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

#### Computed strongly connected components 
0. recursive  : [l1/7]
1. non_recursive  : [exit_location/1]
2. recursive  : [l2/3]
3. recursive  : [l3/3]
4. non_recursive  : [l3_loop_cont/2]
5. non_recursive  : [l2_loop_cont/7]
6. non_recursive  : [l1_loop_cont/7]
7. non_recursive  : [l0/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l1/7
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into l2/3
3. SCC is partially evaluated into l3/3
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into l2_loop_cont/7
6. SCC is partially evaluated into l1_loop_cont/7
7. SCC is partially evaluated into l0/6

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

### Specialization of cost equations l1/7 
* 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 l1/7 
* CEs [16] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR l1(F,X,Y,Z,A1,B1,C1) 
* RF of phase [14]: [Y]

#### Partial ranking functions of CR l1(F,X,Y,Z,A1,B1,C1) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    Y


### Specialization of cost equations l2/3 
* CE 8 is refined into CE [17] 
* CE 9 is refined into CE [18] 
* CE 7 is refined into CE [19] 


### Cost equations --> "Loop" of l2/3 
* CEs [19] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [18] --> Loop 19 

### Ranking functions of CR l2(F,Z,A1) 
* RF of phase [17]: [F]

#### Partial ranking functions of CR l2(F,Z,A1) 
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    F


### Specialization of cost equations l3/3 
* CE 13 is refined into CE [20] 
* CE 12 is refined into CE [21] 


### Cost equations --> "Loop" of l3/3 
* CEs [21] --> Loop 20 
* CEs [20] --> Loop 21 

### Ranking functions of CR l3(A,B,Z) 

#### Partial ranking functions of CR l3(A,B,Z) 


### Specialization of cost equations l2_loop_cont/7 
* CE 11 is refined into CE [22,23,24] 
* CE 10 is refined into CE [25] 


### Cost equations --> "Loop" of l2_loop_cont/7 
* CEs [23] --> Loop 22 
* CEs [22] --> Loop 23 
* CEs [25] --> Loop 24 
* CEs [24] --> Loop 25 

### Ranking functions of CR l2_loop_cont(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR l2_loop_cont(A,B,C,D,E,F,G) 


### Specialization of cost equations l1_loop_cont/7 
* CE 6 is refined into CE [26,27,28,29,30,31,32,33] 
* CE 5 is refined into CE [34] 


### Cost equations --> "Loop" of l1_loop_cont/7 
* CEs [27,28] --> Loop 26 
* CEs [29] --> Loop 27 
* CEs [32] --> Loop 28 
* CEs [31] --> Loop 29 
* CEs [26] --> Loop 30 
* CEs [34] --> Loop 31 
* CEs [30] --> Loop 32 
* CEs [33] --> Loop 33 

### Ranking functions of CR l1_loop_cont(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR l1_loop_cont(A,B,C,D,E,F,G) 


### Specialization of cost equations l0/6 
* CE 1 is refined into CE [35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50] 


### Cost equations --> "Loop" of l0/6 
* CEs [42,43] --> Loop 34 
* CEs [50] --> Loop 35 
* CEs [49] --> Loop 36 
* CEs [36,37,38,41] --> Loop 37 
* CEs [39,40] --> Loop 38 
* CEs [48] --> Loop 39 
* CEs [47] --> Loop 40 
* CEs [44] --> Loop 41 
* CEs [46] --> Loop 42 
* CEs [45] --> Loop 43 
* CEs [35] --> Loop 44 

### Ranking functions of CR l0(A,B,F,X,Y,Z) 

#### Partial ranking functions of CR l0(A,B,F,X,Y,Z) 


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

#### Cost of chains of l1(F,X,Y,Z,A1,B1,C1):
* Chain [[14],16]: 1*it(14)+0
  Such that:it(14) =< Y

  with precondition: [Z=2,Y>=1] 

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

  with precondition: [Z=4,C1=0,Y>=1] 

* Chain [16]: 0
  with precondition: [Z=2] 

* Chain [15]: 0
  with precondition: [Z=4,A1=F,B1=X,Y=C1,0>=Y] 


