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

#### Computed strongly connected components 
0. recursive  : [f1/9]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f300/5]
3. non_recursive  : [f1_loop_cont/6]
4. non_recursive  : [f2/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/9
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f1_loop_cont/6
4. SCC is partially evaluated into f2/5

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

### Specialization of cost equations f1/9 
* CE 9 is refined into CE [12] 
* CE 8 is refined into CE [13] 
* CE 2 is refined into CE [14] 
* CE 3 is refined into CE [15] 
* CE 5 is refined into CE [16] 
* CE 6 is refined into CE [17] 
* CE 4 is refined into CE [18] 
* CE 7 is refined into CE [19] 


### Cost equations --> "Loop" of f1/9 
* CEs [14] --> Loop 12 
* CEs [15] --> Loop 13 
* CEs [16] --> Loop 14 
* CEs [17] --> Loop 15 
* CEs [18] --> Loop 16 
* CEs [19] --> Loop 17 
* CEs [12] --> Loop 18 
* CEs [13] --> Loop 19 

### Ranking functions of CR f1(A,B,C,D,G,H,I,J,K) 

#### Partial ranking functions of CR f1(A,B,C,D,G,H,I,J,K) 
* Partial RF of phase [12,13,16]:
  - RF of loop [12:1,13:1]:
    -A+B


### Specialization of cost equations f1_loop_cont/6 
* CE 11 is refined into CE [20] 
* CE 10 is refined into CE [21] 


### Cost equations --> "Loop" of f1_loop_cont/6 
* CEs [20] --> Loop 20 
* CEs [21] --> Loop 21 

### Ranking functions of CR f1_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR f1_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations f2/5 
* CE 1 is refined into CE [22,23,24,25,26,27,28,29,30,31,32,33] 


### Cost equations --> "Loop" of f2/5 
* CEs [32,33] --> Loop 22 
* CEs [30,31] --> Loop 23 
* CEs [24] --> Loop 24 
* CEs [25,26,29] --> Loop 25 
* CEs [22,23,28] --> Loop 26 
* CEs [27] --> Loop 27 

### Ranking functions of CR f2(A,B,C,D,G) 

#### Partial ranking functions of CR f2(A,B,C,D,G) 


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

#### Cost of chains of f1(A,B,C,D,G,H,I,J,K):
* Chain [[17]]...: 1*it(17)+0
  with precondition: [A=B] 

* Chain [[17],18]: 1*it(17)+0
  with precondition: [G=3,A=B] 

* Chain [[17],15,19]: 1*it(17)+1
  with precondition: [G=2,A=B,A+1=H,A=I,0>=J+1] 

* Chain [[17],15,18]: 1*it(17)+1
  with precondition: [G=3,A=B] 

* Chain [[17],14,19]: 1*it(17)+1
  with precondition: [G=2,A=B,A+1=H,A=I,J>=1] 

* Chain [[17],14,18]: 1*it(17)+1
  with precondition: [G=3,A=B] 

* Chain [[12,13,16]]...: 2*it(12)+1*it(16)+0
  Such that:aux(3) =< -A+B
it(12) =< aux(3)

  with precondition: [B>=A+1] 

* Chain [[12,13,16],[17]]...: 2*it(12)+2*it(16)+0
  Such that:aux(4) =< -A+B
it(12) =< aux(4)

  with precondition: [B>=A+1] 

* Chain [[12,13,16],[17],18]: 2*it(12)+2*it(16)+0
  Such that:aux(5) =< -A+B
it(12) =< aux(5)

  with precondition: [G=3,B>=A+1] 

* Chain [[12,13,16],[17],15,19]: 2*it(12)+2*it(16)+1
  Such that:aux(6) =< -A+I
it(12) =< aux(6)

  with precondition: [G=2,B+1=H,B=I,0>=J+1,B>=A+1] 

* Chain [[12,13,16],[17],15,18]: 2*it(12)+2*it(16)+1
  Such that:aux(7) =< -A+B
it(12) =< aux(7)

  with precondition: [G=3,B>=A+1] 

* Chain [[12,13,16],[17],14,19]: 2*it(12)+2*it(16)+1
  Such that:aux(8) =< -A+I
it(12) =< aux(8)

  with precondition: [G=2,B+1=H,B=I,J>=1,B>=A+1] 

* Chain [[12,13,16],[17],14,18]: 2*it(12)+2*it(16)+1
  Such that:aux(9) =< -A+B
it(12) =< aux(9)

  with precondition: [G=3,B>=A+1] 

* Chain [[12,13,16],18]: 2*it(12)+1*it(16)+0
  Such that:aux(10) =< -A+B
it(12) =< aux(10)

  with precondition: [G=3,B>=A+1] 

* Chain [[12,13,16],15,19]: 2*it(12)+1*it(16)+1
  Such that:aux(11) =< -A+I
it(12) =< aux(11)

  with precondition: [G=2,B+1=H,B=I,0>=J+1,B>=A+1] 

* Chain [[12,13,16],15,18]: 2*it(12)+1*it(16)+1
  Such that:aux(12) =< -A+B
it(12) =< aux(12)

  with precondition: [G=3,B>=A+1] 

* Chain [[12,13,16],14,19]: 2*it(12)+1*it(16)+1
  Such that:aux(13) =< -A+I
it(12) =< aux(13)

  with precondition: [G=2,B+1=H,B=I,J>=1,B>=A+1] 

* Chain [[12,13,16],14,18]: 2*it(12)+1*it(16)+1
  Such that:aux(14) =< -A+B
it(12) =< aux(14)

  with precondition: [G=3,B>=A+1] 

* Chain [19]: 0
  with precondition: [G=2,J=C,A=H,B=I,A>=B+1] 

* Chain [18]: 0
  with precondition: [G=3] 

* Chain [15,19]: 1
  with precondition: [G=2,A=B,A+1=H,A=I,0>=J+1] 

* Chain [15,18]: 1
  with precondition: [G=3,A=B] 

* Chain [14,19]: 1
  with precondition: [G=2,A=B,A+1=H,A=I,J>=1] 

* Chain [14,18]: 1
  with precondition: [G=3,A=B] 


#### Cost of chains of f1_loop_cont(A,B,C,D,E,F):
* Chain [21]: 0
  with precondition: [A=2] 

* Chain [20]: 0
  with precondition: [A=3] 


#### Cost of chains of f2(A,B,C,D,G):
* Chain [27]: 0
  with precondition: [] 

* Chain [26]: 1*aux(22)+0
  with precondition: [B=A] 

* Chain [25]: 20*s(46)+15*s(47)+1
  Such that:aux(23) =< -A+B
s(46) =< aux(23)

  with precondition: [B>=A+1] 

* Chain [24]: 0
  with precondition: [A>=B+1] 

* Chain [23]...: 1*aux(24)+0
  with precondition: [B=A] 

* Chain [22]...: 8*s(57)+6*s(58)+0
  Such that:aux(25) =< -A+B
s(57) =< aux(25)

  with precondition: [B>=A+1] 


Closed-form bounds of f2(A,B,C,D,G): 
-------------------------------------
* Chain [27] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [26] with precondition: [B=A] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [25] with precondition: [B>=A+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [24] with precondition: [A>=B+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [23]... with precondition: [B=A] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [22]... with precondition: [B>=A+1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f2(A,B,C,D,G): inf 
Asymptotic class: infinity 
* Total analysis performed in 213 ms.

