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

#### Computed strongly connected components 
0. recursive  : [f9/32]
1. non_recursive  : [exit_location/1]
2. recursive  : [f5/27]
3. non_recursive  : [f0/19]
4. non_recursive  : [f12/19]
5. non_recursive  : [f5_loop_cont/20]
6. non_recursive  : [f9_loop_cont/20]
7. non_recursive  : [f6/19]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f9/32
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f5/27
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into f5_loop_cont/20
6. SCC is partially evaluated into f9_loop_cont/20
7. SCC is partially evaluated into f6/19

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

### Specialization of cost equations f9/32 
* CE 3 is refined into CE [14] 
* CE 4 is refined into CE [15] 
* CE 2 is refined into CE [16] 


### Cost equations --> "Loop" of f9/32 
* CEs [16] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR f9(A,B,C,D,E,F,G,H,I,J,L,M,N,O,Q,R,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1) 
* RF of phase [14]: [-B+17,-C+16]

#### Partial ranking functions of CR f9(A,B,C,D,E,F,G,H,I,J,L,M,N,O,Q,R,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    -B+17
    -C+16


### Specialization of cost equations f5/27 
* CE 10 is refined into CE [17] 
* CE 7 is refined into CE [18] 
* CE 9 is refined into CE [19] 
* CE 8 is refined into CE [20] 


### Cost equations --> "Loop" of f5/27 
* CEs [20] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [18] --> Loop 19 
* CEs [19] --> Loop 20 

### Ranking functions of CR f5(E,F,G,H,I,J,K,L,M,N,O,P,Q,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1) 
* RF of phase [17]: [F+1]

#### Partial ranking functions of CR f5(E,F,G,H,I,J,K,L,M,N,O,P,Q,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1) 
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    F+1


### Specialization of cost equations f5_loop_cont/20 
* CE 13 is refined into CE [21] 
* CE 12 is refined into CE [22] 
* CE 11 is refined into CE [23] 


### Cost equations --> "Loop" of f5_loop_cont/20 
* CEs [21] --> Loop 21 
* CEs [22] --> Loop 22 
* CEs [23] --> Loop 23 

### Ranking functions of CR f5_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 f5_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 f9_loop_cont/20 
* CE 6 is refined into CE [24,25,26,27,28,29] 
* CE 5 is refined into CE [30] 


### Cost equations --> "Loop" of f9_loop_cont/20 
* CEs [28] --> Loop 24 
* CEs [25,26] --> Loop 25 
* CEs [27] --> Loop 26 
* CEs [24] --> Loop 27 
* CEs [29] --> Loop 28 
* CEs [30] --> Loop 29 

### Ranking functions of CR f9_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 f9_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 f6/19 
* CE 1 is refined into CE [31,32,33,34,35,36,37] 


### Cost equations --> "Loop" of f6/19 
* CEs [31,32,33,34,35,36,37] --> Loop 30 

### Ranking functions of CR f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,B1) 

#### Partial ranking functions of CR f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,B1) 


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

#### Cost of chains of f9(A,B,C,D,E,F,G,H,I,J,L,M,N,O,Q,R,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1):
* Chain [[14],16]: 1*it(14)+0
  Such that:it(14) =< -C+16

  with precondition: [A=17,B1=4,C+1=B,15>=C,C>=0] 

* Chain [[14],15]: 1*it(14)+0
  Such that:it(14) =< -B+17

  with precondition: [A=17,B1=5,C1=17,D1=16,F1=1,I1=0,Q1=14,C+1=B,H1=L1,E1=P1,15>=C,C>=0] 

* Chain [16]: 0
  with precondition: [A=17,B1=4,B=C+1,B>=1] 


#### Cost of chains of f5(E,F,G,H,I,J,K,L,M,N,O,P,Q,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1):
* Chain [[17],20]: 1*it(17)+0
  Such that:it(17) =< -E+N1

  with precondition: [H=0,B1=3,F1=0,L1=0,K=I1,J1=K1,C1=N1,C1+D1=E+F,E>=0,C1>=E+1,E+F>=C1] 

* Chain [[17],19]: 1*it(17)+0
  Such that:it(17) =< -E+C1

  with precondition: [H=0,B1=2,F1=J1,C1=N1+1,Q=O1,C1+D1=E+F,E>=0,C1>=E+1,E+F>=C1] 

* Chain [[17],18]: 1*it(17)+0
  Such that:it(17) =< F+1

  with precondition: [H=0,B1=4,E>=0,F>=0] 

* Chain [20]: 0
  with precondition: [H=0,N=0,B1=3,F1=0,L1=0,E1=G,I1=K,M1=O,E=C1,F=D1,M=J1,M=K1,E=N1,E>=0,F>=0] 

* Chain [19]: 0
  with precondition: [B1=2,F1=G,J1=L,K1=M,L1=N,M1=O,N1=P,O1=Q,E=C1,F=D1,E>=1,F>=0] 

* Chain [18]: 0
  with precondition: [B1=4] 


#### Cost of chains of f5_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T):
* Chain [23]: 0
  with precondition: [A=2,B=17] 

* Chain [22]: 0
  with precondition: [A=3,B=17] 

* Chain [21]: 0
  with precondition: [A=4,B=17] 


#### Cost of chains of f9_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T):
* Chain [29]: 0
  with precondition: [A=4,B=17] 

* Chain [28]: 0
  with precondition: [A=5,B=17] 

* Chain [27]: 0
  with precondition: [A=5,B=17,I=0,O=0,F>=0,G>=0] 

* Chain [26]: 1*s(1)+0
  Such that:s(1) =< G+1

  with precondition: [A=5,B=17,I=0,F>=0,G>=0] 

* Chain [25]: 2*s(2)+0
  Such that:aux(1) =< G
s(2) =< aux(1)

  with precondition: [A=5,B=17,I=0,F>=0,G>=1] 

* Chain [24]: 0
  with precondition: [A=5,B=17,F>=1,G>=0] 


#### Cost of chains of f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,B1):
* Chain [30]: 1*aux(3)+0
  with precondition: [] 


Closed-form bounds of f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,B1): 
-------------------------------------
* Chain [30] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,B1): inf 
Asymptotic class: infinity 
* Total analysis performed in 290 ms.

