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

#### Computed strongly connected components 
0. recursive  : [f1/28]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f300/24]
3. non_recursive  : [f1_loop_cont/25]
4. non_recursive  : [f2/24]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/28
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f1_loop_cont/25
4. SCC is partially evaluated into f2/24

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

### Specialization of cost equations f1/28 
* CE 9 is refined into CE [12] 
* CE 6 is refined into CE [13] 
* CE 7 is refined into CE [14] 
* CE 8 is refined into CE [15] 
* CE 2 is refined into CE [16] 
* CE 3 is refined into CE [17] 
* CE 4 is refined into CE [18] 
* CE 5 is refined into CE [19] 


### Cost equations --> "Loop" of f1/28 
* CEs [16] --> Loop 12 
* CEs [17] --> Loop 13 
* CEs [18] --> Loop 14 
* CEs [19] --> Loop 15 
* CEs [12] --> Loop 16 
* CEs [13] --> Loop 17 
* CEs [14] --> Loop 18 
* CEs [15] --> Loop 19 

### Ranking functions of CR f1(J,K,L,M,N,O,P,Q,R,S,T,U,V,W,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1) 

#### Partial ranking functions of CR f1(J,K,L,M,N,O,P,Q,R,S,T,U,V,W,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1) 


### Specialization of cost equations f1_loop_cont/25 
* CE 11 is refined into CE [20] 
* CE 10 is refined into CE [21] 


### Cost equations --> "Loop" of f1_loop_cont/25 
* CEs [20] --> Loop 20 
* CEs [21] --> Loop 21 

### Ranking functions of CR f1_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) 

#### Partial ranking functions of CR f1_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y) 


### Specialization of cost equations f2/24 
* CE 1 is refined into CE [22,23,24,25,26,27,28,29,30,31,32,33] 


### Cost equations --> "Loop" of f2/24 
* CEs [32,33] --> Loop 22 
* CEs [30,31] --> Loop 23 
* CEs [23,25,29] --> Loop 24 
* CEs [24,26,28] --> Loop 25 
* CEs [22] --> Loop 26 
* CEs [27] --> Loop 27 

### Ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,H1) 

#### Partial ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,H1) 


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

#### Cost of chains of f1(J,K,L,M,N,O,P,Q,R,S,T,U,V,W,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1):
* Chain [[14,15]]...: 2*it(14)+0
  with precondition: [J>=1] 

* Chain [[14,15],18]: 2*it(14)+0
  with precondition: [H1=2,L=J1,M=K1,J>=1] 

* Chain [[14,15],16]: 2*it(14)+0
  with precondition: [H1=3,J>=1] 

* Chain [[12,13]]...: 2*it(12)+0
  with precondition: [0>=J+1] 

* Chain [[12,13],17]: 2*it(12)+0
  with precondition: [H1=2,T=R1,U=S1,V=T1,0>=J+1] 

* Chain [[12,13],16]: 2*it(12)+0
  with precondition: [H1=3,0>=J+1] 

* Chain [19]: 0
  with precondition: [J=0,H1=2,J1=L,K1=M,L1=N,M1=O,N1=P,O1=Q,P1=R,Q1=S,S1=U,T1=V] 

* Chain [18]: 0
  with precondition: [H1=2,J1=L,K1=M,M1=O,N1=P,P1=R,Q1=S,J>=1] 

* Chain [17]: 0
  with precondition: [H1=2,M1=O,N1=P,P1=R,Q1=S,R1=T,S1=U,T1=V,0>=J+1] 

* Chain [16]: 0
  with precondition: [H1=3] 


#### Cost of chains of f1_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y):
* Chain [21]: 0
  with precondition: [A=2,C=B,C=D,C=E,C=F,C=G,C=H,C=I,C=J] 

* Chain [20]: 0
  with precondition: [A=3,C=B,C=D,C=E,C=F,C=G,C=H,C=I,C=J] 


#### Cost of chains of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,H1):
* Chain [27]: 0
  with precondition: [] 

* Chain [26]: 0
  with precondition: [J=0] 

* Chain [25]: 1*aux(1)+0
  with precondition: [0>=J+1] 

* Chain [24]: 1*aux(2)+0
  with precondition: [J>=1] 

* Chain [23]...: 1*aux(3)+0
  with precondition: [0>=J+1] 

* Chain [22]...: 1*aux(4)+0
  with precondition: [J>=1] 


Closed-form bounds of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,H1): 
-------------------------------------
* Chain [27] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [26] with precondition: [J=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [25] with precondition: [0>=J+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [24] with precondition: [J>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [23]... with precondition: [0>=J+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [22]... with precondition: [J>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,H1): inf 
Asymptotic class: infinity 
* Total analysis performed in 292 ms.

