/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_Loopus2011_ex3_bb1_in/3,eval_Loopus2011_ex3_bb2_in/3]
1. non_recursive  : [eval_Loopus2011_ex3_stop/1]
2. non_recursive  : [eval_Loopus2011_ex3_bb3_in/1]
3. non_recursive  : [eval_Loopus2011_ex3_bb1_in_loop_cont/2]
4. non_recursive  : [eval_Loopus2011_ex3_bb0_in/3]
5. non_recursive  : [eval_Loopus2011_ex3_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_Loopus2011_ex3_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_Loopus2011_ex3_bb0_in/3
5. SCC is partially evaluated into eval_Loopus2011_ex3_start/3

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

### Specialization of cost equations eval_Loopus2011_ex3_bb1_in/3 
* CE 7 is refined into CE [8] 
* CE 6 is refined into CE [9] 
* CE 4 is refined into CE [10] 
* CE 5 is refined into CE [11] 
* CE 3 is refined into CE [12] 


### Cost equations --> "Loop" of eval_Loopus2011_ex3_bb1_in/3 
* CEs [10] --> Loop 8 
* CEs [11] --> Loop 9 
* CEs [12] --> Loop 10 
* CEs [8] --> Loop 11 
* CEs [9] --> Loop 12 

### Ranking functions of CR eval_Loopus2011_ex3_bb1_in(V_b,V__0,B) 
* RF of phase [8]: [-V__0+255]
* RF of phase [9]: [-V__0+255]
* RF of phase [10]: [V__0]

#### Partial ranking functions of CR eval_Loopus2011_ex3_bb1_in(V_b,V__0,B) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    -V__0+255
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    -V__0+255
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    V__0


### Specialization of cost equations eval_Loopus2011_ex3_bb0_in/3 
* CE 2 is refined into CE [13,14,15,16,17] 


### Cost equations --> "Loop" of eval_Loopus2011_ex3_bb0_in/3 
* CEs [17] --> Loop 13 
* CEs [16] --> Loop 14 
* CEs [15] --> Loop 15 
* CEs [14] --> Loop 16 
* CEs [13] --> Loop 17 

### Ranking functions of CR eval_Loopus2011_ex3_bb0_in(V_x,V_b,B) 

#### Partial ranking functions of CR eval_Loopus2011_ex3_bb0_in(V_x,V_b,B) 


### Specialization of cost equations eval_Loopus2011_ex3_start/3 
* CE 1 is refined into CE [18,19,20,21,22] 


### Cost equations --> "Loop" of eval_Loopus2011_ex3_start/3 
* CEs [22] --> Loop 18 
* CEs [21] --> Loop 19 
* CEs [20] --> Loop 20 
* CEs [19] --> Loop 21 
* CEs [18] --> Loop 22 

### Ranking functions of CR eval_Loopus2011_ex3_start(V_x,V_b,B) 

#### Partial ranking functions of CR eval_Loopus2011_ex3_start(V_x,V_b,B) 


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

#### Cost of chains of eval_Loopus2011_ex3_bb1_in(V_b,V__0,B):
* Chain [[10],12]: 1*it(10)+0
  Such that:it(10) =< V__0

  with precondition: [V_b=0,B=2,254>=V__0,V__0>=1] 

* Chain [[9],11]: 1*it(9)+0
  Such that:it(9) =< -V__0+255

  with precondition: [B=2,0>=V_b+1,254>=V__0,V__0>=1] 

* Chain [[8],11]: 1*it(8)+0
  Such that:it(8) =< -V__0+255

  with precondition: [B=2,254>=V__0,V_b>=1,V__0>=1] 

* Chain [12]: 0
  with precondition: [B=2,0>=V__0] 

* Chain [11]: 0
  with precondition: [B=2,V__0>=255] 


#### Cost of chains of eval_Loopus2011_ex3_bb0_in(V_x,V_b,B):
* Chain [17]: 1*s(1)+0
  Such that:s(1) =< V_x

  with precondition: [V_b=0,254>=V_x,V_x>=1] 

* Chain [16]: 1*s(2)+0
  Such that:s(2) =< -V_x+255

  with precondition: [254>=V_x,0>=V_b+1,V_x>=1] 

* Chain [15]: 1*s(3)+0
  Such that:s(3) =< -V_x+255

  with precondition: [254>=V_x,V_x>=1,V_b>=1] 

* Chain [14]: 0
  with precondition: [0>=V_x] 

* Chain [13]: 0
  with precondition: [V_x>=255] 


#### Cost of chains of eval_Loopus2011_ex3_start(V_x,V_b,B):
* Chain [22]: 1*s(4)+0
  Such that:s(4) =< V_x

  with precondition: [V_b=0,254>=V_x,V_x>=1] 

* Chain [21]: 1*s(5)+0
  Such that:s(5) =< -V_x+255

  with precondition: [254>=V_x,0>=V_b+1,V_x>=1] 

* Chain [20]: 1*s(6)+0
  Such that:s(6) =< -V_x+255

  with precondition: [254>=V_x,V_x>=1,V_b>=1] 

* Chain [19]: 0
  with precondition: [0>=V_x] 

* Chain [18]: 0
  with precondition: [V_x>=255] 


Closed-form bounds of eval_Loopus2011_ex3_start(V_x,V_b,B): 
-------------------------------------
* Chain [22] with precondition: [V_b=0,254>=V_x,V_x>=1] 
    - Upper bound: V_x 
    - Complexity: n 
* Chain [21] with precondition: [254>=V_x,0>=V_b+1,V_x>=1] 
    - Upper bound: -V_x+255 
    - Complexity: n 
* Chain [20] with precondition: [254>=V_x,V_x>=1,V_b>=1] 
    - Upper bound: -V_x+255 
    - Complexity: n 
* Chain [19] with precondition: [0>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [18] with precondition: [V_x>=255] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_Loopus2011_ex3_start(V_x,V_b,B): max([nat(V_x),nat(-V_x+255)]) 
Asymptotic class: n 
* Total analysis performed in 110 ms.