/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^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_alain_bb4_in/6,eval_alain_bb5_in/6]
1. recursive  : [eval_alain_bb2_in/5,eval_alain_bb3_in/6,eval_alain_bb4_in_loop_cont/9,eval_alain_bb6_in/8]
2. non_recursive  : [eval_alain_stop/1]
3. non_recursive  : [eval_alain_bb7_in/1]
4. non_recursive  : [eval_alain_bb2_in_loop_cont/2]
5. non_recursive  : [eval_alain_bb1_in/6]
6. non_recursive  : [eval_alain_bb0_in/6]
7. non_recursive  : [eval_alain_start/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_alain_bb4_in/6
1. SCC is partially evaluated into eval_alain_bb2_in/5
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_alain_bb1_in/6
6. SCC is partially evaluated into eval_alain_bb0_in/6
7. SCC is partially evaluated into eval_alain_start/6

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

### Specialization of cost equations eval_alain_bb4_in/6 
* CE 14 is refined into CE [15] 
* CE 13 is refined into CE [16] 


### Cost equations --> "Loop" of eval_alain_bb4_in/6 
* CEs [16] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR eval_alain_bb4_in(V_y,V__14,V__1,B,C,D) 
* RF of phase [15]: [V__14]

#### Partial ranking functions of CR eval_alain_bb4_in(V_y,V__14,V__1,B,C,D) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    V__14


### Specialization of cost equations eval_alain_bb2_in/5 
* CE 12 is refined into CE [17] 
* CE 11 is refined into CE [18,19] 


### Cost equations --> "Loop" of eval_alain_bb2_in/5 
* CEs [19] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [17] --> Loop 19 

### Ranking functions of CR eval_alain_bb2_in(V_y,V__03,V__02,V__01,B) 
* RF of phase [17,18]: [V__02]

#### Partial ranking functions of CR eval_alain_bb2_in(V_y,V__03,V__02,V__01,B) 
* Partial RF of phase [17,18]:
  - RF of loop [17:1,18:1]:
    V__02


### Specialization of cost equations eval_alain_bb1_in/6 
* CE 10 is refined into CE [20,21] 
* CE 9 is refined into CE [22] 
* CE 8 is refined into CE [23] 
* CE 5 is refined into CE [24] 
* CE 7 is refined into CE [25] 
* CE 6 is refined into CE [26] 


### Cost equations --> "Loop" of eval_alain_bb1_in/6 
* CEs [21] --> Loop 20 
* CEs [22] --> Loop 21 
* CEs [23] --> Loop 22 
* CEs [24] --> Loop 23 
* CEs [25] --> Loop 24 
* CEs [26] --> Loop 25 
* CEs [20] --> Loop 26 

### Ranking functions of CR eval_alain_bb1_in(V_x,V_y,V_z,V_n1,V_n2,B) 

#### Partial ranking functions of CR eval_alain_bb1_in(V_x,V_y,V_z,V_n1,V_n2,B) 


### Specialization of cost equations eval_alain_bb0_in/6 
* CE 3 is refined into CE [27] 
* CE 2 is refined into CE [28] 
* CE 4 is refined into CE [29,30,31,32,33,34,35] 


### Cost equations --> "Loop" of eval_alain_bb0_in/6 
* CEs [27] --> Loop 27 
* CEs [28] --> Loop 28 
* CEs [35] --> Loop 29 
* CEs [34] --> Loop 30 
* CEs [33] --> Loop 31 
* CEs [32] --> Loop 32 
* CEs [31] --> Loop 33 
* CEs [30] --> Loop 34 
* CEs [29] --> Loop 35 

### Ranking functions of CR eval_alain_bb0_in(V_x,V_y,V_z,V_n1,V_n2,B) 

#### Partial ranking functions of CR eval_alain_bb0_in(V_x,V_y,V_z,V_n1,V_n2,B) 


### Specialization of cost equations eval_alain_start/6 
* CE 1 is refined into CE [36,37,38,39,40,41,42,43,44] 


### Cost equations --> "Loop" of eval_alain_start/6 
* CEs [44] --> Loop 36 
* CEs [43] --> Loop 37 
* CEs [42] --> Loop 38 
* CEs [41] --> Loop 39 
* CEs [40] --> Loop 40 
* CEs [39] --> Loop 41 
* CEs [38] --> Loop 42 
* CEs [37] --> Loop 43 
* CEs [36] --> Loop 44 

