/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_cryptRandWriteFile_bb3_in/4,eval_cryptRandWriteFile_bb4_in/4]
1. recursive  : [eval_cryptRandWriteFile_bb1_in/2,eval_cryptRandWriteFile_bb2_in/2,eval_cryptRandWriteFile_bb3_in_loop_cont/5,eval_cryptRandWriteFile_bb5_in/4]
2. non_recursive  : [eval_cryptRandWriteFile_stop/1]
3. non_recursive  : [eval_cryptRandWriteFile_bb6_in/1]
4. non_recursive  : [eval_cryptRandWriteFile_bb1_in_loop_cont/2]
5. non_recursive  : [eval_cryptRandWriteFile_bb0_in/2]
6. non_recursive  : [eval_cryptRandWriteFile_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_cryptRandWriteFile_bb3_in/4
1. SCC is partially evaluated into eval_cryptRandWriteFile_bb1_in/2
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval_cryptRandWriteFile_bb0_in/2
6. SCC is partially evaluated into eval_cryptRandWriteFile_start/2

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

### Specialization of cost equations eval_cryptRandWriteFile_bb3_in/4 
* CE 7 is refined into CE [8] 
* CE 6 is refined into CE [9] 


### Cost equations --> "Loop" of eval_cryptRandWriteFile_bb3_in/4 
* CEs [9] --> Loop 8 
* CEs [8] --> Loop 9 

### Ranking functions of CR eval_cryptRandWriteFile_bb3_in(V__0_,V_i_0,B,C) 
* RF of phase [8]: [V__0_-V_i_0,-V_i_0+256]

#### Partial ranking functions of CR eval_cryptRandWriteFile_bb3_in(V__0_,V_i_0,B,C) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    V__0_-V_i_0
    -V_i_0+256


### Specialization of cost equations eval_cryptRandWriteFile_bb1_in/2 
* CE 5 is refined into CE [10] 
* CE 4 is refined into CE [11] 
* CE 3 is refined into CE [12] 


### Cost equations --> "Loop" of eval_cryptRandWriteFile_bb1_in/2 
* CEs [11] --> Loop 10 
* CEs [12] --> Loop 11 
* CEs [10] --> Loop 12 

### Ranking functions of CR eval_cryptRandWriteFile_bb1_in(V__0,B) 
* RF of phase [10]: [V__0-255]

#### Partial ranking functions of CR eval_cryptRandWriteFile_bb1_in(V__0,B) 
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    V__0-255


### Specialization of cost equations eval_cryptRandWriteFile_bb0_in/2 
* CE 2 is refined into CE [13,14,15,16] 


### Cost equations --> "Loop" of eval_cryptRandWriteFile_bb0_in/2 
* CEs [16] --> Loop 13 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [13] --> Loop 16 

### Ranking functions of CR eval_cryptRandWriteFile_bb0_in(V_bytes,B) 

#### Partial ranking functions of CR eval_cryptRandWriteFile_bb0_in(V_bytes,B) 


### Specialization of cost equations eval_cryptRandWriteFile_start/2 
* CE 1 is refined into CE [17,18,19,20] 


### Cost equations --> "Loop" of eval_cryptRandWriteFile_start/2 
* CEs [20] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [18] --> Loop 19 
* CEs [17] --> Loop 20 

### Ranking functions of CR eval_cryptRandWriteFile_start(V_bytes,B) 

#### Partial ranking functions of CR eval_cryptRandWriteFile_start(V_bytes,B) 


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

#### Cost of chains of eval_cryptRandWriteFile_bb3_in(V__0_,V_i_0,B,C):
* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< -V_i_0+C

  with precondition: [B=2,V__0_=C,256>=V__0_,V_i_0>=0,V__0_>=V_i_0+1] 


#### Cost of chains of eval_cryptRandWriteFile_bb1_in(V__0,B):
* Chain [[10],12]: 1*it(10)+1*s(3)+0
  Such that:aux(4) =< V__0
it(10) =< aux(4)
s(3) =< aux(4)*256

  with precondition: [B=3,V__0>=256] 

* Chain [[10],11,12]: 1*it(10)+1*s(3)+1*s(4)+1
  Such that:s(4) =< 255
aux(5) =< V__0
s(4) =< aux(5)
it(10) =< aux(5)
s(3) =< aux(5)*256

  with precondition: [B=3,V__0>=257] 

* Chain [12]: 0
  with precondition: [B=3,0>=V__0] 

* Chain [11,12]: 1*s(4)+1
  Such that:s(4) =< V__0

  with precondition: [B=3,255>=V__0,V__0>=1] 


#### Cost of chains of eval_cryptRandWriteFile_bb0_in(V_bytes,B):
* Chain [16]: 1*s(5)+1
  Such that:s(5) =< V_bytes

  with precondition: [255>=V_bytes,V_bytes>=1] 

* Chain [15]: 0
  with precondition: [0>=V_bytes] 

* Chain [14]: 1*s(7)+1*s(8)+0
  Such that:s(6) =< V_bytes
s(7) =< s(6)
s(8) =< s(6)*256

  with precondition: [V_bytes>=256] 

* Chain [13]: 1*s(9)+1*s(11)+1*s(12)+1
  Such that:s(9) =< 255
s(10) =< V_bytes
s(9) =< s(10)
s(11) =< s(10)
s(12) =< s(10)*256

  with precondition: [V_bytes>=257] 


#### Cost of chains of eval_cryptRandWriteFile_start(V_bytes,B):
* Chain [20]: 1*s(13)+1
  Such that:s(13) =< V_bytes

  with precondition: [255>=V_bytes,V_bytes>=1] 

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

* Chain [18]: 1*s(15)+1*s(16)+0
  Such that:s(14) =< V_bytes
s(15) =< s(14)
s(16) =< s(14)*256

  with precondition: [V_bytes>=256] 

* Chain [17]: 1*s(17)+1*s(19)+1*s(20)+1
  Such that:s(17) =< 255
s(18) =< V_bytes
s(17) =< s(18)
s(19) =< s(18)
s(20) =< s(18)*256

  with precondition: [V_bytes>=257] 


Closed-form bounds of eval_cryptRandWriteFile_start(V_bytes,B): 
-------------------------------------
* Chain [20] with precondition: [255>=V_bytes,V_bytes>=1] 
    - Upper bound: V_bytes+1 
    - Complexity: n 
* Chain [19] with precondition: [0>=V_bytes] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [18] with precondition: [V_bytes>=256] 
    - Upper bound: 257*V_bytes 
    - Complexity: n 
* Chain [17] with precondition: [V_bytes>=257] 
    - Upper bound: 257*V_bytes+256 
    - Complexity: n 

### Maximum cost of eval_cryptRandWriteFile_start(V_bytes,B): nat(V_bytes)*256+255+(nat(V_bytes)+1) 
Asymptotic class: n 
* Total analysis performed in 112 ms.