions of CR eval_start_bb5_in_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR eval_start_bb5_in_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations eval_start_bb3_in_loop_cont/8 
* CE 12 is refined into CE [29,30,31,32] 
* CE 11 is refined into CE [33] 


### Cost equations --> "Loop" of eval_start_bb3_in_loop_cont/8 
* CEs [30] --> Loop 29 
* CEs [29,32] --> Loop 30 
* CEs [31] --> Loop 31 
* CEs [33] --> Loop 32 

### Ranking functions of CR eval_start_bb3_in_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR eval_start_bb3_in_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations eval_start_bb1_in_loop_cont/8 
* CE 7 is refined into CE [34,35,36,37,38,39,40,41] 
* CE 6 is refined into CE [42] 


### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/8 
* CEs [35,36] --> Loop 33 
* CEs [38] --> Loop 34 
* CEs [41] --> Loop 35 
* CEs [39] --> Loop 36 
* CEs [37] --> Loop 37 
* CEs [40] --> Loop 38 
* CEs [34] --> Loop 39 
* CEs [42] --> Loop 40 

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

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


### Specialization of cost equations eval_start_5/7 
* CE 2 is refined into CE [43,44,45,46,47,48,49,50,51,52,53,54,55,56,57] 


### Cost equations --> "Loop" of eval_start_5/7 
* CEs [44,52] --> Loop 41 
* CEs [45] --> Loop 42 
* CEs [56,57] --> Loop 43 
* CEs [53] --> Loop 44 
* CEs [54] --> Loop 45 
* CEs [51] --> Loop 46 
* CEs [50] --> Loop 47 
* CEs [48] --> Loop 48 
* CEs [47] --> Loop 49 
* CEs [46] --> Loop 50 
* CEs [55] --> Loop 51 
* CEs [49] --> Loop 52 
* CEs [43] --> Loop 53 

### Ranking functions of CR eval_start_5(V__0,V__01,V__1,V__12,V_x,V_y,B) 

#### Partial ranking functions of CR eval_start_5(V__0,V__01,V__1,V__12,V_x,V_y,B) 


### Specialization of cost equations eval_start_start/7 
* CE 1 is refined into CE [58,59,60,61,62,63,64,65,66,67,68,69,70] 


### Cost equations --> "Loop" of eval_start_start/7 
* CEs [70] --> Loop 54 
* CEs [69] --> Loop 55 
* CEs [68] --> Loop 56 
* CEs [67] --> Loop 57 
* CEs [66] --> Loop 58 
* CEs [65] --> Loop 59 
* CEs [64] --> Loop 60 
* CEs [63] --> Loop 61 
* CEs [62] --> Loop 62 
* CEs [61] --> Loop 63 
* CEs [60] --> Loop 64 
* CEs [59] --> Loop 65 
* CEs [58] --> Loop 66 

### Ranking functions of CR eval_start_start(V__0,V__01,V__1,V__12,V_x,V_y,B) 

#### Partial ranking functions of CR eval_start_start(V__0,V__01,V__1,V__12,V_x,V_y,B) 


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

#### Cost of chains of eval_start_bb1_in(V__0,V__01,V__12,B,C,D,E):
* Chain [[18],20]: 1*it(18)+0
  Such that:it(18) =< V__0-V__01

  with precondition: [B=3,V__0>=V__01+1] 

* Chain [[18],19]: 1*it(18)+0
  Such that:it(18) =< -V__0/999+C/999

  with precondition: [B=5,1000*V__0=999*V__01+C,1000*V__0=999*V__01+D,1000*V__0=999*V__01+E,V__0>=V__01+1] 

* Chain [20]: 0
  with precondition: [B=3] 

* Chain [19]: 0
  with precondition: [B=5,V__0=C,V__01=D,V__01=E,V__01>=V__0] 


#### Cost of chains of eval_start_bb3_in(V__1,V__12,B,C):
* Chain [[21],23]: 1*it(21)+0
  Such that:it(21) =< V__12

  with precondition: [B=3,V__12>=1] 

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

  with precondition: [B=4,C=0,V__12>=1] 

* Chain [23]: 0
  with precondition: [B=3] 

* Chain [22]: 0
  with precondition: [B=4,V__12=C,0>=V__12] 


#### Cost of chains of eval_start_bb5_in(V__1,B,C):
* Chain [[24],26]: 1*it(24)+0
  Such that:it(24) =< -V__1

  with precondition: [B=2,C=0,0>=V__1+1] 

