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

#### Computed strongly connected components 
0. recursive  : [f12/23,f20/23]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f5/12]
3. non_recursive  : [f12_loop_cont/13]
4. non_recursive  : [f0/12]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f12/23
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f12_loop_cont/13
4. SCC is partially evaluated into f0/12

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

### Specialization of cost equations f12/23 
* 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 f12/23 
* CEs [11] --> Loop 8 
* CEs [12] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR f12(A,B,C,D,E,F,G,H,I,J,K,N,O,P,Q,R,S,T,U,V,W,X,Y) 
* RF of phase [8]: [A]

#### Partial ranking functions of CR f12(A,B,C,D,E,F,G,H,I,J,K,N,O,P,Q,R,S,T,U,V,W,X,Y) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    A


### Specialization of cost equations f12_loop_cont/13 
* CE 8 is refined into CE [13] 
* CE 7 is refined into CE [14] 


### Cost equations --> "Loop" of f12_loop_cont/13 
* CEs [13] --> Loop 12 
* CEs [14] --> Loop 13 

### Ranking functions of CR f12_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M) 

#### Partial ranking functions of CR f12_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M) 


### Specialization of cost equations f0/12 
* CE 1 is refined into CE [15] 
* CE 2 is refined into CE [16,17,18,19,20,21,22] 


### Cost equations --> "Loop" of f0/12 
* CEs [21,22] --> Loop 14 
* CEs [15,16,17,18,19,20] --> Loop 15 

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

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


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

#### Cost of chains of f12(A,B,C,D,E,F,G,H,I,J,K,N,O,P,Q,R,S,T,U,V,W,X,Y):
* Chain [[9]]...: 1*it(9)+0
  with precondition: [0>=A+1] 

* Chain [[9],10]: 1*it(9)+0
  with precondition: [N=3,0>=A+1] 

* Chain [[8],11]: 1*it(8)+0
  Such that:it(8) =< A

  with precondition: [N=2,O=0,R=0,S=0,T=0,U=0,X=0,Y=0,P=Q,V=W,A>=1] 

* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< A

  with precondition: [N=3,A>=1] 

* Chain [11]: 0
  with precondition: [A=0,N=2,O=0,R=0,S=0,X=0,Y=0,P=B,Q=C,T=F,U=G,W=V] 

* Chain [10]: 0
  with precondition: [N=3] 


#### Cost of chains of f12_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M):
* Chain [13]: 0
  with precondition: [A=2] 

* Chain [12]: 0
  with precondition: [A=3] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,N):
* Chain [15]: 1*aux(1)+0
  with precondition: [] 

* Chain [14]...: 1*aux(2)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,K,N): 
-------------------------------------
* Chain [15] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [14]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,N): inf 
Asymptotic class: infinity 
* Total analysis performed in 136 ms.

