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

#### Computed strongly connected components 
0. recursive  : [f7/39]
1. non_recursive  : [exit_location/1]
2. recursive  : [f62/39]
3. non_recursive  : [f118/21]
4. non_recursive  : [f62_loop_cont/22]
5. non_recursive  : [f7_loop_cont/22]
6. non_recursive  : [f0/21]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f7/39
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f62/39
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f62_loop_cont/22
5. SCC is partially evaluated into f7_loop_cont/22
6. SCC is partially evaluated into f0/21

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

### Specialization of cost equations f7/39 
* CE 3 is refined into CE [12] 
* CE 4 is refined into CE [13] 
* CE 2 is refined into CE [14] 


### Cost equations --> "Loop" of f7/39 
* CEs [14] --> Loop 12 
* CEs [12] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR f7(B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2) 
* RF of phase [12]: [-B+8]

#### Partial ranking functions of CR f7(B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    -B+8


### Specialization of cost equations f62/39 
* CE 9 is refined into CE [15] 
* CE 8 is refined into CE [16] 
* CE 7 is refined into CE [17] 


### Cost equations --> "Loop" of f62/39 
* CEs [17] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [16] --> Loop 17 

### Ranking functions of CR f62(B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2) 
* RF of phase [15]: [-B+8]

#### Partial ranking functions of CR f62(B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    -B+8


### Specialization of cost equations f62_loop_cont/22 
* CE 11 is refined into CE [18] 
* CE 10 is refined into CE [19] 


### Cost equations --> "Loop" of f62_loop_cont/22 
* CEs [18] --> Loop 18 
* CEs [19] --> Loop 19 

### Ranking functions of CR f62_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V) 

#### Partial ranking functions of CR f62_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V) 


### Specialization of cost equations f7_loop_cont/22 
* CE 6 is refined into CE [20,21,22,23] 
* CE 5 is refined into CE [24] 


### Cost equations --> "Loop" of f7_loop_cont/22 
* CEs [21] --> Loop 20 
* CEs [20,23] --> Loop 21 
* CEs [22] --> Loop 22 
* CEs [24] --> Loop 23 

### Ranking functions of CR f7_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V) 

#### Partial ranking functions of CR f7_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V) 


### Specialization of cost equations f0/21 
* CE 1 is refined into CE [25,26,27,28] 


### Cost equations --> "Loop" of f0/21 
* CEs [25,26,27,28] --> Loop 24 

### Ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L1) 

#### 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,T,L1) 


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

#### Cost of chains of f7(B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< -B+8

  with precondition: [L1=3,7>=B,B>=0] 

* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< -B+8

  with precondition: [L1=4,M1=0,Z1+3196=0,P1=R1+Y1,N1=T1+W1,N1+T1=V1,P1+R1=X1,7>=B,B>=0] 

* Chain [14]: 0
  with precondition: [L1=3,B>=0] 


#### Cost of chains of f62(B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2):
* Chain [[15],17]: 1*it(15)+0
  Such that:it(15) =< -B+8

  with precondition: [L1=2,M1=8,Z1+3196=0,P1=R1+Y1,N1=T1+W1,N1+T1=V1,P1+R1=X1,7>=B] 

* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< -B+8

  with precondition: [L1=3,7>=B] 

* Chain [17]: 0
  with precondition: [L1=2,N1=C,O1=D,P1=E,Q1=F,R1=G,S1=H,T1=I,U1=J,V1=K,W1=L,X1=M,Y1=N,Z1=O,A2=P,B2=Q,C2=R,D2=S,E2=T,B=M1,B>=8] 

* Chain [16]: 0
  with precondition: [L1=3] 


#### Cost of chains of f62_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V):
* Chain [19]: 0
  with precondition: [A=2,B=8] 

* Chain [18]: 0
  with precondition: [A=3,B=8] 


#### Cost of chains of f7_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V):
* Chain [23]: 0
  with precondition: [A=3,B=8] 

* Chain [22]: 0
  with precondition: [A=4,B=8] 

* Chain [21]: 2*s(1)+0
  Such that:aux(1) =< -C+8
s(1) =< aux(1)

  with precondition: [A=4,B=8,7>=C] 

* Chain [20]: 0
  with precondition: [A=4,B=8,C>=8] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L1):
* Chain [24]: 40
  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,T,L1): 
-------------------------------------
* Chain [24] with precondition: [] 
    - Upper bound: 40 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L1): 40 
Asymptotic class: constant 
* Total analysis performed in 283 ms.