* Chain [[24],25]: 1*it(24)+0
  Such that:it(24) =< -V__1

  with precondition: [B=3,0>=V__1+1] 

* Chain [26]: 0
  with precondition: [B=2,V__1=C,V__1>=0] 

* Chain [25]: 0
  with precondition: [B=3] 


#### Cost of chains of eval_start_bb5_in_loop_cont(A,B,C,D,E,F,G,H):
* Chain [28]: 0
  with precondition: [A=2] 

* Chain [27]: 0
  with precondition: [A=3] 


#### Cost of chains of eval_start_bb3_in_loop_cont(A,B,C,D,E,F,G,H):
* Chain [32]: 0
  with precondition: [A=3,D=B] 

* Chain [31]: 0
  with precondition: [A=4,D=B] 

* Chain [30]: 2*s(1)+0
  Such that:aux(1) =< -D
s(1) =< aux(1)

  with precondition: [A=4,D=B,0>=D+1] 

* Chain [29]: 0
  with precondition: [A=4,D=B,D>=0] 


#### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H):
* Chain [40]: 0
  with precondition: [A=3] 

* Chain [39]: 0
  with precondition: [A=5] 

* Chain [38]: 2*s(4)+0
  Such that:s(3) =< -B
s(4) =< s(3)

  with precondition: [A=5,0>=B+1,0>=E] 

* Chain [37]: 1*s(5)+2*s(7)+0
  Such that:s(6) =< -B
s(5) =< E
s(7) =< s(6)

  with precondition: [A=5,0>=B+1,E>=1] 

* Chain [36]: 0
  with precondition: [A=5,0>=E] 

* Chain [35]: 0
  with precondition: [A=5,0>=E,B>=0] 

* Chain [34]: 1*s(8)+0
  Such that:s(8) =< E

  with precondition: [A=5,B>=0,E>=1] 

* Chain [33]: 2*s(9)+0
  Such that:aux(2) =< E
s(9) =< aux(2)

  with precondition: [A=5,E>=1] 


#### Cost of chains of eval_start_5(V__0,V__01,V__1,V__12,V_x,V_y,B):
* Chain [53]: 0
  with precondition: [] 

* Chain [52]: 0
  with precondition: [V_x=0,V_y=0] 

* Chain [51]: 1*s(11)+0
  Such that:s(11) =< -V_y/1000

  with precondition: [1000*V_x=999*V_y,0>=V_x+999] 

* Chain [50]: 2*s(13)+0
  Such that:s(12) =< -V_x
s(13) =< s(12)

  with precondition: [0>=V_x+1,0>=V_y,V_y>=V_x] 

* Chain [49]: 1*s(15)+2*s(16)+0
  Such that:s(14) =< -V_x
s(15) =< V_y
s(16) =< s(14)

  with precondition: [0>=V_x+1,V_y>=1] 

* Chain [48]: 0
  with precondition: [0>=V_y,V_y>=V_x] 

* Chain [47]: 1*s(17)+0
  Such that:s(17) =< V_y

  with precondition: [V_x>=0,V_y>=1,V_y>=V_x] 

* Chain [46]: 2*s(19)+0
  Such that:s(18) =< V_y
s(19) =< s(18)

  with precondition: [V_y>=1,V_y>=V_x] 

* Chain [45]: 1*s(20)+0
  Such that:s(20) =< V_x-V_y

  with precondition: [999*V_y>=1000*V_x,V_x>=V_y+1] 

* Chain [44]: 1*s(21)+2*s(23)+0
  Such that:s(22) =< -1000*V_x+999*V_y
s(21) =< V_x-V_y
s(23) =< s(22)

  with precondition: [999*V_y>=1000*V_x+1,V_x>=V_y+1] 

* Chain [43]: 2*s(24)+3*s(25)+0
  Such that:aux(3) =< V_x-V_y
aux(4) =< 1000*V_x-999*V_y
s(24) =< aux(3)
s(25) =< aux(4)

  with precondition: [1000*V_x>=999*V_y+1,V_x>=V_y+1] 

* Chain [42]: 0
  with precondition: [V_y>=V_x] 

* Chain [41]: 2*s(29)+0
  Such that:aux(5) =< V_x-V_y
s(29) =< aux(5)

  with precondition: [V_x>=V_y+1] 


