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

#### Computed strongly connected components 
0. recursive  : [f300/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f1/4]
3. non_recursive  : [f300_loop_cont/5]
4. non_recursive  : [f2/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f300/7
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f300_loop_cont/5
4. SCC is partially evaluated into f2/4

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

### Specialization of cost equations f300/7 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 
* CE 3 is refined into CE [11] 
* CE 4 is refined into CE [12] 
* CE 2 is refined into CE [13] 


### Cost equations --> "Loop" of f300/7 
* CEs [11] --> Loop 9 
* CEs [12] --> Loop 10 
* CEs [13] --> Loop 11 
* CEs [9] --> Loop 12 
* CEs [10] --> Loop 13 

### Ranking functions of CR f300(A,B,C,E,F,G,H) 
* RF of phase [9]: [-A]
* RF of phase [10]: [-A,-B-1]

#### Partial ranking functions of CR f300(A,B,C,E,F,G,H) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    -A
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    -A
    -B-1


### Specialization of cost equations f300_loop_cont/5 
* CE 8 is refined into CE [14] 
* CE 7 is refined into CE [15] 


### Cost equations --> "Loop" of f300_loop_cont/5 
* CEs [14] --> Loop 14 
* CEs [15] --> Loop 15 

### Ranking functions of CR f300_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f300_loop_cont(A,B,C,D,E) 


### Specialization of cost equations f2/4 
* CE 1 is refined into CE [16,17,18,19,20,21,22,23,24,25] 


### Cost equations --> "Loop" of f2/4 
* CEs [21] --> Loop 16 
* CEs [20,25] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [18,24] --> Loop 19 
* CEs [23] --> Loop 20 
* CEs [16,17] --> Loop 21 
* CEs [22] --> Loop 22 

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

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


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

#### Cost of chains of f300(A,B,C,E,F,G,H):
* Chain [[10],13]: 1*it(10)+0
  Such that:it(10) =< -B+G

  with precondition: [E=2,F=0,A+G=B,0>=A+1,A>=B+1] 

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

  with precondition: [E=3,0>=A+1,0>=B+2] 

* Chain [[10],11,[9],13]: 1*it(9)+1*it(10)+1
  Such that:it(10) =< -A-G+99
it(9) =< G

  with precondition: [E=2,F=0,A+G=B+100,0>=B+2,B>=A] 

* Chain [[10],11,[9],12]: 1*it(9)+1*it(10)+1
  Such that:it(9) =< -A+B+100
it(10) =< -B

  with precondition: [E=3,0>=B+2,B>=A] 

* Chain [[10],11,12]: 1*it(10)+1
  Such that:it(10) =< -B

  with precondition: [E=3,0>=B+2,B>=A] 

* Chain [[9],13]: 1*it(9)+0
  Such that:it(9) =< -A

  with precondition: [E=2,F=0,A+G=B,0>=A+1,B>=0] 

* Chain [[9],12]: 1*it(9)+0
  Such that:it(9) =< -A

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

* Chain [13]: 0
  with precondition: [E=2,G=B,A=F,A>=0] 

* Chain [12]: 0
  with precondition: [E=3] 

* Chain [11,[9],13]: 1*it(9)+1
  Such that:it(9) =< -A+99

  with precondition: [B+1=0,E=2,F=0,A+G=99,0>=A+1] 

* Chain [11,[9],12]: 1*it(9)+1
  Such that:it(9) =< -A+99

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

* Chain [11,12]: 1
  with precondition: [B+1=0,E=3,0>=A+1] 


#### Cost of chains of f300_loop_cont(A,B,C,D,E):
* Chain [15]: 0
  with precondition: [A=2] 

* Chain [14]: 0
  with precondition: [A=3] 


#### Cost of chains of f2(A,B,C,E):
* Chain [22]: 0
  with precondition: [] 

* Chain [21]: 2*s(5)+1
  Such that:aux(2) =< -A+99
s(5) =< aux(2)

  with precondition: [B+1=0,0>=A+1] 

* Chain [20]: 1*s(7)+0
  Such that:s(7) =< -A
s(7) =< -B

  with precondition: [0>=A+1,0>=B+2] 

* Chain [19]: 2*s(8)+0
  Such that:aux(3) =< -A
s(8) =< aux(3)

  with precondition: [0>=A+1,B>=0] 

* Chain [18]: 1*s(10)+0
  Such that:s(10) =< -A

  with precondition: [0>=A+1,A>=B+1] 

* Chain [17]: 3*s(11)+2*s(12)+1
  Such that:aux(4) =< -A+B+100
aux(5) =< -B
s(12) =< aux(4)
s(11) =< aux(5)

  with precondition: [0>=B+2,B>=A] 

* Chain [16]: 0
  with precondition: [A>=0] 


Closed-form bounds of f2(A,B,C,E): 
-------------------------------------
* Chain [22] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [21] with precondition: [B+1=0,0>=A+1] 
    - Upper bound: -2*A+199 
    - Complexity: n 
* Chain [20] with precondition: [0>=A+1,0>=B+2] 
    - Upper bound: -A 
    - Complexity: n 
* Chain [19] with precondition: [0>=A+1,B>=0] 
    - Upper bound: -2*A 
    - Complexity: n 
* Chain [18] with precondition: [0>=A+1,A>=B+1] 
    - Upper bound: -A 
    - Complexity: n 
* Chain [17] with precondition: [0>=B+2,B>=A] 
    - Upper bound: -2*A-B+201 
    - Complexity: n 
* Chain [16] with precondition: [A>=0] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of f2(A,B,C,E): max([max([nat(-A+99)*2+1,nat(-B)*3+1+nat(-A+B+100)*2]),nat(-A)*2]) 
Asymptotic class: n 
* Total analysis performed in 104 ms.

