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

#### Computed strongly connected components 
0. non_recursive  : [f1/12]
1. recursive  : [f2/13]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f2_loop_cont/13]
4. non_recursive  : [f300/12]

#### Obtained direct recursion through partial evaluation 
0. SCC is completely evaluated into other SCCs
1. SCC is partially evaluated into f2/13
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f2_loop_cont/13
4. SCC is partially evaluated into f300/12

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

### Specialization of cost equations f2/13 
* CE 5 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10] 


### Cost equations --> "Loop" of f2/13 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR f2(A,B,C,D,E,F,G,S,T,U,V,W,X) 

#### Partial ranking functions of CR f2(A,B,C,D,E,F,G,S,T,U,V,W,X) 


### Specialization of cost equations f2_loop_cont/13 
* CE 7 is refined into CE [11] 
* CE 6 is refined into CE [12] 


### Cost equations --> "Loop" of f2_loop_cont/13 
* CEs [11] --> Loop 11 
* CEs [12] --> Loop 12 

### Ranking functions of CR f2_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M) 

#### Partial ranking functions of CR f2_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M) 


### Specialization of cost equations f300/12 
* CE 2 is refined into CE [13,14,15,16,17] 
* CE 1 is refined into CE [18] 


### Cost equations --> "Loop" of f300/12 
* CEs [14] --> Loop 13 
* CEs [15] --> Loop 14 
* CEs [18] --> Loop 15 
* CEs [13] --> Loop 16 
* CEs [16,17] --> Loop 17 

### Ranking functions of CR f300(A,B,C,D,E,F,G,H,I,J,K,S) 

#### Partial ranking functions of CR f300(A,B,C,D,E,F,G,H,I,J,K,S) 


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

#### Cost of chains of f2(A,B,C,D,E,F,G,S,T,U,V,W,X):
* Chain [[8]]...: 1*it(8)+0
  with precondition: [E=F,A>=2] 

* Chain [[8],9]: 1*it(8)+0
  with precondition: [S=3,E=F,A>=2] 

* Chain [10]: 0
  with precondition: [S=2,V=D,F=E,F=W,1>=A] 

* Chain [9]: 0
  with precondition: [S=3,F=E] 


#### Cost of chains of f2_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M):
* Chain [12]: 0
  with precondition: [A=2,I>=1] 

* Chain [11]: 0
  with precondition: [A=3,I>=1] 


#### Cost of chains of f300(A,B,C,D,E,F,G,H,I,J,K,S):
* Chain [17]...: 1*aux(1)+0
  with precondition: [A>=2,H>=1] 

* Chain [16]: 0
  with precondition: [1>=A,H>=1] 

* Chain [15]: 0
  with precondition: [0>=H] 

* Chain [14]: 1*s(3)+0
  with precondition: [A>=2,H>=1] 

* Chain [13]: 0
  with precondition: [H>=1] 


Closed-form bounds of f300(A,B,C,D,E,F,G,H,I,J,K,S): 
-------------------------------------
* Chain [17]... with precondition: [A>=2,H>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [16] with precondition: [1>=A,H>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [0>=H] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [14] with precondition: [A>=2,H>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [13] with precondition: [H>=1] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of f300(A,B,C,D,E,F,G,H,I,J,K,S): inf 
Asymptotic class: infinity 
* Total analysis performed in 48 ms.

