/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_foo_bb2_in/4,eval_foo_bb3_in/4]
1. recursive  : [eval_foo_bb1_in/2,eval_foo_bb2_in_loop_cont/4,eval_foo_bb4_in/3]
2. non_recursive  : [eval_foo_stop/1]
3. non_recursive  : [eval_foo_bb5_in/1]
4. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
5. non_recursive  : [eval_foo_bb0_in/2]
6. non_recursive  : [eval_foo_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb2_in/4
1. SCC is partially evaluated into eval_foo_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_foo_bb0_in/2
6. SCC is partially evaluated into eval_foo_start/3

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

### Specialization of cost equations eval_foo_bb2_in/4 
* CE 7 is refined into CE [8] 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 


### Cost equations --> "Loop" of eval_foo_bb2_in/4 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_foo_bb2_in(V__0,V__01,B,C) 
* RF of phase [8]: [-V__01+10]

#### Partial ranking functions of CR eval_foo_bb2_in(V__0,V__01,B,C) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    -V__01+10


### Specialization of cost equations eval_foo_bb1_in/2 
* CE 4 is refined into CE [11] 
* CE 3 is refined into CE [12,13] 


### Cost equations --> "Loop" of eval_foo_bb1_in/2 
* CEs [12] --> Loop 11 
* CEs [13] --> Loop 12 
* CEs [11] --> Loop 13 

### Ranking functions of CR eval_foo_bb1_in(V__0,B) 
* RF of phase [11]: [-V__0+3]
* RF of phase [12]: [-V__0+5]

#### Partial ranking functions of CR eval_foo_bb1_in(V__0,B) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    -V__0+3
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    -V__0+5


### Specialization of cost equations eval_foo_bb0_in/2 
* CE 2 is refined into CE [14,15,16] 


### Cost equations --> "Loop" of eval_foo_bb0_in/2 
* CEs [16] --> Loop 14 
* CEs [15] --> Loop 15 
* CEs [14] --> Loop 16 

### 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/3 
* CE 1 is refined into CE [17,18,19] 


### Cost equations --> "Loop" of eval_foo_start/3 
* CEs [19] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [17] --> Loop 19 

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

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


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

#### Cost of chains of eval_foo_bb2_in(V__0,V__01,B,C):
* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< -V__01+10

  with precondition: [B=2,C=10,4>=V__0,9>=V__01,V__0>=3,V__01>=0] 

* Chain [10]: 0
  with precondition: [V__01=0,B=2,C=0,2>=V__0] 


#### Cost of chains of eval_foo_bb1_in(V__0,B):
* Chain [[12],13]: 1*it(12)+1*s(3)+0
  Such that:aux(4) =< -V__0+5
it(12) =< aux(4)
s(3) =< aux(4)*10

  with precondition: [B=3,4>=V__0,V__0>=3] 

* Chain [[11],[12],13]: 1*it(11)+1*it(12)+1*s(3)+0
  Such that:aux(4) =< 2
it(11) =< -V__0+3
it(12) =< aux(4)
s(3) =< aux(4)*10

  with precondition: [B=3,2>=V__0] 

* Chain [13]: 0
  with precondition: [B=3,V__0>=5] 


#### Cost of chains of eval_foo_bb0_in(V_i,B):
* Chain [16]: 1*s(5)+1*s(6)+0
  Such that:s(4) =< -V_i+5
s(5) =< s(4)
s(6) =< s(4)*10

  with precondition: [4>=V_i,V_i>=3] 

* Chain [15]: 1*s(8)+1*s(9)+1*s(10)+0
  Such that:s(7) =< 2
s(8) =< -V_i+3
s(9) =< s(7)
s(10) =< s(7)*10

  with precondition: [2>=V_i] 

* Chain [14]: 0
  with precondition: [V_i>=5] 


#### Cost of chains of eval_foo_start(V_i,V_j,B):
* Chain [19]: 1*s(12)+1*s(13)+0
  Such that:s(11) =< -V_i+5
s(12) =< s(11)
s(13) =< s(11)*10

  with precondition: [4>=V_i,V_i>=3] 

* Chain [18]: 1*s(15)+1*s(16)+1*s(17)+0
  Such that:s(14) =< 2
s(15) =< -V_i+3
s(16) =< s(14)
s(17) =< s(14)*10

  with precondition: [2>=V_i] 

* Chain [17]: 0
  with precondition: [V_i>=5] 


Closed-form bounds of eval_foo_start(V_i,V_j,B): 
-------------------------------------
* Chain [19] with precondition: [4>=V_i,V_i>=3] 
    - Upper bound: -11*V_i+55 
    - Complexity: n 
* Chain [18] with precondition: [2>=V_i] 
    - Upper bound: -V_i+25 
    - Complexity: n 
* Chain [17] with precondition: [V_i>=5] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_foo_start(V_i,V_j,B): max([nat(-V_i+5)*11,nat(-V_i+3)+22]) 
Asymptotic class: n 
* Total analysis performed in 101 ms.