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


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_render_ht_LeafBlock_in/4,eval_render_ht_NewDefault_in/4,eval_render_ht_bb1_in/3,eval_render_ht_bb3_in/4]
1. non_recursive  : [eval_render_ht_stop/1]
2. non_recursive  : [eval_render_ht_bb2_in/1]
3. non_recursive  : [eval_render_ht_bb1_in_loop_cont/2]
4. non_recursive  : [eval_render_ht_bb0_in/3]
5. non_recursive  : [eval_render_ht_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_render_ht_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_render_ht_bb0_in/3
5. SCC is partially evaluated into eval_render_ht_start/3

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

### Specialization of cost equations eval_render_ht_bb1_in/3 
* CE 4 is refined into CE [5] 
* CE 3 is refined into CE [6] 


### Cost equations --> "Loop" of eval_render_ht_bb1_in/3 
* CEs [6] --> Loop 5 
* CEs [5] --> Loop 6 

### Ranking functions of CR eval_render_ht_bb1_in(V_level,V__0,B) 
* RF of phase [6]: [V_level-V__0-7]

#### Partial ranking functions of CR eval_render_ht_bb1_in(V_level,V__0,B) 
* Partial RF of phase [6]:
  - RF of loop [6:1]:
    V_level-V__0-7


### Specialization of cost equations eval_render_ht_bb0_in/3 
* CE 2 is refined into CE [7,8] 


### Cost equations --> "Loop" of eval_render_ht_bb0_in/3 
* CEs [8] --> Loop 7 
* CEs [7] --> Loop 8 

### Ranking functions of CR eval_render_ht_bb0_in(V_level,V_old_level,B) 

#### Partial ranking functions of CR eval_render_ht_bb0_in(V_level,V_old_level,B) 


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


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

### Ranking functions of CR eval_render_ht_start(V_level,V_old_level,B) 

#### Partial ranking functions of CR eval_render_ht_start(V_level,V_old_level,B) 


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

#### Cost of chains of eval_render_ht_bb1_in(V_level,V__0,B):
* Chain [[6],5]: 1*it(6)+0
  Such that:it(6) =< V_level-V__0

  with precondition: [B=2,V_level>=V__0+8] 

* Chain [5]: 0
  with precondition: [B=2,V__0+7>=V_level] 


#### Cost of chains of eval_render_ht_bb0_in(V_level,V_old_level,B):
* Chain [8]: 0
  with precondition: [V_old_level+7>=V_level] 

* Chain [7]: 1*s(1)+0
  Such that:s(1) =< V_level-V_old_level

  with precondition: [V_level>=V_old_level+8] 


#### Cost of chains of eval_render_ht_start(V_level,V_old_level,B):
* Chain [10]: 0
  with precondition: [V_old_level+7>=V_level] 

* Chain [9]: 1*s(2)+0
  Such that:s(2) =< V_level-V_old_level

  with precondition: [V_level>=V_old_level+8] 


Closed-form bounds of eval_render_ht_start(V_level,V_old_level,B): 
-------------------------------------
* Chain [10] with precondition: [V_old_level+7>=V_level] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [9] with precondition: [V_level>=V_old_level+8] 
    - Upper bound: V_level-V_old_level 
    - Complexity: n 

### Maximum cost of eval_render_ht_start(V_level,V_old_level,B): nat(V_level-V_old_level) 
Asymptotic class: n 
* Total analysis performed in 47 ms.