/export/starexec/sandbox/solver/bin/starexec_run_C /export/starexec/sandbox/benchmark/theBenchmark.c /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_t07_bb1_in/4,eval_t07_bb2_in/4]
1. recursive  : [eval_t07_bb3_in/3,eval_t07_bb4_in/3]
2. recursive  : [eval_t07_bb5_in/2,eval_t07_bb6_in/2]
3. non_recursive  : [eval_t07_stop/1]
4. non_recursive  : [eval_t07_bb7_in/1]
5. non_recursive  : [eval_t07_bb5_in_loop_cont/2]
6. non_recursive  : [eval_t07_bb3_in_loop_cont/3]
7. non_recursive  : [eval_t07_bb1_in_loop_cont/3]
8. non_recursive  : [eval_t07_bb0_in/3]
9. non_recursive  : [eval_t07_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_t07_bb1_in/4
1. SCC is partially evaluated into eval_t07_bb3_in/3
2. SCC is partially evaluated into eval_t07_bb5_in/2
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_t07_bb3_in_loop_cont/3
7. SCC is partially evaluated into eval_t07_bb1_in_loop_cont/3
8. SCC is partially evaluated into eval_t07_bb0_in/3
9. SCC is partially evaluated into eval_t07_start/3

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

### Specialization of cost equations eval_t07_bb1_in/4 
* CE 4 is refined into CE [11] 
* CE 3 is refined into CE [12] 


### Cost equations --> "Loop" of eval_t07_bb1_in/4 
* CEs [12] --> Loop 11 
* CEs [11] --> Loop 12 

### Ranking functions of CR eval_t07_bb1_in(V__01,V__0,B,C) 
* RF of phase [11]: [V__0]

#### Partial ranking functions of CR eval_t07_bb1_in(V__01,V__0,B,C) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    V__0


### Specialization of cost equations eval_t07_bb3_in/3 
* CE 7 is refined into CE [13] 
* CE 6 is refined into CE [14] 


### Cost equations --> "Loop" of eval_t07_bb3_in/3 
* CEs [14] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR eval_t07_bb3_in(V__1,B,C) 
* RF of phase [13]: [V__1]

#### Partial ranking functions of CR eval_t07_bb3_in(V__1,B,C) 
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    V__1


### Specialization of cost equations eval_t07_bb5_in/2 
* CE 10 is refined into CE [15] 
* CE 9 is refined into CE [16] 


### Cost equations --> "Loop" of eval_t07_bb5_in/2 
* CEs [16] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR eval_t07_bb5_in(V__2,B) 
* RF of phase [15]: [V__2]

#### Partial ranking functions of CR eval_t07_bb5_in(V__2,B) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    V__2


### Specialization of cost equations eval_t07_bb3_in_loop_cont/3 
* CE 8 is refined into CE [17,18] 


### Cost equations --> "Loop" of eval_t07_bb3_in_loop_cont/3 
* CEs [18] --> Loop 17 
* CEs [17] --> Loop 18 

### Ranking functions of CR eval_t07_bb3_in_loop_cont(A,B,C) 

#### Partial ranking functions of CR eval_t07_bb3_in_loop_cont(A,B,C) 


### Specialization of cost equations eval_t07_bb1_in_loop_cont/3 
* CE 5 is refined into CE [19,20] 


### Cost equations --> "Loop" of eval_t07_bb1_in_loop_cont/3 
* CEs [19] --> Loop 19 
* CEs [20] --> Loop 20 

### Ranking functions of CR eval_t07_bb1_in_loop_cont(A,B,C) 

#### Partial ranking functions of CR eval_t07_bb1_in_loop_cont(A,B,C) 


### Specialization of cost equations eval_t07_bb0_in/3 
* CE 2 is refined into CE [21,22,23,24] 


### Cost equations --> "Loop" of eval_t07_bb0_in/3 
* CEs [24] --> Loop 21 
* CEs [23] --> Loop 22 
* CEs [22] --> Loop 23 
* CEs [21] --> Loop 24 

