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

#### Computed strongly connected components 
0. recursive  : [f2/49]
1. recursive  : [f1/30,f2_loop_cont/31]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f1_loop_cont/2]
4. non_recursive  : [f999/30]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/49
1. SCC is partially evaluated into f1/30
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f999/30

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

### Specialization of cost equations f2/49 
* CE 12 is refined into CE [13] 
* CE 7 is refined into CE [14] 
* CE 9 is refined into CE [15] 
* CE 10 is refined into CE [16] 
* CE 11 is refined into CE [17] 
* CE 8 is refined into CE [18] 


### Cost equations --> "Loop" of f2/49 
* CEs [17] --> Loop 13 
* CEs [18] --> Loop 14 
* CEs [13] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [14] --> Loop 17 
* CEs [16] --> Loop 18 

### Ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,T,U,V,W,X,Y,Z,A1,B1,C1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2) 

#### Partial ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,T,U,V,W,X,Y,Z,A1,B1,C1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2) 


### Specialization of cost equations f1/30 
* CE 2 is refined into CE [19,20] 
* CE 6 is refined into CE [21] 
* CE 3 is refined into CE [22,23,24,25,26,27,28] 
* CE 5 is refined into CE [29] 
* CE 4 is refined into CE [30] 


### Cost equations --> "Loop" of f1/30 
* CEs [29] --> Loop 19 
* CEs [30] --> Loop 20 
* CEs [27] --> Loop 21 
* CEs [26] --> Loop 22 
* CEs [25] --> Loop 23 
* CEs [24] --> Loop 24 
* CEs [23] --> Loop 25 
* CEs [22] --> Loop 26 
* CEs [28] --> Loop 27 
* CEs [19] --> Loop 28 
* CEs [21] --> Loop 29 
* CEs [20] --> Loop 30 

### Ranking functions of CR f1(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,E1) 

#### Partial ranking functions of CR f1(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,E1) 
* Partial RF of phase [19,20,21,22,23,24,25,26,27]:
  - RF of loop [19:1]:
    C depends on loops [20:1,21:1,22:1,23:1,24:1,25:1,26:1,27:1] 
  - RF of loop [20:1]:
    C+H depends on loops [21:1,22:1,23:1,24:1,25:1,26:1,27:1] 
  - RF of loop [24:1]:
    C+D+H depends on loops [21:1,22:1,23:1,25:1,26:1,27:1] 
  - RF of loop [26:1]:
    C/2+D/2+H/2+I/2-1/2 depends on loops [21:1,23:1,25:1,27:1] 


### Specialization of cost equations f999/30 
* CE 1 is refined into CE [31,32,33,34] 


### Cost equations --> "Loop" of f999/30 
* CEs [33,34] --> Loop 31 
* CEs [31,32] --> Loop 32 

### Ranking functions of CR f999(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,E1) 

#### Partial ranking functions of CR f999(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,E1) 


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

#### Cost of chains of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,T,U,V,W,X,Y,Z,A1,B1,C1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2):
* Chain [[13,14]]...: 2*it(13)+0
  with precondition: [A=0,B=0,C=0,E1>=2,3>=E1] 

* Chain [[13,14],18]: 2*it(13)+0
  with precondition: [A=0,B=0,C=0,E1=2,F1=1,G1=1,I1=0,J1=0,K1=0,L1=0,M1=0,N1=0,J+Q1=L+O1,G+N+Y+A1=S1+Y1+A2,F+M+X+Z+B1=R1+X1+Z1+B2,H1+O1+P1+T1+U1+V1+W1+1=D+E+H+I+J+K+T+U+V+W,H1>=0,O1>=J+1,H1+T1+U1+2*O1>=2*J+D+H+I+T+U+1,H1+O1+T1+U1+1>=D+H+I+J+T+U] 

* Chain [[13,14],17]: 2*it(13)+0
  with precondition: [A=0,B=0,C=0,E1=2,F1=1,G1=1,I1=0,M1=0,J+Q1=L+O1,G+N+Y+A1=L1+S1+Y1+A2,F+M+X+Z+B1=K1+R1+X1+Z1+B2,D+E+H+I+J+K+T+U+V+W=H1+J1+N1+O1+P1+T1+U1+V1+W1+1,H1>=0,O1>=J,H1+N1+T1+U1+2*O1>=2*J+D+H+I+T+U,H1+N1+O1+T1+U1+1>=D+H+I+J+T+U] 