#### Cost of chains of l2(F,Z,A1):
* Chain [[17],19]: 1*it(17)+0
  Such that:it(17) =< F

  with precondition: [Z=2,F>=1] 

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

  with precondition: [Z=3,A1=0,F>=1] 

* Chain [19]: 0
  with precondition: [Z=2] 

* Chain [18]: 0
  with precondition: [Z=3,F=A1,0>=F] 


#### Cost of chains of l3(A,B,Z):
* Chain [[20]]...: 1*it(20)+0
  with precondition: [A>=1,Z=2] 

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

* Chain [21]: 0
  with precondition: [Z=2] 


#### Cost of chains of l2_loop_cont(A,B,C,D,E,F,G):
* Chain [25]...: 1*s(1)+0
  with precondition: [A=3,B>=1] 

* Chain [24]: 0
  with precondition: [A=2] 

* Chain [23]: 0
  with precondition: [A=3] 

* Chain [22]: 1*s(2)+0
  with precondition: [A=3,B>=1] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F,G):
* Chain [33]...: 1*s(3)+0
  with precondition: [A=4,0>=D,B>=1] 

* Chain [32]...: 1*s(4)+1*s(5)+0
  Such that:s(4) =< D

  with precondition: [A=4,B>=1,D>=1] 

* Chain [31]: 0
  with precondition: [A=2] 

* Chain [30]: 0
  with precondition: [A=4] 

* Chain [29]: 0
  with precondition: [A=4,0>=D] 

* Chain [28]: 1*s(6)+0
  with precondition: [A=4,0>=D,B>=1] 

* Chain [27]: 1*s(7)+1*s(8)+0
  Such that:s(7) =< D

  with precondition: [A=4,B>=1,D>=1] 

* Chain [26]: 2*s(9)+0
  Such that:aux(1) =< D
s(9) =< aux(1)

  with precondition: [A=4,D>=1] 


#### Cost of chains of l0(A,B,F,X,Y,Z):
* Chain [44]: 0
  with precondition: [] 

* Chain [43]: 0
  with precondition: [0>=F,0>=Y] 

* Chain [42]: 1*s(11)+0
  with precondition: [0>=F,0>=Y,A>=1] 

* Chain [41]: 0
  with precondition: [0>=Y] 

* Chain [40]: 1*s(12)+1*s(13)+0
  Such that:s(12) =< F

  with precondition: [0>=Y,A>=1,F>=1] 

* Chain [39]: 2*s(15)+0
  Such that:s(14) =< F
s(15) =< s(14)

  with precondition: [0>=Y,F>=1] 

* Chain [38]: 2*s(16)+3*s(17)+0
  Such that:aux(2) =< Y
s(16) =< aux(2)

  with precondition: [A>=1,Y>=1] 

* Chain [37]: 4*s(21)+2*s(26)+0
  Such that:aux(3) =< Y
s(21) =< aux(3)

  with precondition: [Y>=1] 

* Chain [36]...: 1*s(27)+0
  with precondition: [0>=F,0>=Y,A>=1] 

* Chain [35]...: 1*s(28)+1*s(29)+0
  Such that:s(28) =< F

  with precondition: [0>=Y,A>=1,F>=1] 

* Chain [34]...: 2*s(30)+3*s(31)+0
  Such that:aux(4) =< Y
s(30) =< aux(4)

  with precondition: [A>=1,Y>=1] 


Closed-form bounds of l0(A,B,F,X,Y,Z): 
-------------------------------------
* Chain [44] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [43] with precondition: [0>=F,0>=Y] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [42] with precondition: [0>=F,0>=Y,A>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [41] with precondition: [0>=Y] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [40] with precondition: [0>=Y,A>=1,F>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [39] with precondition: [0>=Y,F>=1] 
    - Upper bound: 2*F 
    - Complexity: n 
* Chain [38] with precondition: [A>=1,Y>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [37] with precondition: [Y>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [36]... with precondition: [0>=F,0>=Y,A>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [35]... with precondition: [0>=Y,A>=1,F>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [34]... with precondition: [A>=1,Y>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,F,X,Y,Z): inf 
Asymptotic class: infinity 
* Total analysis performed in 109 ms.

