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

#### Computed strongly connected components 
0. recursive  : [eval_wise__critedge_in/5,eval_wise_bb1_in/5]
1. non_recursive  : [eval_wise_stop/5]
2. non_recursive  : [eval_wise_bb2_in/5]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [eval_wise_bb1_in_loop_cont/6]
5. non_recursive  : [eval_wise_2/5]
6. non_recursive  : [eval_wise_1/5]
7. non_recursive  : [eval_wise_0/5]
8. non_recursive  : [eval_wise_bb0_in/5]
9. non_recursive  : [eval_wise_start/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_wise_bb1_in/5
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into eval_wise_bb1_in_loop_cont/6
5. SCC is partially evaluated into eval_wise_2/5
6. SCC is completely evaluated into other SCCs
7. SCC is completely evaluated into other SCCs
8. SCC is completely evaluated into other SCCs
9. SCC is partially evaluated into eval_wise_start/5

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

### Specialization of cost equations eval_wise_bb1_in/5 
* CE 8 is refined into CE [11] 
* CE 7 is refined into CE [12] 
* CE 5 is refined into CE [13] 
* CE 6 is refined into CE [14] 


### Cost equations --> "Loop" of eval_wise_bb1_in/5 
* CEs [13] --> Loop 11 
* CEs [14] --> Loop 12 
* CEs [11] --> Loop 13 
* CEs [12] --> Loop 14 

### Ranking functions of CR eval_wise_bb1_in(V__0,V__01,B,C,D) 
* RF of phase [11]: [V__0-V__01-2]
* RF of phase [12]: [-V__0+V__01-2]

#### Partial ranking functions of CR eval_wise_bb1_in(V__0,V__01,B,C,D) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    V__0-V__01-2
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    -V__0+V__01-2


### Specialization of cost equations eval_wise_bb1_in_loop_cont/6 
* CE 10 is refined into CE [15] 
* CE 9 is refined into CE [16] 


### Cost equations --> "Loop" of eval_wise_bb1_in_loop_cont/6 
* CEs [15] --> Loop 15 
* CEs [16] --> Loop 16 

### Ranking functions of CR eval_wise_bb1_in_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR eval_wise_bb1_in_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations eval_wise_2/5 
* CE 4 is refined into CE [17,18,19,20,21,22] 
* CE 3 is refined into CE [23] 
* CE 2 is refined into CE [24] 


### Cost equations --> "Loop" of eval_wise_2/5 
* CEs [17,22] --> Loop 17 
* CEs [19,21] --> Loop 18 
* CEs [18] --> Loop 19 
* CEs [20] --> Loop 20 
* CEs [23] --> Loop 21 
* CEs [24] --> Loop 22 

### Ranking functions of CR eval_wise_2(V__0,V__01,V_x,V_y,B) 

#### Partial ranking functions of CR eval_wise_2(V__0,V__01,V_x,V_y,B) 


### Specialization of cost equations eval_wise_start/5 
* CE 1 is refined into CE [25,26,27,28,29,30] 


### Cost equations --> "Loop" of eval_wise_start/5 
* CEs [30] --> Loop 23 
* CEs [29] --> Loop 24 
* CEs [28] --> Loop 25 
* CEs [27] --> Loop 26 
* CEs [26] --> Loop 27 
* CEs [25] --> Loop 28 

### Ranking functions of CR eval_wise_start(V__0,V__01,V_x,V_y,B) 

#### Partial ranking functions of CR eval_wise_start(V__0,V__01,V_x,V_y,B) 


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

#### Cost of chains of eval_wise_bb1_in(V__0,V__01,B,C,D):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< -V__0+D

  with precondition: [B=2,V__01=C+2,V__01=D,V__0>=0,V__01>=V__0+3] 

* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< -V__0+V__01

  with precondition: [B=3,V__0>=0,V__01>=V__0+3] 

* Chain [[11],14]: 1*it(11)+0
  Such that:it(11) =< -V__01+D

  with precondition: [B=2,V__0=C,V__0=D+2,V__01>=0,V__0>=V__01+3] 

* Chain [[11],13]: 1*it(11)+0
  Such that:it(11) =< V__0-V__01

  with precondition: [B=3,V__01>=0,V__0>=V__01+3] 

* Chain [14]: 0
  with precondition: [B=2,V__0=C,V__01=D,V__0>=0,V__01>=0,V__01+2>=V__0,V__0+2>=V__01] 

* Chain [13]: 0
  with precondition: [B=3,V__0>=0,V__01>=0] 


#### Cost of chains of eval_wise_bb1_in_loop_cont(A,B,C,D,E,F):
* Chain [16]: 0
  with precondition: [A=2,D>=0,E>=0] 

* Chain [15]: 0
  with precondition: [A=3,D>=0,E>=0] 


#### Cost of chains of eval_wise_2(V__0,V__01,V_x,V_y,B):
* Chain [22]: 0
  with precondition: [0>=V_x+1] 

* Chain [21]: 0
  with precondition: [0>=V_y+1] 

* Chain [20]: 0
  with precondition: [V_x>=0,V_y>=0] 

* Chain [19]: 0
  with precondition: [V_x>=0,V_y>=0,V_y+2>=V_x,V_x+2>=V_y] 

* Chain [18]: 2*s(1)+0
  Such that:aux(1) =< -V_x+V_y
s(1) =< aux(1)

  with precondition: [V_x>=0,V_y>=V_x+3] 

* Chain [17]: 2*s(3)+0
  Such that:aux(2) =< V_x-V_y
s(3) =< aux(2)

  with precondition: [V_y>=0,V_x>=V_y+3] 


#### Cost of chains of eval_wise_start(V__0,V__01,V_x,V_y,B):
* Chain [28]: 0
  with precondition: [0>=V_x+1] 

* Chain [27]: 0
  with precondition: [0>=V_y+1] 

* Chain [26]: 0
  with precondition: [V_x>=0,V_y>=0] 

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

* Chain [24]: 2*s(6)+0
  Such that:s(5) =< -V_x+V_y
s(6) =< s(5)

  with precondition: [V_x>=0,V_y>=V_x+3] 

* Chain [23]: 2*s(8)+0
  Such that:s(7) =< V_x-V_y
s(8) =< s(7)

  with precondition: [V_y>=0,V_x>=V_y+3] 


Closed-form bounds of eval_wise_start(V__0,V__01,V_x,V_y,B): 
-------------------------------------
* Chain [28] with precondition: [0>=V_x+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [27] with precondition: [0>=V_y+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [26] with precondition: [V_x>=0,V_y>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [25] with precondition: [V_x>=0,V_y>=0,V_y+2>=V_x,V_x+2>=V_y] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [24] with precondition: [V_x>=0,V_y>=V_x+3] 
    - Upper bound: -2*V_x+2*V_y 
    - Complexity: n 
* Chain [23] with precondition: [V_y>=0,V_x>=V_y+3] 
    - Upper bound: 2*V_x-2*V_y 
    - Complexity: n 

### Maximum cost of eval_wise_start(V__0,V__01,V_x,V_y,B): max([nat(-V_x+V_y)*2,nat(V_x-V_y)*2]) 
Asymptotic class: n 
* Total analysis performed in 83 ms.

