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

#### Computed strongly connected components 
0. recursive  : [l2/10,l3/10,l4/10]
1. recursive  : [l1/13,l2_loop_cont/14]
2. non_recursive  : [exit_location/1]
3. recursive  : [l5/5,l6/5]
4. non_recursive  : [l5_loop_cont/2]
5. non_recursive  : [l1_loop_cont/8]
6. non_recursive  : [l0/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l2/10
1. SCC is partially evaluated into l1/13
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into l5/5
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into l1_loop_cont/8
6. SCC is partially evaluated into l0/7

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

### Specialization of cost equations l2/10 
* CE 12 is refined into CE [16] 
* CE 11 is refined into CE [17] 
* CE 10 is refined into CE [18] 
* CE 8 is refined into CE [19] 
* CE 9 is refined into CE [20] 


### Cost equations --> "Loop" of l2/10 
* CEs [19] --> Loop 16 
* CEs [20] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [17] --> Loop 19 
* CEs [18] --> Loop 20 

### Ranking functions of CR l2(A,B,C,D,T2,U2,V2,W2,X2,Y2) 
* RF of phase [16,17]: [T2]

#### Partial ranking functions of CR l2(A,B,C,D,T2,U2,V2,W2,X2,Y2) 
* Partial RF of phase [16,17]:
  - RF of loop [16:1,17:1]:
    T2


### Specialization of cost equations l1/13 
* CE 2 is refined into CE [21,22] 
* CE 5 is refined into CE [23] 
* CE 3 is refined into CE [24,25] 
* CE 4 is refined into CE [26,27] 


### Cost equations --> "Loop" of l1/13 
* CEs [26] --> Loop 21 
* CEs [27] --> Loop 22 
* CEs [23] --> Loop 23 
* CEs [22] --> Loop 24 
* CEs [21] --> Loop 25 
* CEs [24] --> Loop 26 
* CEs [25] --> Loop 27 

### Ranking functions of CR l1(A,B,C,D,T1,T2,U2,V2,W2,X2,Y2,Z2,A3) 
* RF of phase [21,22]: [T1]

#### Partial ranking functions of CR l1(A,B,C,D,T1,T2,U2,V2,W2,X2,Y2,Z2,A3) 
* Partial RF of phase [21,22]:
  - RF of loop [21:1,22:1]:
    T1


### Specialization of cost equations l5/5 
* CE 15 is refined into CE [28] 
* CE 14 is refined into CE [29] 
* CE 13 is refined into CE [30] 


### Cost equations --> "Loop" of l5/5 
* CEs [29] --> Loop 28 
* CEs [30] --> Loop 29 
* CEs [28] --> Loop 30 

### Ranking functions of CR l5(A,B,C,D,U2) 
* RF of phase [28,29]: [D]

#### Partial ranking functions of CR l5(A,B,C,D,U2) 
* Partial RF of phase [28,29]:
  - RF of loop [28:1,29:1]:
    D


### Specialization of cost equations l1_loop_cont/8 
* CE 6 is refined into CE [31] 
* CE 7 is refined into CE [32,33] 


### Cost equations --> "Loop" of l1_loop_cont/8 
* CEs [31] --> Loop 31 
* CEs [33] --> Loop 32 
* CEs [32] --> Loop 33 

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

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


### Specialization of cost equations l0/7 
* CE 1 is refined into CE [34,35,36,37,38,39,40,41,42,43,44,45,46] 


### Cost equations --> "Loop" of l0/7 
* CEs [40,41,45] --> Loop 34 
* CEs [38,39,44] --> Loop 35 
* CEs [36,43] --> Loop 36 
* CEs [37] --> Loop 37 
* CEs [35] --> Loop 38 
* CEs [34,42] --> Loop 39 
* CEs [46] --> Loop 40 

### Ranking functions of CR l0(A,B,C,D,T1,T2,U2) 

#### Partial ranking functions of CR l0(A,B,C,D,T1,T2,U2) 


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

#### Cost of chains of l2(A,B,C,D,T2,U2,V2,W2,X2,Y2):
* Chain [[16,17],20]: 2*it(16)+0
  Such that:aux(1) =< T2
aux(2) =< T2-Y2
it(16) =< aux(1)
it(16) =< aux(2)

  with precondition: [U2=2,A+D=X2,A+D=V2+W2,A>=1,Y2>=0,T2>=Y2+1] 

* Chain [[16,17],19]: 2*it(16)+0
  Such that:aux(1) =< T2
aux(2) =< T2-Y2
it(16) =< aux(1)
it(16) =< aux(2)

  with precondition: [U2=3,D=X2,A+D=V2+W2,A>=1,Y2>=0,T2>=Y2+1] 

* Chain [[16,17],18]: 2*it(16)+0
  Such that:aux(3) =< T2
it(16) =< aux(3)

  with precondition: [U2=4,A>=1,T2>=1] 

* Chain [20]: 0
  with precondition: [U2=2,Y2=T2,B=V2,C=W2,B+C=X2,A>=1] 