* Chain [[13,14],16]: 2*it(13)+0
  with precondition: [A=0,B=0,C=0,E1=2,I1=0,J1=0,K1=0,L1=0,N1=0,O1=0,Q1=0,H=M1,L+G1=J+F1,G+N+Y+A1=S1+Y1+A2,F+M+X+Z+B1=R1+X1+Z1+B2,D+E+I+K+L+T+U+V+W=F1+H1+P1+T1+U1+V1+W1,F1>=L+1,H1+T1+U1+2*F1>=2*L+D+I+T+U+2,F1+H1+T1+U1>=D+I+L+T+U] 

* Chain [[13,14],15]: 2*it(13)+0
  with precondition: [A=0,B=0,C=0,E1=3] 

* Chain [18]: 0
  with precondition: [A=0,B=0,C=0,E1=2,F1=1,G1=1,I1=0,J1=0,K1=0,L1=0,M1=0,N1=0,O1=J+1,Q1=L+1,T1=T,U1=U,V1=V,W1=W,X1=X,Y1=Y,Z1=Z,A2=A1,B2=B1,C2=C1,P1=E+K,R1=F+M,S1=G+N,D+H+I=H1+2,D>=1,D+H+I>=2] 

* Chain [17]: 0
  with precondition: [A=0,B=0,C=0,E1=2,F1=1,G1=1,I1=0,M1=0,J1=E,K1=F,L1=G,N1=I,O1=J,P1=K,Q1=L,R1=M,S1=N,T1=T,U1=U,V1=V,W1=W,X1=X,Y1=Y,Z1=Z,A2=A1,B2=B1,C2=C1,D+H=H1+1,D+H>=1] 

* Chain [16]: 0
  with precondition: [A=0,B=0,C=0,E1=2,I1=0,J1=0,K1=0,L1=0,N1=0,O1=0,Q1=0,M1=H,G1=J+1,F1=L+1,T1=T,U1=U,V1=V,W1=W,X1=X,Y1=Y,Z1=Z,A2=A1,B2=B1,C2=C1,P1=E+K,R1=F+M,S1=G+N,D+I=H1+1,D>=1] 

* Chain [15]: 0
  with precondition: [A=0,B=0,C=0,E1=3] 


#### Cost of chains of f1(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,E1):
* Chain [[19,20,21,22,23,24,25,26,27]]...: 17*it(19)+0
  with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 

* Chain [[19,20,21,22,23,24,25,26,27],30]...: 19*it(19)+0
  with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 

* Chain [[19,20,21,22,23,24,25,26,27],29]: 17*it(19)+0
  with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 

* Chain [[19,20,21,22,23,24,25,26,27],28]: 18*it(19)+0
  with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 

* Chain [30]...: 2*s(14)+0
  with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3,A>=1,B>=1] 

* Chain [29]: 0
  with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 

* Chain [28]: 1*s(15)+0
  with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3,A>=1,B>=1] 


#### Cost of chains of f999(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,E1):
* Chain [32]: 1*aux(46)+0
  with precondition: [A=0,B=0,C=0,D=0,E=0,F=0,G=0,I=0,J=0,K=0,L=0,M=0,N=0,O=0,P=0,Q=0,R=0,S=0,T=0,U=0,V=0,W=0,X=0,Y=0,Z=0,A1=0,B1=0,H>=1] 

* Chain [31]...: 1*aux(47)+0
  with precondition: [A=0,B=0,C=0,D=0,E=0,F=0,G=0,I=0,J=0,K=0,L=0,M=0,N=0,O=0,P=0,Q=0,R=0,S=0,T=0,U=0,V=0,W=0,X=0,Y=0,Z=0,A1=0,B1=0,H>=1] 


Closed-form bounds of f999(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,E1): 
-------------------------------------
* Chain [32] with precondition: [A=0,B=0,C=0,D=0,E=0,F=0,G=0,I=0,J=0,K=0,L=0,M=0,N=0,O=0,P=0,Q=0,R=0,S=0,T=0,U=0,V=0,W=0,X=0,Y=0,Z=0,A1=0,B1=0,H>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [31]... with precondition: [A=0,B=0,C=0,D=0,E=0,F=0,G=0,I=0,J=0,K=0,L=0,M=0,N=0,O=0,P=0,Q=0,R=0,S=0,T=0,U=0,V=0,W=0,X=0,Y=0,Z=0,A1=0,B1=0,H>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f999(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,E1): inf 
Asymptotic class: infinity 
* Total analysis performed in 1316 ms.

