/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_foo_bb1_in/4,eval_foo_bb2_in/4]
1. non_recursive  : [eval_foo_stop/1]
2. non_recursive  : [eval_foo_bb3_in/1]
3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
4. non_recursive  : [eval_foo_bb0_in/4]
5. non_recursive  : [eval_foo_start/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb1_in/4
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into eval_foo_bb0_in/4
5. SCC is partially evaluated into eval_foo_start/5

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

### Specialization of cost equations eval_foo_bb1_in/4 
* CE 4 is refined into CE [5] 
* CE 3 is refined into CE [6] 


### Cost equations --> "Loop" of eval_foo_bb1_in/4 
* CEs [6] --> Loop 5 
* CEs [5] --> Loop 6 

### Ranking functions of CR eval_foo_bb1_in(V_x,V__02,V__01,B) 
* RF of phase [5]: [V_x/2-V__02/2-V__01/2]

#### Partial ranking functions of CR eval_foo_bb1_in(V_x,V__02,V__01,B) 
* Partial RF of phase [5]:
  - RF of loop [5:1]:
    V_x/2-V__02/2-V__01/2


### Specialization of cost equations eval_foo_bb0_in/4 
* CE 2 is refined into CE [7,8] 


### Cost equations --> "Loop" of eval_foo_bb0_in/4 
* CEs [8] --> Loop 7 
* CEs [7] --> Loop 8 

### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 

#### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 


### Specialization of cost equations eval_foo_start/5 
* CE 1 is refined into CE [9,10] 


### Cost equations --> "Loop" of eval_foo_start/5 
* CEs [10] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_foo_start(V_c,V_x,V_y,V_z,B) 

#### Partial ranking functions of CR eval_foo_start(V_c,V_x,V_y,V_z,B) 


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

#### Cost of chains of eval_foo_bb1_in(V_x,V__02,V__01,B):
* Chain [[5],6]: 1*it(5)+0
  Such that:it(5) =< V_x/2-V__02/2-V__01/2

  with precondition: [B=2,V_x>=V__01+V__02+1] 

* Chain [6]: 0
  with precondition: [B=2,V__01+V__02>=V_x] 


#### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_z,B):
* Chain [8]: 0
  with precondition: [V_y+V_z>=V_x] 

* Chain [7]: 1*s(1)+0
  Such that:s(1) =< V_x/2-V_y/2-V_z/2

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


#### Cost of chains of eval_foo_start(V_c,V_x,V_y,V_z,B):
* Chain [10]: 0
  with precondition: [V_y+V_z>=V_x] 

* Chain [9]: 1*s(2)+0
  Such that:s(2) =< V_x/2-V_y/2-V_z/2

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


Closed-form bounds of eval_foo_start(V_c,V_x,V_y,V_z,B): 
-------------------------------------
* Chain [10] with precondition: [V_y+V_z>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [9] with precondition: [V_x>=V_y+V_z+1] 
    - Upper bound: V_x/2-V_y/2-V_z/2 
    - Complexity: n 

### Maximum cost of eval_foo_start(V_c,V_x,V_y,V_z,B): nat(V_x/2-V_y/2-V_z/2) 
Asymptotic class: n 
* Total analysis performed in 50 ms.