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

#### Computed strongly connected components 
0. recursive  : [eval_catmouse_bb1_in/5,eval_catmouse_bb2_in/5]
1. non_recursive  : [eval_catmouse_stop/4]
2. non_recursive  : [eval_catmouse_bb3_in/4]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [eval_catmouse_bb1_in_loop_cont/5]
5. non_recursive  : [eval_catmouse_5/4]
6. non_recursive  : [eval_catmouse_4/4]
7. non_recursive  : [eval_catmouse_3/4]
8. non_recursive  : [eval_catmouse_2/4]
9. non_recursive  : [eval_catmouse_1/4]
10. non_recursive  : [eval_catmouse_0/4]
11. non_recursive  : [eval_catmouse_bb0_in/4]
12. non_recursive  : [eval_catmouse_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_catmouse_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_catmouse_bb1_in_loop_cont/5
5. SCC is partially evaluated into eval_catmouse_5/4
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 completely evaluated into other SCCs
10. SCC is completely evaluated into other SCCs
11. SCC is completely evaluated into other SCCs
12. SCC is partially evaluated into eval_catmouse_start/4

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

### Specialization of cost equations eval_catmouse_bb1_in/5 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 
* CE 3 is refined into CE [11] 
* CE 4 is refined into CE [12] 


### Cost equations --> "Loop" of eval_catmouse_bb1_in/5 
* CEs [11] --> Loop 9 
* CEs [12] --> Loop 10 
* CEs [9] --> Loop 11 
* CEs [10] --> Loop 12 

### Ranking functions of CR eval_catmouse_bb1_in(V_m,V_n,V_x_0,B,C) 

#### Partial ranking functions of CR eval_catmouse_bb1_in(V_m,V_n,V_x_0,B,C) 
* Partial RF of phase [9,10]:
  - RF of loop [9:1]:
    -V_m+V_x_0 depends on loops [10:1] 
  - RF of loop [10:1]:
    V_m-V_x_0+1 depends on loops [9:1] 
    V_n-V_x_0+1 depends on loops [9:1] 


### Specialization of cost equations eval_catmouse_bb1_in_loop_cont/5 
* CE 8 is refined into CE [13] 
* CE 7 is refined into CE [14] 


### Cost equations --> "Loop" of eval_catmouse_bb1_in_loop_cont/5 
* CEs [13] --> Loop 13 
* CEs [14] --> Loop 14 

### Ranking functions of CR eval_catmouse_bb1_in_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR eval_catmouse_bb1_in_loop_cont(A,B,C,D,E) 


### Specialization of cost equations eval_catmouse_5/4 
* CE 2 is refined into CE [15,16,17,18,19,20] 


### Cost equations --> "Loop" of eval_catmouse_5/4 
* CEs [19,20] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [18] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [17] --> Loop 19 

### Ranking functions of CR eval_catmouse_5(V_m,V_n,V_x_0,B) 

#### Partial ranking functions of CR eval_catmouse_5(V_m,V_n,V_x_0,B) 


### Specialization of cost equations eval_catmouse_start/4 
* CE 1 is refined into CE [21,22,23,24,25] 


### Cost equations --> "Loop" of eval_catmouse_start/4 
* CEs [25] --> Loop 20 
* CEs [24] --> Loop 21 
* CEs [23] --> Loop 22 
* CEs [22] --> Loop 23 
* CEs [21] --> Loop 24 

### Ranking functions of CR eval_catmouse_start(V_m,V_n,V_x_0,B) 

#### Partial ranking functions of CR eval_catmouse_start(V_m,V_n,V_x_0,B) 


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

#### Cost of chains of eval_catmouse_bb1_in(V_m,V_n,V_x_0,B,C):
* Chain [[9,10]]...: 2*it(9)+0
  with precondition: [V_n>=V_x_0] 

* Chain [[9,10],12]: 2*it(9)+0
  with precondition: [B=2,V_n+1=C,V_m>=V_n,V_n>=V_x_0] 

* Chain [[9,10],11]: 2*it(9)+0
  with precondition: [B=3,V_n>=V_x_0] 

* Chain [12]: 0
  with precondition: [B=2,V_x_0=C,V_x_0>=V_n+1] 

* Chain [11]: 0
  with precondition: [B=3] 


#### Cost of chains of eval_catmouse_bb1_in_loop_cont(A,B,C,D,E):
* Chain [14]: 0
  with precondition: [A=2] 

* Chain [13]: 0
  with precondition: [A=3] 


#### Cost of chains of eval_catmouse_5(V_m,V_n,V_x_0,B):
* Chain [19]: 0
  with precondition: [] 

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

* Chain [17]: 2*s(1)+0
  with precondition: [V_n>=0] 

* Chain [16]: 2*s(2)+0
  with precondition: [V_n>=0,V_m>=V_n] 

* Chain [15]...: 1*aux(7)+0
  with precondition: [V_n>=0] 


#### Cost of chains of eval_catmouse_start(V_m,V_n,V_x_0,B):
* Chain [24]: 0
  with precondition: [] 

* Chain [23]: 0
  with precondition: [0>=V_n+1] 

* Chain [22]: 2*s(5)+0
  with precondition: [V_n>=0] 

* Chain [21]: 2*s(6)+0
  with precondition: [V_n>=0,V_m>=V_n] 

* Chain [20]...: 1*s(7)+0
  with precondition: [V_n>=0] 


Closed-form bounds of eval_catmouse_start(V_m,V_n,V_x_0,B): 
-------------------------------------
* Chain [24] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [23] with precondition: [0>=V_n+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [22] with precondition: [V_n>=0] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [21] with precondition: [V_n>=0,V_m>=V_n] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [20]... with precondition: [V_n>=0] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of eval_catmouse_start(V_m,V_n,V_x_0,B): inf 
Asymptotic class: infinity 
* Total analysis performed in 53 ms.

