/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_0/2,eval_foo_1/3,eval_foo_bb1_in/2,eval_foo_bb2_in/2]
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/2]
5. non_recursive  : [eval_foo_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb1_in/2
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/2
5. SCC is partially evaluated into eval_foo_start/2

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

### Specialization of cost equations eval_foo_bb1_in/2 
* CE 5 is refined into CE [6] 
* CE 4 is refined into CE [7] 
* CE 3 is refined into CE [8] 


### Cost equations --> "Loop" of eval_foo_bb1_in/2 
* CEs [7] --> Loop 6 
* CEs [8] --> Loop 7 
* CEs [6] --> Loop 8 

### Ranking functions of CR eval_foo_bb1_in(V__0,B) 
* RF of phase [6,7]: [-V__0+255]

#### Partial ranking functions of CR eval_foo_bb1_in(V__0,B) 
* Partial RF of phase [6,7]:
  - RF of loop [6:1,7:1]:
    -V__0+255


### Specialization of cost equations eval_foo_bb0_in/2 
* CE 2 is refined into CE [9,10] 


### Cost equations --> "Loop" of eval_foo_bb0_in/2 
* CEs [10] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_foo_bb0_in(V_i,B) 

#### Partial ranking functions of CR eval_foo_bb0_in(V_i,B) 


### Specialization of cost equations eval_foo_start/2 
* CE 1 is refined into CE [11,12] 


### Cost equations --> "Loop" of eval_foo_start/2 
* CEs [12] --> Loop 11 
* CEs [11] --> Loop 12 

### Ranking functions of CR eval_foo_start(V_i,B) 

#### Partial ranking functions of CR eval_foo_start(V_i,B) 


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

#### Cost of chains of eval_foo_bb1_in(V__0,B):
* Chain [[6,7],8]: 2*it(6)+0
  Such that:aux(1) =< -V__0+255
aux(2) =< -V__0+256
it(6) =< aux(1)
it(6) =< aux(2)

  with precondition: [B=2,254>=V__0] 

* Chain [8]: 0
  with precondition: [B=2,V__0>=255] 


#### Cost of chains of eval_foo_bb0_in(V_i,B):
* Chain [10]: 2*s(3)+0
  Such that:s(1) =< -V_i+255
s(2) =< -V_i+256
s(3) =< s(1)
s(3) =< s(2)

  with precondition: [254>=V_i] 

* Chain [9]: 0
  with precondition: [V_i>=255] 


#### Cost of chains of eval_foo_start(V_i,B):
* Chain [12]: 2*s(6)+0
  Such that:s(4) =< -V_i+255
s(5) =< -V_i+256
s(6) =< s(4)
s(6) =< s(5)

  with precondition: [254>=V_i] 

* Chain [11]: 0
  with precondition: [V_i>=255] 


Closed-form bounds of eval_foo_start(V_i,B): 
-------------------------------------
* Chain [12] with precondition: [254>=V_i] 
    - Upper bound: -2*V_i+510 
    - Complexity: n 
* Chain [11] with precondition: [V_i>=255] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_foo_start(V_i,B): nat(-V_i+255)*2 
Asymptotic class: n 
* Total analysis performed in 48 ms.