#### Cost of chains of eval_start_start(V__0,V__01,V__1,V__12,V_x,V_y,B):
* Chain [66]: 0
  with precondition: [] 

* Chain [65]: 0
  with precondition: [V_x=0,V_y=0] 

* Chain [64]: 1*s(31)+0
  Such that:s(31) =< -V_y/1000

  with precondition: [1000*V_x=999*V_y,0>=V_x+999] 

* Chain [63]: 2*s(33)+0
  Such that:s(32) =< -V_x
s(33) =< s(32)

  with precondition: [0>=V_x+1,0>=V_y,V_y>=V_x] 

* Chain [62]: 1*s(35)+2*s(36)+0
  Such that:s(34) =< -V_x
s(35) =< V_y
s(36) =< s(34)

  with precondition: [0>=V_x+1,V_y>=1] 

* Chain [61]: 0
  with precondition: [0>=V_y,V_y>=V_x] 

* Chain [60]: 1*s(37)+0
  Such that:s(37) =< V_y

  with precondition: [V_x>=0,V_y>=1,V_y>=V_x] 

* Chain [59]: 2*s(39)+0
  Such that:s(38) =< V_y
s(39) =< s(38)

  with precondition: [V_y>=1,V_y>=V_x] 

* Chain [58]: 1*s(40)+0
  Such that:s(40) =< V_x-V_y

  with precondition: [999*V_y>=1000*V_x,V_x>=V_y+1] 

* Chain [57]: 1*s(42)+2*s(43)+0
  Such that:s(41) =< -1000*V_x+999*V_y
s(42) =< V_x-V_y
s(43) =< s(41)

  with precondition: [999*V_y>=1000*V_x+1,V_x>=V_y+1] 

* Chain [56]: 2*s(46)+3*s(47)+0
  Such that:s(44) =< V_x-V_y
s(45) =< 1000*V_x-999*V_y
s(46) =< s(44)
s(47) =< s(45)

  with precondition: [1000*V_x>=999*V_y+1,V_x>=V_y+1] 

* Chain [55]: 0
  with precondition: [V_y>=V_x] 

* Chain [54]: 2*s(49)+0
  Such that:s(48) =< V_x-V_y
s(49) =< s(48)

  with precondition: [V_x>=V_y+1] 


Closed-form bounds of eval_start_start(V__0,V__01,V__1,V__12,V_x,V_y,B): 
-------------------------------------
* Chain [66] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [65] with precondition: [V_x=0,V_y=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [64] with precondition: [1000*V_x=999*V_y,0>=V_x+999] 
    - Upper bound: -V_y/1000 
    - Complexity: n 
* Chain [63] with precondition: [0>=V_x+1,0>=V_y,V_y>=V_x] 
    - Upper bound: -2*V_x 
    - Complexity: n 
* Chain [62] with precondition: [0>=V_x+1,V_y>=1] 
    - Upper bound: -2*V_x+V_y 
    - Complexity: n 
* Chain [61] with precondition: [0>=V_y,V_y>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [60] with precondition: [V_x>=0,V_y>=1,V_y>=V_x] 
    - Upper bound: V_y 
    - Complexity: n 
* Chain [59] with precondition: [V_y>=1,V_y>=V_x] 
    - Upper bound: 2*V_y 
    - Complexity: n 
* Chain [58] with precondition: [999*V_y>=1000*V_x,V_x>=V_y+1] 
    - Upper bound: V_x-V_y 
    - Complexity: n 
* Chain [57] with precondition: [999*V_y>=1000*V_x+1,V_x>=V_y+1] 
    - Upper bound: -1999*V_x+1997*V_y 
    - Complexity: n 
* Chain [56] with precondition: [1000*V_x>=999*V_y+1,V_x>=V_y+1] 
    - Upper bound: 3002*V_x-2999*V_y 
    - Complexity: n 
* Chain [55] with precondition: [V_y>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [54] with precondition: [V_x>=V_y+1] 
    - Upper bound: 2*V_x-2*V_y 
    - Complexity: n 

### Maximum cost of eval_start_start(V__0,V__01,V__1,V__12,V_x,V_y,B): max([max([max([nat(-V_y/1000),nat(-V_x)*2]),nat(V_y)+max([nat(V_y),nat(-V_x)*2])]),nat(V_x-V_y)+max([nat(-1000*V_x+999*V_y)*2,nat(1000*V_x-999*V_y)*3+nat(V_x-V_y)])]) 
Asymptotic class: n 
* Total analysis performed in 372 ms.