/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^2))  

Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [eval_perfect1_bb3_in/4,eval_perfect1_bb4_in/4]
1. recursive  : [eval_perfect1_bb2_in/5,eval_perfect1_bb3_in_loop_cont/7,eval_perfect1_bb5_in/6]
2. non_recursive  : [eval_perfect1_stop/1]
3. non_recursive  : [eval_perfect1_bb7_in/1]
4. non_recursive  : [eval_perfect1_bb6_in/2]
5. non_recursive  : [eval_perfect1_bb2_in_loop_cont/3]
6. non_recursive  : [eval_perfect1_bb1_in/2]
7. non_recursive  : [eval_perfect1_bb0_in/2]
8. non_recursive  : [eval_perfect1_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_perfect1_bb3_in/4
1. SCC is partially evaluated into eval_perfect1_bb2_in/5
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into eval_perfect1_bb6_in/2
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into eval_perfect1_bb1_in/2
7. SCC is partially evaluated into eval_perfect1_bb0_in/2
8. SCC is partially evaluated into eval_perfect1_start/2

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

### Specialization of cost equations eval_perfect1_bb3_in/4 
* CE 13 is refined into CE [14] 
* CE 12 is refined into CE [15] 


### Cost equations --> "Loop" of eval_perfect1_bb3_in/4 
* CEs [15] --> Loop 13 
* CEs [14] --> Loop 14 

### Ranking functions of CR eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C) 
* RF of phase [13]: [-V_y1_0+V_y2_1+1,V_y2_1]

#### Partial ranking functions of CR eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C) 
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    -V_y1_0+V_y2_1+1
    V_y2_1


### Specialization of cost equations eval_perfect1_bb2_in/5 
* CE 8 is refined into CE [16] 
* CE 7 is refined into CE [17] 
* CE 5 is refined into CE [18] 
* CE 6 is discarded (unfeasible) 


### Cost equations --> "Loop" of eval_perfect1_bb2_in/5 
* CEs [17] --> Loop 15 
* CEs [18] --> Loop 16 
* CEs [16] --> Loop 17 

### Ranking functions of CR eval_perfect1_bb2_in(V_x,V_y3_0,V_y1_0,B,C) 
* RF of phase [15,16]: [V_y1_0]

#### Partial ranking functions of CR eval_perfect1_bb2_in(V_x,V_y3_0,V_y1_0,B,C) 
* Partial RF of phase [15,16]:
  - RF of loop [15:1]:
    V_y1_0
  - RF of loop [16:1]:
    V_y1_0-1


### Specialization of cost equations eval_perfect1_bb6_in/2 
* CE 10 is refined into CE [19] 
* CE 9 is refined into CE [20] 
* CE 11 is refined into CE [21] 


### Cost equations --> "Loop" of eval_perfect1_bb6_in/2 
* CEs [19] --> Loop 18 
* CEs [20] --> Loop 19 
* CEs [21] --> Loop 20 

### Ranking functions of CR eval_perfect1_bb6_in(V_y3_0,B) 

#### Partial ranking functions of CR eval_perfect1_bb6_in(V_y3_0,B) 


### Specialization of cost equations eval_perfect1_bb1_in/2 
* CE 4 is refined into CE [22,23,24] 


### Cost equations --> "Loop" of eval_perfect1_bb1_in/2 
* CEs [22,23,24] --> Loop 21 

### Ranking functions of CR eval_perfect1_bb1_in(V_x,B) 

#### Partial ranking functions of CR eval_perfect1_bb1_in(V_x,B) 


### Specialization of cost equations eval_perfect1_bb0_in/2 
* CE 3 is refined into CE [25] 
* CE 2 is refined into CE [26] 


### Cost equations --> "Loop" of eval_perfect1_bb0_in/2 
* CEs [25] --> Loop 22 
* CEs [26] --> Loop 23 

### Ranking functions of CR eval_perfect1_bb0_in(V_x,B) 

#### Partial ranking functions of CR eval_perfect1_bb0_in(V_x,B) 


### Specialization of cost equations eval_perfect1_start/2 
* CE 1 is refined into CE [27,28] 


### Cost equations --> "Loop" of eval_perfect1_start/2 
* CEs [28] --> Loop 24 
* CEs [27] --> Loop 25 

### Ranking functions of CR eval_perfect1_start(V_x,B) 

#### Partial ranking functions of CR eval_perfect1_start(V_x,B) 


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

#### Cost of chains of eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C):
* Chain [[13],14]: 1*it(13)+0
  Such that:it(13) =< -V_y1_0+V_y2_1+1

  with precondition: [B=2,C>=0,V_y1_0>=C+1,V_y2_1>=V_y1_0+C] 


#### Cost of chains of eval_perfect1_bb2_in(V_x,V_y3_0,V_y1_0,B,C):
* Chain [[15,16],17]: 2*it(15)+1*s(5)+1*s(6)+0
  Such that:aux(1) =< V_x
aux(5) =< V_y1_0
it(15) =< aux(5)
aux(2) =< aux(1)
s(5) =< it(15)*aux(1)
s(6) =< it(15)*aux(2)

  with precondition: [B=3,V_y1_0>=1,V_x>=V_y3_0,V_x>=V_y1_0+1,V_y3_0>=C+1] 


#### Cost of chains of eval_perfect1_bb6_in(V_y3_0,B):
* Chain [20]: 0
  with precondition: [V_y3_0=0] 

* Chain [19]: 0
  with precondition: [0>=V_y3_0+1] 

* Chain [18]: 0
  with precondition: [V_y3_0>=1] 


#### Cost of chains of eval_perfect1_bb1_in(V_x,B):
* Chain [21]: 6*s(9)+3*s(11)+3*s(12)+0
  Such that:aux(9) =< V_x
s(9) =< aux(9)
s(10) =< aux(9)
s(11) =< s(9)*aux(9)
s(12) =< s(9)*s(10)

  with precondition: [V_x>=2] 


#### Cost of chains of eval_perfect1_bb0_in(V_x,B):
* Chain [23]: 0
  with precondition: [1>=V_x] 

* Chain [22]: 6*s(26)+3*s(28)+3*s(29)+0
  Such that:s(25) =< V_x
s(26) =< s(25)
s(27) =< s(25)
s(28) =< s(26)*s(25)
s(29) =< s(26)*s(27)

  with precondition: [V_x>=2] 


#### Cost of chains of eval_perfect1_start(V_x,B):
* Chain [25]: 0
  with precondition: [1>=V_x] 

* Chain [24]: 6*s(31)+3*s(33)+3*s(34)+0
  Such that:s(30) =< V_x
s(31) =< s(30)
s(32) =< s(30)
s(33) =< s(31)*s(30)
s(34) =< s(31)*s(32)

  with precondition: [V_x>=2] 


Closed-form bounds of eval_perfect1_start(V_x,B): 
-------------------------------------
* Chain [25] with precondition: [1>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [24] with precondition: [V_x>=2] 
    - Upper bound: 6*V_x*V_x+6*V_x 
    - Complexity: n^2 

### Maximum cost of eval_perfect1_start(V_x,B): nat(V_x)*6*nat(V_x)+nat(V_x)*6 
Asymptotic class: n^2 
* Total analysis performed in 193 ms.