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

#### Computed strongly connected components 
0. recursive  : [f1/29]
1. non_recursive  : [exit_location/1]
2. recursive  : [f12/9]
3. non_recursive  : [f12_loop_cont/2]
4. non_recursive  : [f1_loop_cont/30]
5. non_recursive  : [f9/29]
6. non_recursive  : [f8/29]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/29
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f12/9
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f1_loop_cont/30
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into f8/29

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

### Specialization of cost equations f1/29 
* CE 7 is refined into CE [16] 
* CE 6 is refined into CE [17] 
* CE 5 is refined into CE [18] 
* CE 4 is refined into CE [19] 
* CE 8 is refined into CE [20] 
* CE 3 is refined into CE [21] 


### Cost equations --> "Loop" of f1/29 
* CEs [21] --> Loop 15 
* CEs [16] --> Loop 16 
* CEs [17] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [19] --> Loop 19 
* CEs [20] --> Loop 20 

### Ranking functions of CR f1(B,C,D,I,J,K,L,M,N,O,Q,Y,Z,B1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2,J2) 
* RF of phase [15]: [C-J,I-J]

#### Partial ranking functions of CR f1(B,C,D,I,J,K,L,M,N,O,Q,Y,Z,B1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2,J2) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    C-J
    I-J


### Specialization of cost equations f12/9 
* CE 15 is refined into CE [22] 
* CE 14 is refined into CE [23] 
* CE 12 is refined into CE [24] 
* CE 13 is refined into CE [25] 
* CE 11 is refined into CE [26] 


### Cost equations --> "Loop" of f12/9 
* CEs [23] --> Loop 21 
* CEs [24] --> Loop 22 
* CEs [25] --> Loop 23 
* CEs [26] --> Loop 24 
* CEs [22] --> Loop 25 

### Ranking functions of CR f12(A,B,C,D,E,F,G,H,V1) 

#### Partial ranking functions of CR f12(A,B,C,D,E,F,G,H,V1) 


### Specialization of cost equations f1_loop_cont/30 
* CE 10 is refined into CE [27,28,29,30,31] 
* CE 9 is refined into CE [32] 


### Cost equations --> "Loop" of f1_loop_cont/30 
* CEs [29] --> Loop 26 
* CEs [28] --> Loop 27 
* CEs [27] --> Loop 28 
* CEs [32] --> Loop 29 
* CEs [31] --> Loop 30 
* CEs [30] --> Loop 31 

### 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,Z,A1,B1,C1,D1) 

#### 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,Z,A1,B1,C1,D1) 


### Specialization of cost equations f8/29 
* CE 1 is refined into CE [33] 
* CE 2 is refined into CE [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59] 


### Cost equations --> "Loop" of f8/29 
* CEs [38,41,44,47,50,53,56,59] --> Loop 32 
* CEs [37,40,43,46,49,52,55,58] --> Loop 33 
* CEs [33,34,35,36,39,42,45,48,51,54,57] --> Loop 34 

### Ranking functions of CR f8(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,Z,A1,B1,V1) 

#### Partial ranking functions of CR f8(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,Z,A1,B1,V1) 


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

#### Cost of chains of f1(B,C,D,I,J,K,L,M,N,O,Q,Y,Z,B1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2,J2):
* Chain [[15],20]: 1*it(15)+0
  Such that:it(15) =< C-J

  with precondition: [V1=2,C=I,K=M,J>=2,C>=J+1] 

* Chain [[15],19]: 1*it(15)+0
  Such that:it(15) =< -J+F2+1

  with precondition: [V1=3,C=I,K=M,C=F2+1,0>=W1+1,0>=Y1+1,J>=2,X1>=2,A2>=2,C>=J+1,J2>=X1] 

* Chain [[15],18]: 1*it(15)+0
  Such that:it(15) =< -J+F2+1

  with precondition: [V1=3,C=I,K=M,C=F2+1,0>=W1+1,J>=2,X1>=2,Y1>=1,A2>=2,C>=J+1,J2>=X1] 

* Chain [[15],17]: 1*it(15)+0
  Such that:it(15) =< -J+F2+1

  with precondition: [V1=3,C=I,K=M,C=F2+1,0>=Y1+1,J>=2,W1>=1,X1>=2,A2>=2,C>=J+1,J2>=X1] 

* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< C-J

  with precondition: [V1=3,C=I,K=M,C=F2+1,J>=2,W1>=1,X1>=2,Y1>=1,A2>=2,C>=J+1,J2>=X1] 

* Chain [20]: 0
  with precondition: [V1=2,I=C,M=K,J>=2,I>=J] 

* Chain [19]: 0
  with precondition: [V1=3,I=C,I=J,M=K,E2=N,F2=O,M=W1,0>=M+1,0>=Y1+1,I>=2,X1>=2,A2>=2,J2>=X1] 

* Chain [18]: 0
  with precondition: [V1=3,I=C,I=J,M=K,E2=N,F2=O,M=W1,0>=M+1,I>=2,X1>=2,Y1>=1,A2>=2,J2>=X1] 

* Chain [17]: 0
  with precondition: [V1=3,I=C,I=J,M=K,E2=N,F2=O,M=W1,0>=Y1+1,I>=2,M>=1,X1>=2,A2>=2,J2>=X1] 

* Chain [16]: 0
  with precondition: [V1=3,I=C,I=J,M=K,E2=N,F2=O,M=W1,I>=2,M>=1,X1>=2,Y1>=1,A2>=2,J2>=X1] 


#### Cost of chains of f12(A,B,C,D,E,F,G,H,V1):
* Chain [[23,24]]...: 2*it(23)+0
  with precondition: [A>=0,0>=B+1,V1=2] 

* Chain [[23,24],25]: 2*it(23)+0
  with precondition: [V1=2,0>=B+1,A>=0] 

* Chain [[21,22]]...: 2*it(21)+0
  with precondition: [A>=0,B>=1,V1=2] 

* Chain [[21,22],25]: 2*it(21)+0
  with precondition: [V1=2,A>=0,B>=1] 

* Chain [25]: 0
  with precondition: [V1=2] 


#### 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,Z,A1,B1,C1,D1):
* Chain [31]...: 2*s(1)+0
  with precondition: [A=3,T=2,0>=C+1,B>=0] 

* Chain [30]...: 2*s(2)+0
  with precondition: [A=3,T=2,B>=0,C>=1] 

* Chain [29]: 0
  with precondition: [A=2,T=2] 

* Chain [28]: 0
  with precondition: [A=3,T=2] 

* Chain [27]: 2*s(3)+0
  with precondition: [A=3,T=2,0>=C+1,B>=0] 

* Chain [26]: 2*s(4)+0
  with precondition: [A=3,T=2,B>=0,C>=1] 


#### Cost of chains of f8(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,Z,A1,B1,V1):
* Chain [34]: 1*aux(1)+0
  with precondition: [] 

* Chain [33]: 1*aux(2)+0
  with precondition: [A>=0] 

* Chain [32]...: 1*aux(3)+0
  with precondition: [A>=0] 


Closed-form bounds of f8(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,Z,A1,B1,V1): 
-------------------------------------
* Chain [34] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [33] with precondition: [A>=0] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [32]... with precondition: [A>=0] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f8(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,Z,A1,B1,V1): inf 
Asymptotic class: infinity 
* Total analysis performed in 445 ms.

