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


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


WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_perfect_bb2_in/4,eval_perfect_bb3_in/4]
1. recursive  : [eval_perfect_bb1_in/5,eval_perfect_bb2_in_loop_cont/8,eval_perfect_bb4_in/7]
2. non_recursive  : [eval_perfect_stop/1]
3. non_recursive  : [eval_perfect_bb6_in/1]
4. non_recursive  : [eval_perfect_bb5_in/2]
5. non_recursive  : [eval_perfect_bb1_in_loop_cont/3]
6. non_recursive  : [eval_perfect_bb0_in/2]
7. non_recursive  : [eval_perfect_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_perfect_bb2_in/4
1. SCC is partially evaluated into eval_perfect_bb1_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_perfect_bb5_in/2
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into eval_perfect_bb0_in/2
7. SCC is partially evaluated into eval_perfect_start/2

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

### Specialization of cost equations eval_perfect_bb2_in/4 
* CE 12 is refined into CE [13] 
* CE 11 is refined into CE [14] 


### Cost equations --> "Loop" of eval_perfect_bb2_in/4 
* CEs [14] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR eval_perfect_bb2_in(V_1,V_y2_1,B,C) 
* RF of phase [12]: [-V_1+V_y2_1+1,V_y2_1]

#### Partial ranking functions of CR eval_perfect_bb2_in(V_1,V_y2_1,B,C) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    -V_1+V_y2_1+1
    V_y2_1


### Specialization of cost equations eval_perfect_bb1_in/5 
* CE 7 is refined into CE [15] 
* CE 6 is refined into CE [16] 
* CE 4 is refined into CE [17] 
* CE 5 is discarded (unfeasible) 


### Cost equations --> "Loop" of eval_perfect_bb1_in/5 
* CEs [16] --> Loop 14 
* CEs [17] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR eval_perfect_bb1_in(V_x,V_y1_0_sink,V_y3_0,B,C) 
* RF of phase [14,15]: [V_y1_0_sink-1]

#### Partial ranking functions of CR eval_perfect_bb1_in(V_x,V_y1_0_sink,V_y3_0,B,C) 
* Partial RF of phase [14,15]:
  - RF of loop [14:1]:
    V_y1_0_sink-1
  - RF of loop [15:1]:
    V_y1_0_sink-2


### Specialization of cost equations eval_perfect_bb5_in/2 
* CE 9 is refined into CE [18] 
* CE 8 is refined into CE [19] 
* CE 10 is refined into CE [20] 


### Cost equations --> "Loop" of eval_perfect_bb5_in/2 
* CEs [18] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [20] --> Loop 19 

### Ranking functions of CR eval_perfect_bb5_in(V_y3_0,B) 

#### Partial ranking functions of CR eval_perfect_bb5_in(V_y3_0,B) 


### Specialization of cost equations eval_perfect_bb0_in/2 
* CE 3 is refined into CE [21,22,23] 
* CE 2 is refined into CE [24] 


### Cost equations --> "Loop" of eval_perfect_bb0_in/2 
* CEs [21,22,23] --> Loop 20 
* CEs [24] --> Loop 21 

### Ranking functions of CR eval_perfect_bb0_in(V_x,B) 

#### Partial ranking functions of CR eval_perfect_bb0_in(V_x,B) 


### Specialization of cost equations eval_perfect_start/2 
* CE 1 is refined into CE [25,26] 


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

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

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


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

#### Cost of chains of eval_perfect_bb2_in(V_1,V_y2_1,B,C):
* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< -V_1+V_y2_1+1

  with precondition: [B=2,C>=0,V_1>=C+1,V_y2_1>=V_1+C] 


#### Cost of chains of eval_perfect_bb1_in(V_x,V_y1_0_sink,V_y3_0,B,C):
* Chain [[14,15],16]: 2*it(14)+1*s(5)+1*s(6)+0
  Such that:aux(1) =< V_x
aux(5) =< V_y1_0_sink
it(14) =< aux(5)
aux(2) =< aux(1)
s(5) =< it(14)*aux(1)
s(6) =< it(14)*aux(2)

  with precondition: [B=3,V_y1_0_sink>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0,V_y3_0>=C+1] 


#### Cost of chains of eval_perfect_bb5_in(V_y3_0,B):
* Chain [19]: 0
  with precondition: [V_y3_0=0] 

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

* Chain [17]: 0
  with precondition: [V_y3_0>=1] 


#### Cost of chains of eval_perfect_bb0_in(V_x,B):
* Chain [21]: 0
  with precondition: [1>=V_x] 

* Chain [20]: 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_perfect_start(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] 


Closed-form bounds of eval_perfect_start(V_x,B): 
-------------------------------------
* Chain [23] with precondition: [1>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [22] with precondition: [V_x>=2] 
    - Upper bound: 6*V_x*V_x+6*V_x 
    - Complexity: n^2 

### Maximum cost of eval_perfect_start(V_x,B): nat(V_x)*6*nat(V_x)+nat(V_x)*6 
Asymptotic class: n^2 
* Total analysis performed in 189 ms.