/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_bb3_in/4,eval_start_bb4_in/4]
1. recursive  : [eval_start_bb1_in/8,eval_start_bb2_in/8,eval_start_bb3_in_loop_cont/9]
2. non_recursive  : [eval_start_stop/6]
3. non_recursive  : [eval_start_bb5_in/6]
4. non_recursive  : [exit_location/1]
5. non_recursive  : [eval_start_bb1_in_loop_cont/7]
6. non_recursive  : [eval_start_9/6]
7. non_recursive  : [eval_start_8/6]
8. non_recursive  : [eval_start_bb6_in/6]
9. non_recursive  : [eval_start_2/6]
10. non_recursive  : [eval_start_1/6]
11. non_recursive  : [eval_start_0/6]
12. non_recursive  : [eval_start_bb0_in/6]
13. non_recursive  : [eval_start_start/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_start_bb3_in/4
1. SCC is partially evaluated into eval_start_bb1_in/8
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval_start_bb1_in_loop_cont/7
6. SCC is completely evaluated into other SCCs
7. SCC is completely evaluated into other SCCs
8. SCC is completely evaluated into other SCCs
9. SCC is partially evaluated into eval_start_2/6
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 partially evaluated into eval_start_start/6

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

### Specialization of cost equations eval_start_bb3_in/4 
* CE 12 is refined into CE [13] 
* CE 11 is refined into CE [14] 
* CE 10 is refined into CE [15] 


### Cost equations --> "Loop" of eval_start_bb3_in/4 
* CEs [15] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR eval_start_bb3_in(V__0,V_z_0,B,C) 
* RF of phase [13]: [V_z_0]

#### Partial ranking functions of CR eval_start_bb3_in(V__0,V_z_0,B,C) 
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    V_z_0


### Specialization of cost equations eval_start_bb1_in/8 
* CE 6 is refined into CE [16] 
* CE 4 is refined into CE [17,18] 
* CE 7 is refined into CE [19] 
* CE 5 is refined into CE [20,21] 


### Cost equations --> "Loop" of eval_start_bb1_in/8 
* CEs [21] --> Loop 16 
* CEs [20] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [18] --> Loop 19 
* CEs [17] --> Loop 20 
* CEs [19] --> Loop 21 

### Ranking functions of CR eval_start_bb1_in(V__0,V_3,V_y,V_z_0,B,C,D,E) 
* RF of phase [16]: [V__0/2-1/2,V__0/2-V_y/2]
* RF of phase [17]: [V__0]

#### Partial ranking functions of CR eval_start_bb1_in(V__0,V_3,V_y,V_z_0,B,C,D,E) 
* Partial RF of phase [16]:
  - RF of loop [16:1]:
    V__0/2-1/2
    V__0/2-V_y/2
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    V__0


### Specialization of cost equations eval_start_bb1_in_loop_cont/7 
* CE 8 is refined into CE [22] 
* CE 9 is refined into CE [23] 


### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/7 
* CEs [22] --> Loop 22 
* CEs [23] --> Loop 23 

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

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


### Specialization of cost equations eval_start_2/6 
* CE 3 is refined into CE [24,25,26,27,28,29,30,31,32] 
* CE 2 is refined into CE [33] 


### Cost equations --> "Loop" of eval_start_2/6 
* CEs [30,31] --> Loop 24 
* CEs [29] --> Loop 25 
* CEs [28] --> Loop 26 
* CEs [32] --> Loop 27 
* CEs [27] --> Loop 28 
* CEs [33] --> Loop 29 
* CEs [25] --> Loop 30 
* CEs [24,26] --> Loop 31 

### Ranking functions of CR eval_start_2(V__0,V_3,V_x,V_y,V_z_0,B) 

#### Partial ranking functions of CR eval_start_2(V__0,V_3,V_x,V_y,V_z_0,B) 


### Specialization of cost equations eval_start_start/6 
* CE 1 is refined into CE [34,35,36,37,38,39,40,41] 


### Cost equations --> "Loop" of eval_start_start/6 
* CEs [41] --> Loop 32 
* CEs [40] --> Loop 33 
* CEs [39] --> Loop 34 
* CEs [38] --> Loop 35 
* CEs [37] --> Loop 36 
* CEs [36] --> Loop 37 
* CEs [35] --> Loop 38 
* CEs [34] --> Loop 39 

### Ranking functions of CR eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B) 

#### Partial ranking functions of CR eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B) 


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

#### Cost of chains of eval_start_bb3_in(V__0,V_z_0,B,C):
* Chain [[13],15]: 1*it(13)+0
  Such that:it(13) =< V_z_0

  with precondition: [B=2,C=0,V_z_0>=1,V__0>=V_z_0+1] 

* Chain [[13],14]: 1*it(13)+0
  Such that:it(13) =< V_z_0

  with precondition: [B=3,V_z_0>=1,V__0>=V_z_0+1] 

* Chain [15]: 0
  with precondition: [V_z_0=0,B=2,C=0,V__0>=1] 

* Chain [14]: 0
  with precondition: [B=3,V_z_0>=0,V__0>=V_z_0+1] 


#### Cost of chains of eval_start_bb1_in(V__0,V_3,V_y,V_z_0,B,C,D,E):
* Chain [[17],21]: 1*it(17)+0
  Such that:it(17) =< V__0

  with precondition: [V_y=0,B=3,V__0>=1] 

