/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_textbook_ex1_bb1_in/3,eval_textbook_ex1_bb2_in/3]
1. non_recursive  : [eval_textbook_ex1_stop/1]
2. non_recursive  : [eval_textbook_ex1_bb3_in/1]
3. non_recursive  : [eval_textbook_ex1_bb1_in_loop_cont/2]
4. non_recursive  : [eval_textbook_ex1_bb0_in/3]
5. non_recursive  : [eval_textbook_ex1_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_textbook_ex1_bb1_in/3
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_textbook_ex1_bb0_in/3
5. SCC is partially evaluated into eval_textbook_ex1_start/3

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

### Specialization of cost equations eval_textbook_ex1_bb1_in/3 
* CE 4 is refined into CE [5] 
* CE 3 is refined into CE [6] 


### Cost equations --> "Loop" of eval_textbook_ex1_bb1_in/3 
* CEs [6] --> Loop 5 
* CEs [5] --> Loop 6 

### Ranking functions of CR eval_textbook_ex1_bb1_in(V_b,V_i_0,B) 
* RF of phase [5]: [V_b-V_i_0+1]

#### Partial ranking functions of CR eval_textbook_ex1_bb1_in(V_b,V_i_0,B) 
* Partial RF of phase [5]:
  - RF of loop [5:1]:
    V_b-V_i_0+1


### Specialization of cost equations eval_textbook_ex1_bb0_in/3 
* CE 2 is refined into CE [7,8] 


### Cost equations --> "Loop" of eval_textbook_ex1_bb0_in/3 
* CEs [7] --> Loop 7 
* CEs [8] --> Loop 8 

### Ranking functions of CR eval_textbook_ex1_bb0_in(V_a,V_b,B) 

#### Partial ranking functions of CR eval_textbook_ex1_bb0_in(V_a,V_b,B) 


### Specialization of cost equations eval_textbook_ex1_start/3 
* CE 1 is refined into CE [9,10] 


### Cost equations --> "Loop" of eval_textbook_ex1_start/3 
* CEs [10] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_textbook_ex1_start(V_a,V_b,B) 

#### Partial ranking functions of CR eval_textbook_ex1_start(V_a,V_b,B) 


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

#### Cost of chains of eval_textbook_ex1_bb1_in(V_b,V_i_0,B):
* Chain [[5],6]: 1*it(5)+0
  Such that:it(5) =< V_b-V_i_0+1

  with precondition: [B=2,V_b>=V_i_0] 

* Chain [6]: 0
  with precondition: [B=2,V_i_0>=V_b+1] 


#### Cost of chains of eval_textbook_ex1_bb0_in(V_a,V_b,B):
* Chain [8]: 1*s(1)+0
  Such that:s(1) =< -V_a+V_b+1

  with precondition: [V_b>=V_a] 

* Chain [7]: 0
  with precondition: [V_a>=V_b+1] 


#### Cost of chains of eval_textbook_ex1_start(V_a,V_b,B):
* Chain [10]: 1*s(2)+0
  Such that:s(2) =< -V_a+V_b+1

  with precondition: [V_b>=V_a] 

* Chain [9]: 0
  with precondition: [V_a>=V_b+1] 


Closed-form bounds of eval_textbook_ex1_start(V_a,V_b,B): 
-------------------------------------
* Chain [10] with precondition: [V_b>=V_a] 
    - Upper bound: -V_a+V_b+1 
    - Complexity: n 
* Chain [9] with precondition: [V_a>=V_b+1] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_textbook_ex1_start(V_a,V_b,B): nat(-V_a+V_b+1) 
Asymptotic class: n 
* Total analysis performed in 40 ms.