WARNING: Excluded non-linear constraints:[U=G+E*E]

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

#### Computed strongly connected components 
0. recursive  : [l2/10,l3/10]
1. recursive  : [l1/15,l2_loop_cont/16]
2. non_recursive  : [exit_location/1]
3. recursive  : [l5/2]
4. non_recursive  : [l5_loop_cont/2]
5. non_recursive  : [l1_loop_cont/9]
6. non_recursive  : [l0/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l2/10
1. SCC is partially evaluated into l1/15
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into l5/2
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into l1_loop_cont/9
6. SCC is partially evaluated into l0/8

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

### Specialization of cost equations l2/10 
* CE 11 is refined into CE [14] 
* CE 10 is refined into CE [15] 
* CE 9 is refined into CE [16] 
* CE 8 is refined into CE [17] 


### Cost equations --> "Loop" of l2/10 
* CEs [17] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [16] --> Loop 17 

### Ranking functions of CR l2(A,B,C,D,T2,U3,V3,W3,X3,Y3) 
* RF of phase [14]: [T2]

#### Partial ranking functions of CR l2(A,B,C,D,T2,U3,V3,W3,X3,Y3) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    T2


### Specialization of cost equations l1/15 
* CE 2 is refined into CE [18,19] 
* CE 5 is refined into CE [20] 
* CE 3 is refined into CE [21,22] 
* CE 4 is refined into CE [23,24] 


### Cost equations --> "Loop" of l1/15 
* CEs [24] --> Loop 18 
* CEs [23] --> Loop 19 
* CEs [20] --> Loop 20 
* CEs [19] --> Loop 21 
* CEs [18] --> Loop 22 
* CEs [22] --> Loop 23 
* CEs [21] --> Loop 24 

### Ranking functions of CR l1(A,B,C,D,T1,T2,T3,U3,V3,W3,X3,Y3,Z3,A4,B4) 
* RF of phase [18,19]: [T1]

#### Partial ranking functions of CR l1(A,B,C,D,T1,T2,T3,U3,V3,W3,X3,Y3,Z3,A4,B4) 
* Partial RF of phase [18,19]:
  - RF of loop [18:1,19:1]:
    T1


### Specialization of cost equations l5/2 
* CE 13 is refined into CE [25] 
* CE 12 is refined into CE [26] 


### Cost equations --> "Loop" of l5/2 
* CEs [26] --> Loop 25 
* CEs [25] --> Loop 26 

### Ranking functions of CR l5(T3,U3) 
* RF of phase [25]: [T3]

#### Partial ranking functions of CR l5(T3,U3) 
* Partial RF of phase [25]:
  - RF of loop [25:1]:
    T3


### Specialization of cost equations l1_loop_cont/9 
* CE 6 is refined into CE [27] 
* CE 7 is refined into CE [28,29] 


### Cost equations --> "Loop" of l1_loop_cont/9 
* CEs [27] --> Loop 27 
* CEs [29] --> Loop 28 
* CEs [28] --> Loop 29 

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

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


### Specialization of cost equations l0/8 
* CE 1 is refined into CE [30,31,32,33,34,35,36,37,38,39,40,41,42] 


### Cost equations --> "Loop" of l0/8 
* CEs [34,35,41] --> Loop 30 
* CEs [36,37,40] --> Loop 31 
* CEs [32,33,39] --> Loop 32 
* CEs [30,31,38] --> Loop 33 
* CEs [42] --> Loop 34 

### Ranking functions of CR l0(A,B,C,D,T1,T2,T3,U3) 

#### Partial ranking functions of CR l0(A,B,C,D,T1,T2,T3,U3) 


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

#### Cost of chains of l2(A,B,C,D,T2,U3,V3,W3,X3,Y3):
* Chain [[14],17]: 1*it(14)+0
  Such that:it(14) =< T2-Y3

  with precondition: [U3=2,D=V3,A=W3,D=X3,A>=1,Y3>=0,T2>=Y3+1] 

* Chain [[14],16]: 1*it(14)+0
  Such that:it(14) =< T2-Y3

  with precondition: [U3=3,D=V3,A=W3,D=X3,A>=1,Y3>=0,T2>=Y3+1] 

