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

#### Computed strongly connected components 
0. recursive  : [f41/1]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f41_loop_cont/2]
3. non_recursive  : [f29/18]
4. non_recursive  : [f21/18]
5. non_recursive  : [f0/18]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f41/1
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f29/18
4. SCC is partially evaluated into f21/18
5. SCC is partially evaluated into f0/18

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

### Specialization of cost equations f41/1 
* CE 7 is refined into CE [10] 
* CE 6 is refined into CE [11] 


### Cost equations --> "Loop" of f41/1 
* CEs [11] --> Loop 9 
* CEs [10] --> Loop 10 

### Ranking functions of CR f41(T) 

#### Partial ranking functions of CR f41(T) 


### Specialization of cost equations f29/18 
* CE 8 is discarded (unfeasible) 
* CE 9 is refined into CE [12,13] 


### Cost equations --> "Loop" of f29/18 
* CEs [13] --> Loop 11 
* CEs [12] --> Loop 12 

### Ranking functions of CR f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T) 

#### Partial ranking functions of CR f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T) 


### Specialization of cost equations f21/18 
* CE 5 is refined into CE [14,15] 
* CE 4 is discarded (unfeasible) 


### Cost equations --> "Loop" of f21/18 
* CEs [15] --> Loop 13 
* CEs [14] --> Loop 14 

### Ranking functions of CR f21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T) 

#### Partial ranking functions of CR f21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T) 


### Specialization of cost equations f0/18 
* CE 2 is refined into CE [16,17] 
* CE 3 is refined into CE [18,19] 
* CE 1 is refined into CE [20,21] 


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

### Ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T) 

#### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T) 


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

#### Cost of chains of f41(T):
* Chain [[9]]...: 1*it(9)+0
  with precondition: [T=2] 

* Chain [[9],10]: 1*it(9)+0
  with precondition: [T=2] 

* Chain [10]: 0
  with precondition: [T=2] 


#### Cost of chains of f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T):
* Chain [12]: 1*s(2)+0
  with precondition: [A=0,H=0,I=C,I=J,0>=M,K>=M] 

* Chain [11]...: 1*s(3)+0
  with precondition: [A=0,H=0,I=C,I=J,0>=M,K>=M] 


#### Cost of chains of f21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T):
* Chain [14]: 1*s(4)+0
  with precondition: [A=1,0>=M,K>=M] 

* Chain [13]...: 1*s(5)+0
  with precondition: [A=1,0>=M,K>=M] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T):
* Chain [18]: 1*s(6)+0
  with precondition: [0>=K] 

* Chain [17]: 1*aux(2)+0
  with precondition: [K>=1] 

* Chain [16]...: 1*s(9)+0
  with precondition: [0>=K] 

* Chain [15]...: 1*aux(3)+0
  with precondition: [K>=1] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T): 
-------------------------------------
* Chain [18] with precondition: [0>=K] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [17] with precondition: [K>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [16]... with precondition: [0>=K] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [15]... with precondition: [K>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,T): inf 
Asymptotic class: infinity 
* Total analysis performed in 54 ms.

