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

#### Computed strongly connected components 
0. recursive  : [f2/25,f4/25]
1. recursive  : [f1/14,f2_loop_cont/15]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f1_loop_cont/2]
4. non_recursive  : [f0/14]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/25
1. SCC is partially evaluated into f1/14
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f0/14

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

### Specialization of cost equations f2/25 
* CE 8 is refined into CE [9] 
* CE 6 is refined into CE [10] 
* CE 7 is refined into CE [11] 


### Cost equations --> "Loop" of f2/25 
* CEs [11] --> Loop 8 
* CEs [9] --> Loop 9 
* CEs [10] --> Loop 10 

### Ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1) 

#### Partial ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1) 


### Specialization of cost equations f1/14 
* CE 2 is refined into CE [12,13,14] 
* CE 5 is refined into CE [15] 
* CE 3 is refined into CE [16,17,18] 
* CE 4 is refined into CE [19] 


### Cost equations --> "Loop" of f1/14 
* CEs [16,19] --> Loop 11 
* CEs [17] --> Loop 12 
* CEs [18] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [12,15] --> Loop 15 
* CEs [14] --> Loop 16 

### Ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,V) 

#### Partial ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,V) 


### Specialization of cost equations f0/14 
* CE 1 is refined into CE [20,21,22,23] 


### Cost equations --> "Loop" of f0/14 
* CEs [23] --> Loop 17 
* CEs [22] --> Loop 18 
* CEs [21] --> Loop 19 
* CEs [20] --> Loop 20 

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

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


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

#### Cost of chains of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1):
* Chain [[8]]...: 1*it(8)+0
  with precondition: [E=J,D=I,C=H,B=G,A=0,D>=1,7>=D,E>=1,7>=E,F=0,K=2,L>=1,M>=1,V>=2,3>=V] 

* Chain [[8],10]: 1*it(8)+0
  with precondition: [A=0,F=0,K=2,V=2,Z=2,E1=2,G1=1,B=G,C=H,D=I,E=J,B1=W,X=C1,Y=D1,A1=F1,7>=D,7>=E,7>=A1,1>=B1,D>=1,E>=1,L>=1,M>=1,A1>=1,B1>=0] 

* Chain [[8],9]: 1*it(8)+0
  with precondition: [A=0,F=0,K=2,V=3,B=G,C=H,D=I,E=J,7>=D,7>=E,D>=1,E>=1,L>=1,M>=1] 

* Chain [10]: 0
  with precondition: [A=0,F=0,K=2,V=2,Z=2,E1=2,G1=1,G=B,H=C,I=D,J=E,C1=X,D1=Y,W=B1,A1=F1,7>=I,7>=J,1>=W,7>=A1,I>=1,J>=1,W>=0,A1>=1] 

* Chain [9]: 0
  with precondition: [A=0,F=0,K=2,V=3,G=B,H=C,I=D,J=E,7>=I,7>=J,I>=1,J>=1] 


#### Cost of chains of f1(A,B,C,D,E,F,G,H,I,J,K,L,M,V):
* Chain [[11,12,13]]...: 5*it(11)+0
  with precondition: [V=3] 

* Chain [[11,12,13],16]...: 6*it(11)+0
  with precondition: [V=3,L>=1,M>=1] 

* Chain [[11,12,13],15]: 5*it(11)+0
  with precondition: [V=3] 

* Chain [[11,12,13],14]: 6*it(11)+0
  with precondition: [V=3,L>=1,M>=1] 

* Chain [16]...: 1*s(7)+0
  with precondition: [V=3,L>=1,M>=1] 

* Chain [15]: 0
  with precondition: [V=3] 

* Chain [14]: 1*s(8)+0
  with precondition: [V=3,L>=1,M>=1] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,V):
* Chain [20]: 1*s(14)+0
  with precondition: [] 

* Chain [19]: 1*s(15)+0
  with precondition: [L>=1,M>=1] 

* Chain [18]...: 5*s(16)+0
  with precondition: [] 

* Chain [17]...: 1*s(17)+0
  with precondition: [L>=1,M>=1] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,V): 
-------------------------------------
* Chain [20] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [19] with precondition: [L>=1,M>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [18]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [17]... with precondition: [L>=1,M>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,V): inf 
Asymptotic class: infinity 
* Total analysis performed in 261 ms.