* Chain [[17],20]: 1*it(17)+0
  Such that:it(17) =< V__0

  with precondition: [V_y=0,B=3,V__0>=2] 

* Chain [[17],18]: 1*it(17)+0
  Such that:it(17) =< V__0

  with precondition: [V_y=0,B=4,C=0,D=0,E=0,V__0>=1] 

* Chain [[16],21]: 1*it(16)+1*s(3)+0
  Such that:s(3) =< V__0
it(16) =< V__0/2-V_y/2

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

* Chain [[16],20]: 1*it(16)+1*s(3)+0
  Such that:s(3) =< V__0-V_y
it(16) =< V__0/2-V_y/2

  with precondition: [B=3,V_y>=1,V__0>=2*V_y+2] 

* Chain [[16],19]: 1*it(16)+1*s(3)+1*s(4)+0
  Such that:s(3) =< V__0-V_y
it(16) =< V__0/2-V_y/2
s(4) =< V_y

  with precondition: [B=3,V_y>=1,V__0>=2*V_y+2] 

* Chain [[16],18]: 1*it(16)+1*s(3)+0
  Such that:s(3) =< V__0-D
it(16) =< V__0/2-V_y/2

  with precondition: [B=4,E=0,C=D,V_y>=1,C>=0,V_y>=C,V__0>=V_y+C+1] 

* Chain [21]: 0
  with precondition: [B=3,V_y>=0] 

* Chain [20]: 0
  with precondition: [B=3,V_y>=0,V__0>=V_y+1] 

* Chain [19]: 1*s(4)+0
  Such that:s(4) =< V_y

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

* Chain [18]: 0
  with precondition: [B=4,D=V_3,E=V_z_0,V__0=C,V_y>=0,V_y>=V__0] 


#### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G):
* Chain [23]: 0
  with precondition: [A=3,E>=0] 

* Chain [22]: 0
  with precondition: [A=4,E>=0] 


#### Cost of chains of eval_start_2(V__0,V_3,V_x,V_y,V_z_0,B):
* Chain [31]: 2*s(13)+0
  Such that:aux(3) =< V_x
s(13) =< aux(3)

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

* Chain [30]: 1*s(15)+0
  Such that:s(15) =< V_x

  with precondition: [V_y=0,V_x>=2] 

* Chain [29]: 0
  with precondition: [0>=V_y+1] 

* Chain [28]: 0
  with precondition: [V_y>=0] 

* Chain [27]: 0
  with precondition: [V_y>=0,V_y>=V_x] 

* Chain [26]: 0
  with precondition: [V_y>=0,V_x>=V_y+1] 

* Chain [25]: 1*s(16)+2*s(19)+2*s(20)+0
  Such that:s(17) =< V_x-V_y
s(18) =< V_x/2-V_y/2
s(16) =< V_y
s(19) =< s(17)
s(20) =< s(18)

  with precondition: [V_y>=1,V_x>=2*V_y+2] 

* Chain [24]: 2*s(21)+2*s(22)+1*s(23)+0
  Such that:s(23) =< V_y
aux(4) =< V_x
aux(5) =< V_x/2-V_y/2
s(21) =< aux(4)
s(22) =< aux(5)

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


#### Cost of chains of eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B):
* Chain [39]: 2*s(27)+0
  Such that:s(26) =< V_x
s(27) =< s(26)

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

* Chain [38]: 1*s(28)+0
  Such that:s(28) =< V_x

  with precondition: [V_y=0,V_x>=2] 

* Chain [37]: 0
  with precondition: [0>=V_y+1] 

* Chain [36]: 0
  with precondition: [V_y>=0] 

* Chain [35]: 0
  with precondition: [V_y>=0,V_y>=V_x] 

* Chain [34]: 0
  with precondition: [V_y>=0,V_x>=V_y+1] 

* Chain [33]: 1*s(31)+2*s(32)+2*s(33)+0
  Such that:s(29) =< V_x-V_y
s(30) =< V_x/2-V_y/2
s(31) =< V_y
s(32) =< s(29)
s(33) =< s(30)

  with precondition: [V_y>=1,V_x>=2*V_y+2] 

* Chain [32]: 1*s(34)+2*s(37)+2*s(38)+0
  Such that:s(35) =< V_x
s(36) =< V_x/2-V_y/2
s(34) =< V_y
s(37) =< s(35)
s(38) =< s(36)

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


Closed-form bounds of eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B): 
-------------------------------------
* Chain [39] with precondition: [V_y=0,V_x>=1] 
    - Upper bound: 2*V_x 
    - Complexity: n 
* Chain [38] with precondition: [V_y=0,V_x>=2] 
    - Upper bound: V_x 
    - Complexity: n 
* Chain [37] with precondition: [0>=V_y+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [36] with precondition: [V_y>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [V_y>=0,V_y>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [V_y>=0,V_x>=V_y+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [V_y>=1,V_x>=2*V_y+2] 
    - Upper bound: 3*V_x-2*V_y 
    - Complexity: n 
* Chain [32] with precondition: [V_y>=1,V_x>=V_y+1] 
    - Upper bound: 3*V_x 
    - Complexity: n 

### Maximum cost of eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B): max([nat(V_x-V_y)*2+nat(V_y)+nat(V_x/2-V_y/2)*2,nat(V_x/2-V_y/2)*2+nat(V_y)+nat(V_x)+nat(V_x)]) 
Asymptotic class: n 
* Total analysis performed in 338 ms.