/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_bb2_in/5,eval_foo_bb3_in/5,eval_foo_bb4_in/5,eval_foo_bb5_in/5]
1. recursive  : [eval_foo_bb1_in/3,eval_foo_bb2_in_loop_cont/6,eval_foo_bb6_in/5]
2. non_recursive  : [eval_foo_stop/1]
3. non_recursive  : [eval_foo_bb7_in/1]
4. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
5. non_recursive  : [eval_foo_bb0_in/3]
6. non_recursive  : [eval_foo_start/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb2_in/5
1. SCC is partially evaluated into eval_foo_bb1_in/3
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/3
6. SCC is partially evaluated into eval_foo_start/5

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

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


### Cost equations --> "Loop" of eval_foo_bb2_in/5 
* CEs [10] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_foo_bb2_in(V__01,V__1,B,C,D) 
* RF of phase [9]: [V__01,V__1]

#### Partial ranking functions of CR eval_foo_bb2_in(V__01,V__1,B,C,D) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    V__01
    V__1


### Specialization of cost equations eval_foo_bb1_in/3 
* CE 4 is refined into CE [11] 
* CE 5 is refined into CE [12] 
* CE 3 is refined into CE [13] 


### Cost equations --> "Loop" of eval_foo_bb1_in/3 
* CEs [13] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR eval_foo_bb1_in(V_y,V__0,B) 
* RF of phase [11]: [V__0,-V_y+V__0+1]

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


### Specialization of cost equations eval_foo_bb0_in/3 
* CE 2 is refined into CE [14,15,16] 


### Cost equations --> "Loop" of eval_foo_bb0_in/3 
* CEs [16] --> Loop 14 
* CEs [15] --> Loop 15 
* CEs [14] --> Loop 16 

### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 

#### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 


### Specialization of cost equations eval_foo_start/5 
* CE 1 is refined into CE [17,18,19] 


### Cost equations --> "Loop" of eval_foo_start/5 
* CEs [19] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [17] --> Loop 19 

### Ranking functions of CR eval_foo_start(V_x,V_y,V_ytmp,V_res,B) 

#### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_ytmp,V_res,B) 


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

#### Cost of chains of eval_foo_bb2_in(V__01,V__1,B,C,D):
* Chain [[9],10]: 1*it(9)+0
  Such that:it(9) =< V__01

  with precondition: [B=2,C=0,V__01+D=V__1,V__01>=1,V__1>=V__01] 


#### Cost of chains of eval_foo_bb1_in(V_y,V__0,B):
* Chain [[11],12]: 1*it(11)+1*s(3)+0
  Such that:it(11) =< -V_y+V__0+1
aux(3) =< V__0
it(11) =< aux(3)
s(3) =< aux(3)

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

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

* Chain [12]: 0
  with precondition: [B=3,V_y>=V__0+1] 


#### Cost of chains of eval_foo_bb0_in(V_x,V_y,B):
* Chain [16]: 0
  with precondition: [0>=V_y] 

* Chain [15]: 1*s(4)+1*s(6)+0
  Such that:s(5) =< V_x
s(4) =< V_x-V_y+1
s(4) =< s(5)
s(6) =< s(5)

  with precondition: [V_y>=1,V_x>=V_y] 

* Chain [14]: 0
  with precondition: [V_y>=V_x+1] 


#### Cost of chains of eval_foo_start(V_x,V_y,V_ytmp,V_res,B):
* Chain [19]: 0
  with precondition: [0>=V_y] 

* Chain [18]: 1*s(8)+1*s(9)+0
  Such that:s(7) =< V_x
s(8) =< V_x-V_y+1
s(8) =< s(7)
s(9) =< s(7)

  with precondition: [V_y>=1,V_x>=V_y] 

* Chain [17]: 0
  with precondition: [V_y>=V_x+1] 


Closed-form bounds of eval_foo_start(V_x,V_y,V_ytmp,V_res,B): 
-------------------------------------
* Chain [19] with precondition: [0>=V_y] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [18] with precondition: [V_y>=1,V_x>=V_y] 
    - Upper bound: 2*V_x-V_y+1 
    - Complexity: n 
* Chain [17] with precondition: [V_y>=V_x+1] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_foo_start(V_x,V_y,V_ytmp,V_res,B): nat(V_x-V_y+1)+nat(V_x) 
Asymptotic class: n 
* Total analysis performed in 119 ms.