* Chain [[14],15]: 1*it(14)+0
  Such that:it(14) =< T2

  with precondition: [U3=4,A>=1,T2>=1] 

* Chain [17]: 0
  with precondition: [U3=2,W3=C,Y3=T2,B=V3,B=X3,A>=1] 

* Chain [16]: 0
  with precondition: [U3=3,V3=B,W3=C,X3=D,Y3=T2,A>=1] 

* Chain [15]: 0
  with precondition: [U3=4,A>=1] 


#### Cost of chains of l1(A,B,C,D,T1,T2,T3,U3,V3,W3,X3,Y3,Z3,A4,B4):
* Chain [[18,19],24]: 2*it(18)+1*s(3)+0
  Such that:aux(11) =< T1
aux(12) =< T1-Z3
it(18) =< aux(11)
it(18) =< aux(12)

  with precondition: [U3=3,A=V3,W3=Y3,W3+X3=A4,Z3>=0,A>=T1,T1>=Z3+2] 

* Chain [[18,19],23]: 2*it(18)+2*s(3)+0
  Such that:aux(38) =< T1
it(18) =< aux(38)

  with precondition: [U3=3,A=V3,A=X3,W3=Y3,Z3>=0,A4>=0,A>=T1,T1>=Z3+2,B+C>=1] 

* Chain [[18,19],22]: 2*it(18)+1*s(3)+0
  Such that:aux(39) =< T1
it(18) =< aux(39)

  with precondition: [U3=4,T1>=2,A>=T1] 

* Chain [[18,19],21]: 2*it(18)+2*s(3)+0
  Such that:aux(65) =< T1
it(18) =< aux(65)

  with precondition: [U3=4,T1>=2,A>=T1,B+C>=1] 

* Chain [[18,19],20]: 2*it(18)+1*s(3)+0
  Such that:aux(66) =< T1
it(18) =< aux(66)

  with precondition: [U3=4,T1>=1,A>=T1] 

* Chain [24]: 0
  with precondition: [U3=3,Y3=D,A=V3,B=W3,C=X3,T1=Z3+1,B+C=A4,T1>=1,A>=T1] 

* Chain [23]: 1*s(4)+0
  Such that:s(4) =< B+C

  with precondition: [U3=3,A=V3,D=W3,A=X3,D=Y3,T1=Z3+1,T1>=1,A4>=0,A>=T1,B+C>=A4+1] 

* Chain [22]: 0
  with precondition: [U3=4,T1>=1,A>=T1] 

* Chain [21]: 1*s(6)+0
  Such that:s(6) =< B+C

  with precondition: [U3=4,T1>=1,A>=T1,B+C>=1] 

* Chain [20]: 0
  with precondition: [U3=4,A>=T1] 


#### Cost of chains of l5(T3,U3):
* Chain [[25],26]: 1*it(25)+0
  Such that:it(25) =< T3

  with precondition: [U3=4,T3>=1] 

* Chain [26]: 0
  with precondition: [U3=4] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [29]: 0
  with precondition: [A=3] 

* Chain [28]: 1*s(11)+0
  Such that:s(11) =< H

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

* Chain [27]: 0
  with precondition: [A=4] 


#### Cost of chains of l0(A,B,C,D,T1,T2,T3,U3):
* Chain [34]: 0
  with precondition: [] 

* Chain [33]: 2*s(12)+2*s(14)+0
  Such that:s(13) =< A
s(14) =< s(13)

  with precondition: [A>=1] 

* Chain [32]: 3*s(16)+1*s(18)+0
  Such that:aux(67) =< B+C
s(16) =< aux(67)

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

* Chain [31]: 6*s(22)+4*s(23)+0
  Such that:aux(70) =< A
s(22) =< aux(70)

  with precondition: [A>=2] 

* Chain [30]: 6*s(33)+7*s(34)+0
  Such that:aux(71) =< A
s(33) =< aux(71)

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


Closed-form bounds of l0(A,B,C,D,T1,T2,T3,U3): 
-------------------------------------
* Chain [34] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [A>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [32] with precondition: [A>=1,B+C>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [31] with precondition: [A>=2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [30] with precondition: [A>=2,B+C>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,C,D,T1,T2,T3,U3): inf 
Asymptotic class: infinity 
* Total analysis performed in 504 ms.

