/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/4,eval_foo_bb3_in/4]
1. recursive  : [eval_foo_bb1_in/4,eval_foo_bb2_in_loop_cont/6,eval_foo_bb4_in/5]
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/4]
6. non_recursive  : [eval_foo_start/4]

#### 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/4
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/4
6. SCC is partially evaluated into eval_foo_start/4

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

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


### Cost equations --> "Loop" of eval_foo_bb2_in/4 
* CEs [8] --> Loop 7 
* CEs [7] --> Loop 8 

### Ranking functions of CR eval_foo_bb2_in(V_z,V__1,B,C) 
* RF of phase [7]: [-V_z+V__1]

#### Partial ranking functions of CR eval_foo_bb2_in(V_z,V__1,B,C) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    -V_z+V__1


### Specialization of cost equations eval_foo_bb1_in/4 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10,11] 


### Cost equations --> "Loop" of eval_foo_bb1_in/4 
* CEs [11] --> Loop 9 
* CEs [10] --> Loop 10 
* CEs [9] --> Loop 11 

### Ranking functions of CR eval_foo_bb1_in(V_z,V__01,V__0,B) 
* RF of phase [9]: [-V__01+V__0,-V_z+V__0]

#### Partial ranking functions of CR eval_foo_bb1_in(V_z,V__01,V__0,B) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    -V__01+V__0
    -V_z+V__0


### Specialization of cost equations eval_foo_bb0_in/4 
* CE 2 is refined into CE [12,13,14,15] 


### Cost equations --> "Loop" of eval_foo_bb0_in/4 
* CEs [13] --> Loop 12 
* CEs [14] --> Loop 13 
* CEs [15] --> Loop 14 
* CEs [12] --> Loop 15 

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

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


### Specialization of cost equations eval_foo_start/4 
* CE 1 is refined into CE [16,17,18,19] 


### Cost equations --> "Loop" of eval_foo_start/4 
* CEs [19] --> Loop 16 
* CEs [18] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [16] --> Loop 19 

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

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


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

#### Cost of chains of eval_foo_bb2_in(V_z,V__1,B,C):
* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< -V_z+V__1

  with precondition: [B=2,V_z=C,V__1>=V_z+1] 

* Chain [8]: 0
  with precondition: [B=2,V__1=C,V_z>=V__1] 


#### Cost of chains of eval_foo_bb1_in(V_z,V__01,V__0,B):
* Chain [[9],11]: 1*it(9)+0
  Such that:it(9) =< -V_z+V__0

  with precondition: [B=3,V__0>=V_z+1,V_z>=V__01] 

* Chain [11]: 0
  with precondition: [B=3,V_z>=V__0] 

* Chain [10,[9],11]: 1*it(9)+1*s(1)+1
  Such that:s(1) =< -V_z+V__01
it(9) =< -V_z+V__0

  with precondition: [B=3,V__01>=V_z+1,V__0>=V_z+2] 

* Chain [10,11]: 1*s(1)+1
  Such that:s(1) =< -V_z+V__01

  with precondition: [B=3,V_z+1=V__0,V__01>=V_z+1] 


#### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_z,B):
* Chain [15]: 1*s(2)+1
  Such that:s(2) =< -V_x+V_y+1

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

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

* Chain [13]: 1*s(3)+0
  Such that:s(3) =< V_x-V_z

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

* Chain [12]: 1*s(4)+1*s(5)+1
  Such that:s(5) =< V_x-V_z
s(4) =< V_y-V_z

  with precondition: [V_x>=V_z+2,V_y>=V_z+1] 


#### Cost of chains of eval_foo_start(V_x,V_y,V_z,B):
* Chain [19]: 1*s(6)+1
  Such that:s(6) =< -V_x+V_y+1

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

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

* Chain [17]: 1*s(7)+0
  Such that:s(7) =< V_x-V_z

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

* Chain [16]: 1*s(8)+1*s(9)+1
  Such that:s(8) =< V_x-V_z
s(9) =< V_y-V_z

  with precondition: [V_x>=V_z+2,V_y>=V_z+1] 


Closed-form bounds of eval_foo_start(V_x,V_y,V_z,B): 
-------------------------------------
* Chain [19] with precondition: [V_x=V_z+1,V_y>=V_x] 
    - Upper bound: -V_x+V_y+2 
    - Complexity: n 
* Chain [18] with precondition: [V_z>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [17] with precondition: [V_z>=V_y,V_x>=V_z+1] 
    - Upper bound: V_x-V_z 
    - Complexity: n 
* Chain [16] with precondition: [V_x>=V_z+2,V_y>=V_z+1] 
    - Upper bound: V_x+V_y-2*V_z+1 
    - Complexity: n 

### Maximum cost of eval_foo_start(V_x,V_y,V_z,B): max([nat(-V_x+V_y+1)+1,nat(V_y-V_z)+1+nat(V_x-V_z)]) 
Asymptotic class: n 
* Total analysis performed in 122 ms.