WARNING: Excluded non-linear constraints:[G=A*A+D]

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

#### Computed strongly connected components 
0. recursive  : [l2/8]
1. recursive  : [l1/6,l2_loop_cont/7]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [l1_loop_cont/2]
4. non_recursive  : [l0/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l2/8
1. SCC is partially evaluated into l1/6
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into l0/6

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

### Specialization of cost equations l2/8 
* CE 8 is refined into CE [9] 
* CE 7 is refined into CE [10] 
* CE 6 is refined into CE [11] 


### Cost equations --> "Loop" of l2/8 
* CEs [11] --> Loop 8 
* CEs [9] --> Loop 9 
* CEs [10] --> Loop 10 

### Ranking functions of CR l2(B,C,D,E,F,G,H,I) 
* RF of phase [8]: [B]

#### Partial ranking functions of CR l2(B,C,D,E,F,G,H,I) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    B


### Specialization of cost equations l1/6 
* CE 2 is refined into CE [12,13] 
* CE 5 is refined into CE [14] 
* CE 3 is refined into CE [15,16] 
* CE 4 is refined into CE [17] 


### Cost equations --> "Loop" of l1/6 
* CEs [15] --> Loop 11 
* CEs [17] --> Loop 12 
* CEs [16] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [12,14] --> Loop 15 

### Ranking functions of CR l1(A,B,C,D,E,F) 

#### Partial ranking functions of CR l1(A,B,C,D,E,F) 
* Partial RF of phase [11,12,13]:
  - RF of loop [11:1,13:1]:
    E
  - RF of loop [12:1]:
    A depends on loops [11:1,13:1] 


### Specialization of cost equations l0/6 
* CE 1 is refined into CE [18,19,20] 


### Cost equations --> "Loop" of l0/6 
* CEs [19,20] --> Loop 16 
* CEs [18] --> Loop 17 

### Ranking functions of CR l0(A,B,C,D,E,F) 

#### Partial ranking functions of CR l0(A,B,C,D,E,F) 


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

#### Cost of chains of l2(B,C,D,E,F,G,H,I):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< B

  with precondition: [F=2,H=3*E,2*H=3*G,H=3*I+3,B>=1,H>=3] 

* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< B

  with precondition: [F=3,B>=1] 

* Chain [10]: 0
  with precondition: [F=2,2*E=G,3*E=H,E=I+1,E>=1] 

* Chain [9]: 0
  with precondition: [F=3] 


#### Cost of chains of l1(A,B,C,D,E,F):
* Chain [[11,12,13],15]: 2*it(11)+1*it(12)+1*s(3)+0
  Such that:aux(5) =< 2*E
aux(55) =< A
aux(56) =< E
it(11) =< aux(56)
aux(14) =< aux(5)*(1/2)
aux(8) =< it(11)*aux(14)
it(12) =< aux(8)+aux(8)+aux(55)

  with precondition: [F=3,A>=0,E>=0,A+E>=1] 

* Chain [[11,12,13],14]: 2*it(11)+1*it(12)+1*s(3)+1*s(5)+0
  Such that:aux(61) =< 2*E
aux(125) =< A
aux(127) =< E
it(11) =< aux(127)
aux(70) =< aux(61)*(1/2)
aux(64) =< it(11)*aux(70)
it(12) =< aux(64)+aux(64)+aux(125)

  with precondition: [F=3,A>=0,E>=0,A+E>=1] 

* Chain [15]: 0
  with precondition: [F=3,A>=0,E>=0] 

* Chain [14]: 1*s(4)+0
  Such that:s(4) =< B

  with precondition: [F=3,A>=0,B>=1,E>=0] 


#### Cost of chains of l0(A,B,C,D,E,F):
* Chain [17]: 1*s(23)+0
  Such that:s(23) =< B

  with precondition: [A>=1,B>=1,E>=1] 

* Chain [16]: 4*s(27)+2*s(30)+3*s(31)+0
  Such that:s(24) =< A
s(25) =< E
s(26) =< 2*E
s(27) =< s(25)
s(28) =< s(26)*(1/2)
s(29) =< s(27)*s(28)
s(30) =< s(29)+s(29)+s(24)

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


Closed-form bounds of l0(A,B,C,D,E,F): 
-------------------------------------
* Chain [17] with precondition: [A>=1,B>=1,E>=1] 
    - Upper bound: B 
    - Complexity: n 
* Chain [16] with precondition: [A>=1,E>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,C,D,E,F): inf 
Asymptotic class: infinity 
* Total analysis performed in 383 ms.