* Chain [19]: 0
  with precondition: [U2=3,V2=B,W2=C,X2=D,Y2=T2,A>=1] 

* Chain [18]: 0
  with precondition: [U2=4,A>=1] 


#### Cost of chains of l1(A,B,C,D,T1,T2,U2,V2,W2,X2,Y2,Z2,A3):
* Chain [[21,22],27]: 2*it(21)+2*s(3)+2*s(10)+0
  Such that:aux(19) =< T1
aux(20) =< T1-Z2
aux(4) =< Y2
s(3) =< aux(4)
it(21) =< aux(19)
it(21) =< aux(20)

  with precondition: [U2=3,A=V2,A+Y2=W2+X2,Z2>=0,A3>=0,A>=T1,T1>=Z2+2,B+C>=1,W2+X2>=A+A3+1] 

* Chain [[21,22],26]: 2*it(21)+2*s(10)+0
  Such that:aux(19) =< T1
aux(20) =< T1-Z2
it(21) =< aux(19)
it(21) =< aux(20)

  with precondition: [U2=3,A=V2,W2+X2=Y2,W2+X2=A3,Z2>=0,A>=T1,T1>=Z2+2] 

* Chain [[21,22],25]: 2*it(21)+2*s(10)+0
  Such that:aux(21) =< T1
it(21) =< aux(21)

  with precondition: [U2=4,T1>=2,A>=T1] 

* Chain [[21,22],24]: 2*it(21)+2*s(10)+2*s(15)+0
  Such that:aux(46) =< T1
it(21) =< aux(46)

  with precondition: [U2=4,T1>=2,A>=T1,B+C>=1] 

* Chain [[21,22],23]: 2*it(21)+2*s(10)+0
  Such that:aux(47) =< T1
it(21) =< aux(47)

  with precondition: [U2=4,T1>=1,A>=T1] 

* Chain [27]: 2*s(3)+0
  Such that:aux(4) =< B+C
s(3) =< aux(4)

  with precondition: [U2=3,A=V2,D=Y2,T1=Z2+1,A+D=W2+X2,T1>=1,A3>=0,A>=T1,B+C>=A3+1] 

* Chain [26]: 0
  with precondition: [U2=3,Y2=D,A=V2,B=W2,C=X2,T1=Z2+1,B+C=A3,T1>=1,A>=T1] 

* Chain [25]: 0
  with precondition: [U2=4,T1>=1,A>=T1] 

* Chain [24]: 2*s(14)+0
  Such that:s(13) =< B+C
s(14) =< s(13)

  with precondition: [U2=4,T1>=1,A>=T1,B+C>=1] 

* Chain [23]: 0
  with precondition: [U2=4,A>=T1] 


#### Cost of chains of l5(A,B,C,D,U2):
* Chain [[28,29],30]: 2*it(28)+0
  Such that:aux(50) =< D
it(28) =< aux(50)

  with precondition: [U2=4,D>=1] 

* Chain [30]: 0
  with precondition: [U2=4] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F,G,H):
* Chain [33]: 0
  with precondition: [A=3] 

* Chain [32]: 2*s(21)+0
  Such that:s(20) =< E
s(21) =< s(20)

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

* Chain [31]: 0
  with precondition: [A=4] 


#### Cost of chains of l0(A,B,C,D,T1,T2,U2):
* Chain [40]: 0
  with precondition: [] 

* Chain [39]: 2*s(23)+2*s(24)+0
  Such that:s(22) =< A
s(23) =< s(22)

  with precondition: [A>=1] 

* Chain [38]: 2*s(26)+0
  Such that:s(25) =< D
s(26) =< s(25)

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

* Chain [37]: 2*s(28)+2*s(30)+0
  Such that:s(27) =< B+C
s(29) =< D
s(30) =< s(29)
s(28) =< s(27)

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

* Chain [36]: 4*s(32)+0
  Such that:aux(51) =< B+C
s(32) =< aux(51)

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

* Chain [35]: 6*s(37)+8*s(38)+0
  Such that:aux(54) =< A
s(37) =< aux(54)

  with precondition: [A>=2] 

* Chain [34]: 14*s(51)+6*s(52)+0
  Such that:aux(57) =< A
s(52) =< aux(57)

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


Closed-form bounds of l0(A,B,C,D,T1,T2,U2): 
-------------------------------------
* Chain [40] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [39] with precondition: [A>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [38] with precondition: [A>=1,D>=1] 
    - Upper bound: 2*D 
    - Complexity: n 
* Chain [37] with precondition: [A>=1,D>=1,B+C>=1] 
    - Upper bound: 2*B+2*C+2*D 
    - Complexity: n 
* Chain [36] with precondition: [A>=1,B+C>=1] 
    - Upper bound: 4*B+4*C 
    - Complexity: n 
* Chain [35] with precondition: [A>=2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [34] with precondition: [A>=2,B+C>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,C,D,T1,T2,U2): inf 
Asymptotic class: infinity 
* Total analysis performed in 421 ms.

