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

#### Computed strongly connected components 
0. recursive  : [f6/32]
1. non_recursive  : [exit_location/1]
2. recursive  : [f11/5]
3. non_recursive  : [f11_loop_cont/2]
4. non_recursive  : [f12/32]
5. non_recursive  : [f6_loop_cont/33]
6. non_recursive  : [f26/32]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f6/32
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f11/5
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f12/32
5. SCC is partially evaluated into f6_loop_cont/33
6. SCC is partially evaluated into f26/32

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

### Specialization of cost equations f6/32 
* CE 5 is refined into CE [14] 
* CE 4 is refined into CE [15] 
* CE 6 is refined into CE [16] 
* CE 2 is refined into CE [17] 
* CE 3 is refined into CE [18] 


### Cost equations --> "Loop" of f6/32 
* CEs [17] --> Loop 14 
* CEs [18] --> Loop 15 
* CEs [14] --> Loop 16 
* CEs [15] --> Loop 17 
* CEs [16] --> Loop 18 

### Ranking functions of CR f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,Z,E1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2) 
* RF of phase [14,15]: [-G+5,H,-I+5,J]

#### Partial ranking functions of CR f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,Z,E1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2) 
* Partial RF of phase [14,15]:
  - RF of loop [14:1,15:1]:
    -G+5
    H
    -I+5
    J


### Specialization of cost equations f11/5 
* CE 13 is refined into CE [19] 
* CE 11 is refined into CE [20] 
* CE 12 is refined into CE [21] 


### Cost equations --> "Loop" of f11/5 
* CEs [20] --> Loop 19 
* CEs [21] --> Loop 20 
* CEs [19] --> Loop 21 

### Ranking functions of CR f11(A,B,C,D,Q1) 

#### Partial ranking functions of CR f11(A,B,C,D,Q1) 


### Specialization of cost equations f12/32 
* CE 9 is refined into CE [22,23,24] 
* CE 10 is refined into CE [25,26,27] 


### Cost equations --> "Loop" of f12/32 
* CEs [24] --> Loop 22 
* CEs [27] --> Loop 23 
* CEs [22,23] --> Loop 24 
* CEs [25,26] --> Loop 25 

### Ranking functions of CR f12(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,E1,Q1) 

#### Partial ranking functions of CR f12(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,E1,Q1) 


### Specialization of cost equations f6_loop_cont/33 
* CE 7 is refined into CE [28,29,30,31] 
* CE 8 is refined into CE [32] 


### Cost equations --> "Loop" of f6_loop_cont/33 
* CEs [29] --> Loop 26 
* CEs [28] --> Loop 27 
* CEs [32] --> Loop 28 
* CEs [31] --> Loop 29 
* CEs [30] --> Loop 30 

### Ranking functions of CR f6_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,E1,F1,G1) 

#### Partial ranking functions of CR f6_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,E1,F1,G1) 


### Specialization of cost equations f26/32 
* CE 1 is refined into CE [33,34,35,36,37,38,39,40,41,42] 


### Cost equations --> "Loop" of f26/32 
* CEs [36,38,40,42] --> Loop 31 
* CEs [33,34,35,37,39,41] --> Loop 32 

### Ranking functions of CR f26(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,E1,Q1) 

#### Partial ranking functions of CR f26(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,E1,Q1) 


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

#### Cost of chains of f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,Z,E1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2):
* Chain [[14,15],18]: 2*it(14)+0
  Such that:aux(9) =< J
it(14) =< aux(9)

  with precondition: [Q1=2,G=I,G+H=5,G+J=5,4>=G,G>=1] 

* Chain [[14,15],17]: 2*it(14)+0
  Such that:aux(10) =< J
aux(11) =< J-Z1
it(14) =< aux(10)
it(14) =< aux(11)

  with precondition: [Q1=3,G=I,R1=S1,R1=T1,F=U1,F=V1,W1=Y1,G+H=5,G+J=5,W1+X1=5,W1+Z1=5,W1+C2=5,4>=W1,G>=1,R1>=B+1,W1>=G+1] 

* Chain [[14,15],16]: 2*it(14)+0
  Such that:aux(12) =< J
aux(13) =< J-Z1
it(14) =< aux(12)
it(14) =< aux(13)

  with precondition: [Q1=3,G=I,R1=S1,R1=T1,F=U1,F=V1,W1=Y1,G+H=5,G+J=5,W1+X1=5,W1+Z1=5,W1+C2=5,4>=W1,G>=1,W1>=G+1,B>=R1+1] 

* Chain [18]: 0
  with precondition: [Q1=2,J=H,G+J=5,I+J=5,4>=J] 

* Chain [17]: 0
  with precondition: [Q1=3,E=F,J=H,A2=K,B2=L,C2=M,R1=S1,R1=T1,E=U1,E=V1,J=X1,J=Z1,G+J=5,I+J=5,J+W1=5,J+Y1=5,4>=J,J>=1,R1>=B+1] 

* Chain [16]: 0
  with precondition: [Q1=3,E=F,J=H,A2=K,B2=L,C2=M,R1=S1,R1=T1,E=U1,E=V1,J=X1,J=Z1,G+J=5,I+J=5,J+W1=5,J+Y1=5,4>=J,J>=1,B>=R1+1] 


#### Cost of chains of f11(A,B,C,D,Q1):
* Chain [[20]]...: 1*it(20)+0
  with precondition: [A=D,A=C,B>=A+1,Q1=2] 

* Chain [[20],21]: 1*it(20)+0
  with precondition: [Q1=2,A=C,A=D,B>=A+1] 

* Chain [[19]]...: 1*it(19)+0
  with precondition: [A=D,A=C,A>=B+1,Q1=2] 

* Chain [[19],21]: 1*it(19)+0
  with precondition: [Q1=2,A=C,A=D,A>=B+1] 

* Chain [21]: 0
  with precondition: [Q1=2,A=C,A=D] 


#### Cost of chains of f12(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,E1,Q1):
* Chain [25]: 1*aux(14)+0
  with precondition: [O=2,P=3,S=4,U=0,D1=4,X=W,X=Y,B>=A+1] 

* Chain [24]: 1*aux(15)+0
  with precondition: [O=2,P=3,S=4,U=0,D1=4,X=W,X=Y,A>=B+1] 

* Chain [23]...: 1*s(3)+0
  with precondition: [O=2,P=3,S=4,U=0,D1=4,X=W,X=Y,B>=A+1] 

* Chain [22]...: 1*s(4)+0
  with precondition: [O=2,P=3,S=4,U=0,D1=4,X=W,X=Y,A>=B+1] 


#### Cost of chains of f6_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,E1,F1,G1):
* Chain [30]...: 1*s(5)+0
  with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,C>=B+1] 

* Chain [29]...: 1*s(6)+0
  with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,B>=C+1] 

* Chain [28]: 0
  with precondition: [A=2,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z] 

* Chain [27]: 1*s(7)+0
  with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,C>=B+1] 

* Chain [26]: 1*s(8)+0
  with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,B>=C+1] 


#### Cost of chains of f26(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,E1,Q1):
* Chain [32]: 1*aux(18)+0
  with precondition: [] 

* Chain [31]...: 1*aux(21)+0
  with precondition: [] 


Closed-form bounds of f26(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,E1,Q1): 
-------------------------------------
* Chain [32] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [31]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f26(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,E1,Q1): inf 
Asymptotic class: infinity 
* Total analysis performed in 447 ms.

