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

#### Computed strongly connected components 
0. recursive  : [f25/7]
1. non_recursive  : [exit_location/1]
2. recursive  : [f40/7]
3. non_recursive  : [f52/19]
4. non_recursive  : [f48/19]
5. non_recursive  : [f40_loop_cont/20]
6. non_recursive  : [f33/19]
7. non_recursive  : [f25_loop_cont/20]
8. non_recursive  : [f18/19]
9. non_recursive  : [f0/19]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f25/7
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f40/7
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f48/19
5. SCC is partially evaluated into f40_loop_cont/20
6. SCC is partially evaluated into f33/19
7. SCC is partially evaluated into f25_loop_cont/20
8. SCC is partially evaluated into f18/19
9. SCC is partially evaluated into f0/19

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

### Specialization of cost equations f25/7 
* CE 6 is refined into CE [18] 
* CE 5 is refined into CE [19] 
* CE 4 is discarded (unfeasible) 
* CE 3 is discarded (unfeasible) 


### Cost equations --> "Loop" of f25/7 
* CEs [18] --> Loop 18 
* CEs [19] --> Loop 19 

### Ranking functions of CR f25(G,H,I,K,S,T,U) 

#### Partial ranking functions of CR f25(G,H,I,K,S,T,U) 


### Specialization of cost equations f40/7 
* CE 12 is discarded (unfeasible) 
* CE 13 is refined into CE [20] 
* CE 11 is refined into CE [21] 
* CE 10 is discarded (unfeasible) 


### Cost equations --> "Loop" of f40/7 
* CEs [21] --> Loop 20 
* CEs [20] --> Loop 21 

### Ranking functions of CR f40(M,N,O,Q,S,T,U) 

#### Partial ranking functions of CR f40(M,N,O,Q,S,T,U) 


### Specialization of cost equations f48/19 
* CE 17 is discarded (unfeasible) 
* CE 16 is refined into CE [22] 


### Cost equations --> "Loop" of f48/19 
* CEs [22] --> Loop 22 

### Ranking functions of CR f48(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) 

#### Partial ranking functions of CR f48(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) 


### Specialization of cost equations f40_loop_cont/20 
* CE 14 is refined into CE [23] 
* CE 15 is refined into CE [24] 


### Cost equations --> "Loop" of f40_loop_cont/20 
* CEs [23] --> Loop 23 
* CEs [24] --> Loop 24 

### Ranking functions of CR f40_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) 

#### Partial ranking functions of CR f40_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) 


### Specialization of cost equations f33/19 
* CE 9 is refined into CE [25,26,27] 


### Cost equations --> "Loop" of f33/19 
* CEs [26,27] --> Loop 25 
* CEs [25] --> Loop 26 

### Ranking functions of CR f33(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) 

#### Partial ranking functions of CR f33(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) 


### Specialization of cost equations f25_loop_cont/20 
* CE 8 is refined into CE [28] 
* CE 7 is refined into CE [29,30] 


### Cost equations --> "Loop" of f25_loop_cont/20 
* CEs [30] --> Loop 27 
* CEs [28] --> Loop 28 
* CEs [29] --> Loop 29 

### Ranking functions of CR f25_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) 

#### Partial ranking functions of CR f25_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) 


### Specialization of cost equations f18/19 
* CE 2 is refined into CE [31,32,33] 


### Cost equations --> "Loop" of f18/19 
* CEs [31,33] --> Loop 30 
* CEs [32] --> Loop 31 

### Ranking functions of CR f18(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) 

#### Partial ranking functions of CR f18(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) 


### Specialization of cost equations f0/19 
* CE 1 is refined into CE [34,35] 


### Cost equations --> "Loop" of f0/19 
* CEs [35] --> Loop 32 
* CEs [34] --> Loop 33 

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

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


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

#### Cost of chains of f25(G,H,I,K,S,T,U):
* Chain [19]: 0
  with precondition: [G+3=0,H=4,I=0,S=2,T=4,U=4] 

* Chain [18]: 0
  with precondition: [G+3=0,H=4,I=0,S=3] 


#### Cost of chains of f40(M,N,O,Q,S,T,U):
* Chain [[20]]...: 1*it(20)+0
  with precondition: [M=3,N+6>=0,O=0] 

* Chain [[20],21]: 1*it(20)+0
  with precondition: [M=3,O=0,S=3,N+6>=0] 

* Chain [21]: 0
  with precondition: [M=3,O=0,S=3,N+6>=0] 


#### Cost of chains of f48(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S):
* Chain [22]: 0
  with precondition: [A=3,B=3,C=0,D=3,E=3,F=3,G+3=0,I=0,M=3,O=0,K=J,K=L] 


#### Cost of chains of f40_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T):
* Chain [24]: 0
  with precondition: [A=3,B=3,C=3,D=0,E=3,F=3,G=3,H+3=0,J=0,N=3,P=0,L=K,L=M] 

* Chain [23]: 0
  with precondition: [A=4,B=3,C=3,D=0,E=3,F=3,G=3,H+3=0,J=0,N=3,P=0,L=K,L=M] 


#### Cost of chains of f33(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S):
* Chain [26]: 1*s(2)+0
  with precondition: [A=3,B=3,C=0,D=3,E=3,F=3,G+3=0,I=0] 

* Chain [25]...: 1*aux(2)+0
  with precondition: [A=3,B=3,C=0,D=3,E=3,F=3,G+3=0,I=0] 


#### Cost of chains of f25_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T):
* Chain [29]: 1*s(5)+0
  with precondition: [A=2,B=3,C=3,D=0,E=3,F=3,G=3,H+3=0,J=0] 

* Chain [28]: 0
  with precondition: [A=3,B=3,C=3,D=0,E=3,F=3,G=3,H+3=0,J=0] 

* Chain [27]...: 1*s(6)+0
  with precondition: [A=2,B=3,C=3,D=0,E=3,F=3,G=3,H+3=0,J=0] 


#### Cost of chains of f18(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S):
* Chain [31]...: 1*s(7)+0
  with precondition: [A=3,B=3,C=0,D=3] 

* Chain [30]: 1*aux(3)+0
  with precondition: [A=3,B=3,C=0,D=3] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S):
* Chain [33]: 1*s(9)+0
  with precondition: [] 

* Chain [32]...: 1*s(10)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S): 
-------------------------------------
* Chain [33] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [32]... with precondition: [] 
    - 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,R,S): inf 
Asymptotic class: infinity 
* Total analysis performed in 137 ms.

