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

#### Computed strongly connected components 
0. recursive  : [f1/31]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f2/22]
3. non_recursive  : [f3/22]
4. non_recursive  : [f1_loop_cont/23]
5. non_recursive  : [f300/22]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/31
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f1_loop_cont/23
5. SCC is partially evaluated into f300/22

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

### Specialization of cost equations f1/31 
* CE 11 is refined into CE [15] 
* CE 9 is refined into CE [16] 
* CE 10 is refined into CE [17] 
* CE 7 is refined into CE [18] 
* CE 8 is refined into CE [19] 
* CE 6 is refined into CE [20] 
* CE 5 is refined into CE [21] 
* CE 3 is refined into CE [22] 
* CE 4 is refined into CE [23] 
* CE 2 is refined into CE [24] 


### Cost equations --> "Loop" of f1/31 
* CEs [21] --> Loop 15 
* CEs [22] --> Loop 16 
* CEs [23] --> Loop 17 
* CEs [24] --> Loop 18 
* CEs [15] --> Loop 19 
* CEs [16] --> Loop 20 
* CEs [17] --> Loop 21 
* CEs [18] --> Loop 22 
* CEs [19] --> Loop 23 
* CEs [20] --> Loop 24 

### Ranking functions of CR f1(F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1) 

#### Partial ranking functions of CR f1(F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1) 


### Specialization of cost equations f1_loop_cont/23 
* CE 14 is refined into CE [25] 
* CE 13 is refined into CE [26] 
* CE 12 is refined into CE [27] 


### Cost equations --> "Loop" of f1_loop_cont/23 
* CEs [25] --> Loop 25 
* CEs [26] --> Loop 26 
* CEs [27] --> Loop 27 

### 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) 

#### 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) 


### Specialization of cost equations f300/22 
* CE 1 is refined into CE [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49] 


### Cost equations --> "Loop" of f300/22 
* CEs [47,48,49] --> Loop 28 
* CEs [41,42,43] --> Loop 29 
* CEs [44,45,46] --> Loop 30 
* CEs [38,39,40] --> Loop 31 
* CEs [30] --> Loop 32 
* CEs [34] --> Loop 33 
* CEs [37] --> Loop 34 
* CEs [33] --> Loop 35 
* CEs [32] --> Loop 36 
* CEs [36] --> Loop 37 
* CEs [31] --> Loop 38 
* CEs [29] --> Loop 39 
* CEs [28] --> Loop 40 
* CEs [35] --> Loop 41 

### Ranking functions of CR f300(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,E1) 

#### Partial ranking functions of CR f300(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,E1) 


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

#### Cost of chains of f1(F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1):
* Chain [[18]]...: 1*it(18)+0
  with precondition: [F+1=G,H=256] 

* Chain [[18],19]: 1*it(18)+0
  with precondition: [H=256,E1=4,F+1=G] 

* Chain [[17]]...: 1*it(17)+0
  with precondition: [G>=F+2,Q=256] 

* Chain [[17],19]: 1*it(17)+0
  with precondition: [Q=256,E1=4,G>=F+2] 

* Chain [[16]]...: 1*it(16)+0
  with precondition: [F+1=G,0>=H] 

* Chain [[16],19]: 1*it(16)+0
  with precondition: [E1=4,F+1=G,0>=H] 

* Chain [[15]]...: 1*it(15)+0
  with precondition: [G>=F+2,0>=Q] 

* Chain [[15],19]: 1*it(15)+0
  with precondition: [E1=4,0>=Q,G>=F+2] 

* Chain [24]: 0
  with precondition: [E1=2,P1=0,Q1=0,R1=0,F1=H,I1=K,J1=L,K1=M,L1=N,M1=O,N1=P,O1=Q,S1=U,F>=G] 

* Chain [23]: 0
  with precondition: [E1=3,G=F+1,O1=Q,H=F1,H=P1,H=Q1,H=R1,255>=H,H>=1] 

* Chain [22]: 0
  with precondition: [E1=3,G=F+1,O1=Q,H=F1,H=P1,H=Q1,H=R1,H>=257] 

* Chain [21]: 0
  with precondition: [E1=3,F1=H,Q=O1,Q=P1,Q=Q1,Q=R1,255>=Q,Q>=1,G>=F+2] 

* Chain [20]: 0
  with precondition: [E1=3,F1=H,Q=O1,Q=P1,Q=Q1,Q=R1,Q>=257,G>=F+2] 

* Chain [19]: 0
  with precondition: [E1=4] 


#### 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):
* Chain [27]: 0
  with precondition: [A=2] 

* Chain [26]: 0
  with precondition: [A=3] 

* Chain [25]: 0
  with precondition: [A=4] 


#### Cost of chains of f300(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,E1):
* Chain [41]: 0
  with precondition: [] 

* Chain [40]: 1*s(1)+0
  with precondition: [H=256,G=F+1] 

* Chain [39]: 1*s(2)+0
  with precondition: [Q=256,G>=F+2] 

* Chain [38]: 0
  with precondition: [G=F+1,255>=H,H>=1] 

* Chain [37]: 1*s(3)+0
  with precondition: [G=F+1,0>=H] 

* Chain [36]: 0
  with precondition: [G=F+1,H>=257] 

* Chain [35]: 0
  with precondition: [255>=Q,Q>=1,G>=F+2] 

* Chain [34]: 1*s(4)+0
  with precondition: [0>=Q,G>=F+2] 

* Chain [33]: 0
  with precondition: [Q>=257,G>=F+2] 

* Chain [32]: 0
  with precondition: [F>=G] 

* Chain [31]...: 1*aux(1)+0
  with precondition: [H=256,G=F+1] 

* Chain [30]...: 1*aux(2)+0
  with precondition: [Q=256,G>=F+2] 

* Chain [29]...: 1*aux(3)+0
  with precondition: [G=F+1,0>=H] 

* Chain [28]...: 1*aux(4)+0
  with precondition: [0>=Q,G>=F+2] 


Closed-form bounds of f300(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,E1): 
-------------------------------------
* Chain [41] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [40] with precondition: [H=256,G=F+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [39] with precondition: [Q=256,G>=F+2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [38] with precondition: [G=F+1,255>=H,H>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [37] with precondition: [G=F+1,0>=H] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [36] with precondition: [G=F+1,H>=257] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [255>=Q,Q>=1,G>=F+2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [0>=Q,G>=F+2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [33] with precondition: [Q>=257,G>=F+2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [32] with precondition: [F>=G] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [31]... with precondition: [H=256,G=F+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [30]... with precondition: [Q=256,G>=F+2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [29]... with precondition: [G=F+1,0>=H] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [28]... with precondition: [0>=Q,G>=F+2] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f300(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,E1): inf 
Asymptotic class: infinity 
* Total analysis performed in 407 ms.

