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

#### Computed strongly connected components 
0. recursive  : [f10/12,f21/12]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f31/8]
3. non_recursive  : [f10_loop_cont/9]
4. non_recursive  : [f0/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f10/12
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f10_loop_cont/9
4. SCC is partially evaluated into f0/8

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

### Specialization of cost equations f10/12 
* CE 9 is refined into CE [12] 
* CE 8 is refined into CE [13] 
* CE 7 is refined into CE [14] 
* CE 2 is refined into CE [15] 
* CE 3 is refined into CE [16] 
* CE 6 is refined into CE [17] 
* CE 4 is refined into CE [18] 
* CE 5 is refined into CE [19] 


### Cost equations --> "Loop" of f10/12 
* CEs [15] --> Loop 12 
* CEs [18] --> Loop 13 
* CEs [16] --> Loop 14 
* CEs [19] --> Loop 15 
* CEs [17] --> Loop 16 
* CEs [12] --> Loop 17 
* CEs [13] --> Loop 18 
* CEs [14] --> Loop 19 

### Ranking functions of CR f10(A,B,C,E,F,G,J,K,L,M,N,O) 

#### Partial ranking functions of CR f10(A,B,C,E,F,G,J,K,L,M,N,O) 
* Partial RF of phase [12,13,14,15,16]:
  - RF of loop [12:1,13:1]:
    C depends on loops [14:1,15:1] 
  - RF of loop [12:1,14:1]:
    -F+3 depends on loops [13:1,15:1,16:1] 
  - RF of loop [13:1,15:1,16:1]:
    F depends on loops [12:1,14:1] 
  - RF of loop [14:1,15:1]:
    -B/2+1/2 depends on loops [16:1] 
  - RF of loop [16:1]:
    B depends on loops [14:1,15:1] 


### Specialization of cost equations f10_loop_cont/9 
* CE 11 is refined into CE [20] 
* CE 10 is refined into CE [21] 


### Cost equations --> "Loop" of f10_loop_cont/9 
* CEs [20] --> Loop 20 
* CEs [21] --> Loop 21 

### Ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f0/8 
* CE 1 is refined into CE [22,23,24,25,26,27] 


### Cost equations --> "Loop" of f0/8 
* CEs [26,27] --> Loop 22 
* CEs [22,23,24,25] --> Loop 23 

### Ranking functions of CR f0(A,B,C,D,E,F,G,J) 

#### Partial ranking functions of CR f0(A,B,C,D,E,F,G,J) 


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

#### Cost of chains of f10(A,B,C,E,F,G,J,K,L,M,N,O):
* Chain [[12,13,14,15,16]]...: 5*it(12)+0
  with precondition: [F>=1,C>=0,2>=F,A>=B,A>=1,E=2] 

* Chain [[12,13,14,15,16],19]: 5*it(12)+0
  with precondition: [E=2,J=2,N=0,O=0,2>=F,A>=1,C>=0,F>=1,M>=0,K>=A,A>=B,K>=L,C+2*K>=A+L+1,C+4*K>=2*A+2*L+F] 

* Chain [[12,13,14,15,16],18]: 5*it(12)+0
  with precondition: [E=2,J=2,N=3,O=1,2>=F,A>=1,C>=0,F>=1,M>=0,K>=A,A>=B,K>=L,C+K>=A+1,C+F+2*K>=2*A+3] 

* Chain [[12,13,14,15,16],17]: 5*it(12)+0
  with precondition: [E=2,J=3,2>=F,A>=1,C>=0,F>=1,A>=B] 

* Chain [17]: 0
  with precondition: [E=2,J=3,A>=1,C>=0,F>=0,A>=B] 


#### Cost of chains of f10_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [21]: 0
  with precondition: [A=2,E=0,F=2] 

* Chain [20]: 0
  with precondition: [A=3,E=0,F=2] 


#### Cost of chains of f0(A,B,C,D,E,F,G,J):
* Chain [23]: 1*aux(37)+0
  with precondition: [] 

* Chain [22]...: 1*aux(38)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,J): 
-------------------------------------
* Chain [23] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [22]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,E,F,G,J): inf 
Asymptotic class: infinity 
* Total analysis performed in 284 ms.