### Ranking functions of CR eval_t07_bb0_in(V_x,V_y,B) 

#### Partial ranking functions of CR eval_t07_bb0_in(V_x,V_y,B) 


### Specialization of cost equations eval_t07_start/3 
* CE 1 is refined into CE [25,26,27,28] 


### Cost equations --> "Loop" of eval_t07_start/3 
* CEs [28] --> Loop 25 
* CEs [27] --> Loop 26 
* CEs [26] --> Loop 27 
* CEs [25] --> Loop 28 

### Ranking functions of CR eval_t07_start(V_x,V_y,B) 

#### Partial ranking functions of CR eval_t07_start(V_x,V_y,B) 


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

#### Cost of chains of eval_t07_bb1_in(V__01,V__0,B,C):
* Chain [[11],12]: 1*it(11)+0
  Such that:it(11) =< -V__01/2+C/2

  with precondition: [B=4,V__01+2*V__0=C,V__0>=1] 

* Chain [12]: 0
  with precondition: [B=4,C=V__01,0>=V__0] 


#### Cost of chains of eval_t07_bb3_in(V__1,B,C):
* Chain [[13],14]: 1*it(13)+0
  Such that:it(13) =< V__1

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

* Chain [14]: 0
  with precondition: [B=3,V__1=C,0>=V__1] 


#### Cost of chains of eval_t07_bb5_in(V__2,B):
* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< V__2

  with precondition: [B=2,V__2>=1] 

* Chain [16]: 0
  with precondition: [B=2,0>=V__2] 


#### Cost of chains of eval_t07_bb3_in_loop_cont(A,B,C):
* Chain [18]: 0
  with precondition: [A=3,0>=B] 

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

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


#### Cost of chains of eval_t07_bb1_in_loop_cont(A,B,C):
* Chain [20]: 0
  with precondition: [A=4,0>=B] 

* Chain [19]: 1*s(2)+0
  Such that:s(2) =< B

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


#### Cost of chains of eval_t07_bb0_in(V_x,V_y,B):
* Chain [24]: 0
  with precondition: [0>=V_x,0>=V_y] 

* Chain [23]: 1*s(3)+0
  Such that:s(3) =< V_y

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

* Chain [22]: 1*s(4)+0
  Such that:s(4) =< V_x

  with precondition: [V_x>=1,0>=2*V_x+V_y] 

* Chain [21]: 1*s(5)+1*s(6)+0
  Such that:s(5) =< V_x
s(6) =< 2*V_x+V_y

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


#### Cost of chains of eval_t07_start(V_x,V_y,B):
* Chain [28]: 0
  with precondition: [0>=V_x,0>=V_y] 

* Chain [27]: 1*s(7)+0
  Such that:s(7) =< V_y

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

* Chain [26]: 1*s(8)+0
  Such that:s(8) =< V_x

  with precondition: [V_x>=1,0>=2*V_x+V_y] 

* Chain [25]: 1*s(9)+1*s(10)+0
  Such that:s(9) =< V_x
s(10) =< 2*V_x+V_y

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


Closed-form bounds of eval_t07_start(V_x,V_y,B): 
-------------------------------------
* Chain [28] with precondition: [0>=V_x,0>=V_y] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [27] with precondition: [0>=V_x,V_y>=1] 
    - Upper bound: V_y 
    - Complexity: n 
* Chain [26] with precondition: [V_x>=1,0>=2*V_x+V_y] 
    - Upper bound: V_x 
    - Complexity: n 
* Chain [25] with precondition: [V_x>=1,V_y+2*V_x>=1] 
    - Upper bound: 3*V_x+V_y 
    - Complexity: n 

### Maximum cost of eval_t07_start(V_x,V_y,B): max([nat(V_y),nat(2*V_x+V_y)+nat(V_x)]) 
Asymptotic class: n 
* Total analysis performed in 120 ms.