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

#### Computed strongly connected components 
0. recursive  : [f7/16]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f19/10]
3. non_recursive  : [f7_loop_cont/11]
4. non_recursive  : [f0/10]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f7/16
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f7_loop_cont/11
4. SCC is partially evaluated into f0/10

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

### Specialization of cost equations f7/16 
* CE 4 is refined into CE [7] 
* CE 3 is refined into CE [8] 
* CE 2 is refined into CE [9] 


### Cost equations --> "Loop" of f7/16 
* CEs [9] --> Loop 7 
* CEs [7] --> Loop 8 
* CEs [8] --> Loop 9 

### Ranking functions of CR f7(B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* RF of phase [7]: [-E+31]

#### Partial ranking functions of CR f7(B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    -E+31


### Specialization of cost equations f7_loop_cont/11 
* CE 6 is refined into CE [10] 
* CE 5 is refined into CE [11] 


### Cost equations --> "Loop" of f7_loop_cont/11 
* CEs [10] --> Loop 10 
* CEs [11] --> Loop 11 

### Ranking functions of CR f7_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 

#### Partial ranking functions of CR f7_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 


### Specialization of cost equations f0/10 
* CE 1 is refined into CE [12,13,14] 


### Cost equations --> "Loop" of f0/10 
* CEs [12,13,14] --> Loop 12 

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

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


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

#### Cost of chains of f7(B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q):
* Chain [[7],9]: 1*it(7)+0
  Such that:it(7) =< -E+31

  with precondition: [B=30,J=2,M=31,L=N,K=O,K=P,K=Q,30>=E] 

* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< -E+31

  with precondition: [B=30,J=3,30>=E] 

* Chain [8]: 0
  with precondition: [B=30,J=3] 


#### Cost of chains of f7_loop_cont(A,B,C,D,E,F,G,H,I,J,K):
* Chain [11]: 0
  with precondition: [A=2,B=30,C=30] 

* Chain [10]: 0
  with precondition: [A=3,B=30,C=30] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J):
* Chain [12]: 58
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J): 
-------------------------------------
* Chain [12] with precondition: [] 
    - Upper bound: 58 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J): 58 
Asymptotic class: constant 
* Total analysis performed in 62 ms.

