/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_foo_bb1_in/5,eval_foo_bb2_in/5]
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/5]
5. non_recursive  : [eval_foo_start/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb1_in/5
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/5
5. SCC is partially evaluated into eval_foo_start/5

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

### Specialization of cost equations eval_foo_bb1_in/5 
* CE 8 is refined into CE [9] 
* CE 7 is discarded (unfeasible) 
* CE 6 is refined into CE [10] 


### Cost equations --> "Loop" of eval_foo_bb1_in/5 
* CEs [10] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_foo_bb1_in(V_a,V_b,V__01,V__0,B) 
* RF of phase [9]: [V__01/2+1/2]

#### Partial ranking functions of CR eval_foo_bb1_in(V_a,V_b,V__01,V__0,B) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    V__01/2+1/2


### Specialization of cost equations eval_foo_bb0_in/5 
* CE 3 is refined into CE [11] 
* CE 2 is refined into CE [12] 
* CE 4 is refined into CE [13] 
* CE 5 is refined into CE [14,15] 


### Cost equations --> "Loop" of eval_foo_bb0_in/5 
* CEs [11] --> Loop 11 
* CEs [12] --> Loop 12 
* CEs [13] --> Loop 13 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 

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

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


### Specialization of cost equations eval_foo_start/5 
* CE 1 is refined into CE [16,17,18,19,20] 


### Cost equations --> "Loop" of eval_foo_start/5 
* CEs [20] --> Loop 16 
* CEs [19] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [17] --> Loop 19 
* CEs [16] --> Loop 20 

### Ranking functions of CR eval_foo_start(V_x,V_y,V_a,V_b,B) 

#### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_a,V_b,B) 


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

#### Cost of chains of eval_foo_bb1_in(V_a,V_b,V__01,V__0,B):
* Chain [[9],10]: 1*it(9)+0
  Such that:it(9) =< V__01/2+1/2

  with precondition: [B=2,V_a=V_b+1,0>=V__0+1,V__01>=0] 

* Chain [10]: 0
  with precondition: [B=2,V_b+1=V_a,0>=V__01+1,0>=V__0+1] 


#### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_a,V_b,B):
* Chain [15]: 0
  with precondition: [V_b+1=V_a,0>=V_x+1,0>=V_y+1] 

* Chain [14]: 1*s(1)+0
  Such that:s(1) =< V_y/2+1/2

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

* Chain [13]: 0
  with precondition: [V_x>=0] 

* Chain [12]: 0
  with precondition: [V_b>=V_a] 

* Chain [11]: 0
  with precondition: [V_a>=V_b+2] 


#### Cost of chains of eval_foo_start(V_x,V_y,V_a,V_b,B):
* Chain [20]: 0
  with precondition: [V_b+1=V_a,0>=V_x+1,0>=V_y+1] 

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

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

* Chain [18]: 0
  with precondition: [V_x>=0] 

* Chain [17]: 0
  with precondition: [V_b>=V_a] 

* Chain [16]: 0
  with precondition: [V_a>=V_b+2] 


Closed-form bounds of eval_foo_start(V_x,V_y,V_a,V_b,B): 
-------------------------------------
* Chain [20] with precondition: [V_b+1=V_a,0>=V_x+1,0>=V_y+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [19] with precondition: [V_b+1=V_a,0>=V_x+1,V_y>=0] 
    - Upper bound: V_y/2+1/2 
    - Complexity: n 
* Chain [18] with precondition: [V_x>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [17] with precondition: [V_b>=V_a] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [V_a>=V_b+2] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_foo_start(V_x,V_y,V_a,V_b,B): nat(V_y/2+1/2) 
Asymptotic class: n 
* Total analysis performed in 92 ms.