### Ranking functions of CR eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B) 

#### Partial ranking functions of CR eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B) 


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

#### Cost of chains of eval_alain_bb4_in(V_y,V__14,V__1,B,C,D):
* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< V__14

  with precondition: [B=2,C=0,V_y=D,V_y>=0,V__14>=1,V__14+V_y>=V__1] 

* Chain [16]: 0
  with precondition: [B=2,V__14=C,V__1=D,0>=V__14,V_y>=0,V__14+V_y>=V__1] 


#### Cost of chains of eval_alain_bb2_in(V_y,V__03,V__02,V__01,B):
* Chain [[17,18],19]: 2*it(17)+1*s(3)+0
  Such that:aux(2) =< V__03
aux(5) =< V__02
it(17) =< aux(5)
s(3) =< it(17)*aux(2)

  with precondition: [B=3,V_y>=0,V__02>=1,V__01>=0,V__03>=2*V_y,V__03>=V__01] 

* Chain [19]: 0
  with precondition: [V__02=0,B=3,V_y>=0,V__01>=0,V__03>=2*V_y,V__03>=V__01] 


#### Cost of chains of eval_alain_bb1_in(V_x,V_y,V_z,V_n1,V_n2,B):
* Chain [26]: 0
  with precondition: [V_n1=0,V_x>=0,V_y>=0,V_z>=0,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [25]: 0
  with precondition: [0>=V_x+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [24]: 0
  with precondition: [0>=V_y+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [23]: 0
  with precondition: [0>=V_z+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [22]: 0
  with precondition: [0>=V_n1+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [21]: 0
  with precondition: [0>=V_n2+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [20]: 2*s(6)+1*s(7)+0
  Such that:s(5) =< V_n1
s(4) =< V_n2
s(6) =< s(5)
s(7) =< s(6)*s(4)

  with precondition: [V_x>=0,V_y>=0,V_z>=0,V_n1>=1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 


#### Cost of chains of eval_alain_bb0_in(V_x,V_y,V_z,V_n1,V_n2,B):
* Chain [35]: 0
  with precondition: [V_n1=0,V_x>=0,V_y>=0,V_z>=0,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [34]: 0
  with precondition: [0>=V_x+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [33]: 0
  with precondition: [0>=V_y+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [32]: 0
  with precondition: [0>=V_z+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [31]: 0
  with precondition: [0>=V_n1+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [30]: 0
  with precondition: [0>=V_n2+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [29]: 2*s(10)+1*s(11)+0
  Such that:s(8) =< V_n1
s(9) =< V_n2
s(10) =< s(8)
s(11) =< s(10)*s(9)

  with precondition: [V_x>=0,V_y>=0,V_z>=0,V_n1>=1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [28]: 0
  with precondition: [2*V_y>=V_n2] 

* Chain [27]: 0
  with precondition: [V_y+V_z>=V_n2] 


#### Cost of chains of eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B):
* Chain [44]: 0
  with precondition: [V_n1=0,V_x>=0,V_y>=0,V_z>=0,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [43]: 0
  with precondition: [0>=V_x+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [42]: 0
  with precondition: [0>=V_y+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [41]: 0
  with precondition: [0>=V_z+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [40]: 0
  with precondition: [0>=V_n1+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [39]: 0
  with precondition: [0>=V_n2+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [38]: 2*s(14)+1*s(15)+0
  Such that:s(12) =< V_n1
s(13) =< V_n2
s(14) =< s(12)
s(15) =< s(14)*s(13)

  with precondition: [V_x>=0,V_y>=0,V_z>=0,V_n1>=1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 

* Chain [37]: 0
  with precondition: [2*V_y>=V_n2] 

* Chain [36]: 0
  with precondition: [V_y+V_z>=V_n2] 


Closed-form bounds of eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B): 
-------------------------------------
* Chain [44] with precondition: [V_n1=0,V_x>=0,V_y>=0,V_z>=0,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [43] with precondition: [0>=V_x+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [42] with precondition: [0>=V_y+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [41] with precondition: [0>=V_z+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [40] with precondition: [0>=V_n1+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [39] with precondition: [0>=V_n2+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [38] with precondition: [V_x>=0,V_y>=0,V_z>=0,V_n1>=1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 
    - Upper bound: 2*V_n1+V_n2*V_n1 
    - Complexity: n^2 
* Chain [37] with precondition: [2*V_y>=V_n2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [36] with precondition: [V_y+V_z>=V_n2] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B): nat(V_n2)*nat(V_n1)+nat(V_n1)*2 
Asymptotic class: n^2 
* Total analysis performed in 274 ms.