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

#### Computed strongly connected components 
0. recursive  : [eval_sipma91_bb1_in/9,eval_sipma91_bb2_in/9]
1. recursive  : [eval_sipma91_bb3_in/13,eval_sipma91_bb4_in/13,eval_sipma91_bb5_in/13,eval_sipma91_bb6_in/13,eval_sipma91_bb7_in/13]
2. non_recursive  : [eval_sipma91_stop/10]
3. non_recursive  : [eval_sipma91_bb8_in/10]
4. non_recursive  : [exit_location/1]
5. non_recursive  : [eval_sipma91_bb3_in_loop_cont/11]
6. non_recursive  : [eval_sipma91_bb1_in_loop_cont/11]
7. non_recursive  : [eval_sipma91_3/10]
8. non_recursive  : [eval_sipma91_2/10]
9. non_recursive  : [eval_sipma91_1/10]
10. non_recursive  : [eval_sipma91_0/10]
11. non_recursive  : [eval_sipma91_bb0_in/10]
12. non_recursive  : [eval_sipma91_start/10]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_sipma91_bb1_in/9
1. SCC is partially evaluated into eval_sipma91_bb3_in/13
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval_sipma91_bb3_in_loop_cont/11
6. SCC is partially evaluated into eval_sipma91_bb1_in_loop_cont/11
7. SCC is partially evaluated into eval_sipma91_3/10
8. SCC is completely evaluated into other SCCs
9. SCC is completely evaluated into other SCCs
10. SCC is completely evaluated into other SCCs
11. SCC is completely evaluated into other SCCs
12. SCC is partially evaluated into eval_sipma91_start/10

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

### Specialization of cost equations eval_sipma91_bb1_in/9 
* CE 5 is refined into CE [16] 
* CE 6 is refined into CE [17] 
* CE 4 is refined into CE [18] 


### Cost equations --> "Loop" of eval_sipma91_bb1_in/9 
* CEs [18] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [17] --> Loop 18 

### Ranking functions of CR eval_sipma91_bb1_in(V_y1_0,V_y1_1,V_y2_0,V_y2_1,B,C,D,E,F) 
* RF of phase [16]: [-V_y1_0/11+101/11]

#### Partial ranking functions of CR eval_sipma91_bb1_in(V_y1_0,V_y1_1,V_y2_0,V_y2_1,B,C,D,E,F) 
* Partial RF of phase [16]:
  - RF of loop [16:1]:
    -V_y1_0/11+101/11


### Specialization of cost equations eval_sipma91_bb3_in/13 
* CE 13 is refined into CE [19] 
* CE 12 is refined into CE [20] 
* CE 10 is refined into CE [21] 
* CE 11 is refined into CE [22] 
* CE 9 is refined into CE [23] 


### Cost equations --> "Loop" of eval_sipma91_bb3_in/13 
* CEs [21] --> Loop 19 
* CEs [22] --> Loop 20 
* CEs [23] --> Loop 21 
* CEs [19] --> Loop 22 
* CEs [20] --> Loop 23 

### Ranking functions of CR eval_sipma91_bb3_in(V_5,V_6,V_y1_1,V_y1_2,V_y2_1,V_y2_2,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR eval_sipma91_bb3_in(V_5,V_6,V_y1_1,V_y1_2,V_y2_1,V_y2_2,B,C,D,E,F,G,H) 
* Partial RF of phase [19,20]:
  - RF of loop [19:1]:
    V_y1_1/9-110/9 depends on loops [20:1] 
    V_y2_1-2
  - RF of loop [20:1]:
    -V_y1_1+111 depends on loops [19:1] 


### Specialization of cost equations eval_sipma91_bb3_in_loop_cont/11 
* CE 15 is refined into CE [24] 
* CE 14 is refined into CE [25] 


### Cost equations --> "Loop" of eval_sipma91_bb3_in_loop_cont/11 
* CEs [24] --> Loop 24 
* CEs [25] --> Loop 25 

### Ranking functions of CR eval_sipma91_bb3_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 

#### Partial ranking functions of CR eval_sipma91_bb3_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 


### Specialization of cost equations eval_sipma91_bb1_in_loop_cont/11 
* CE 8 is refined into CE [26,27,28,29,30,31] 
* CE 7 is refined into CE [32] 


### Cost equations --> "Loop" of eval_sipma91_bb1_in_loop_cont/11 
* CEs [28,31] --> Loop 26 
* CEs [29] --> Loop 27 
* CEs [30] --> Loop 28 
* CEs [26,27] --> Loop 29 
* CEs [32] --> Loop 30 

### Ranking functions of CR eval_sipma91_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 

#### Partial ranking functions of CR eval_sipma91_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 


### Specialization of cost equations eval_sipma91_3/10 
* CE 2 is refined into CE [33] 
* CE 3 is refined into CE [34,35,36,37,38] 


### Cost equations --> "Loop" of eval_sipma91_3/10 
* CEs [33] --> Loop 31 
* CEs [34,35,37,38] --> Loop 32 
* CEs [36] --> Loop 33 

### Ranking functions of CR eval_sipma91_3(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B) 

#### Partial ranking functions of CR eval_sipma91_3(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B) 


### Specialization of cost equations eval_sipma91_start/10 
* CE 1 is refined into CE [39,40,41] 


### Cost equations --> "Loop" of eval_sipma91_start/10 
* CEs [41] --> Loop 34 
* CEs [40] --> Loop 35 
* CEs [39] --> Loop 36 

### Ranking functions of CR eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B) 

#### Partial ranking functions of CR eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B) 


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

#### Cost of chains of eval_sipma91_bb1_in(V_y1_0,V_y1_1,V_y2_0,V_y2_1,B,C,D,E,F):
* Chain [[16],18]: 1*it(16)+0
  Such that:it(16) =< -V_y1_0/11+101/11

  with precondition: [B=3,100>=V_y1_0,V_y2_0>=1] 

* Chain [[16],17]: 1*it(16)+0
  Such that:it(16) =< -V_y1_0/11+101/11

  with precondition: [B=4,C=D,V_y1_0+11*E=11*V_y2_0+C,V_y1_0+11*F=11*V_y2_0+C,111>=C,V_y2_0>=1,C>=101,C>=V_y1_0+11] 

* Chain [18]: 0
  with precondition: [B=3,V_y2_0>=1,11*V_y2_0+89>=V_y1_0] 


#### Cost of chains of eval_sipma91_bb3_in(V_5,V_6,V_y1_1,V_y1_2,V_y2_1,V_y2_2,B,C,D,E,F,G,H):
* Chain [[19,20],22]: 1*it(19)+1*it(20)+0
  Such that:aux(3) =< -V_y1_1+111
it(19) =< V_y2_1
it(20) =< it(19)*9+aux(3)

  with precondition: [B=3,V_y2_1>=2] 

* Chain [[19,20],21,23]: 1*it(19)+1*it(20)+1
  Such that:aux(3) =< -V_y1_1+111
aux(4) =< -V_y1_1+F+11
it(19) =< V_y2_1
it(20) =< it(19)*9+aux(4)
it(20) =< it(19)*9+aux(3)

  with precondition: [B=2,G=1,H=1,E+10*D=C+11,F+10*D=C+10,D>=1,C>=10*D+90,V_y2_1>=D+1,C+9*V_y2_1+1>=9*D+V_y1_1] 

* Chain [[19,20],21,22]: 1*it(19)+1*it(20)+1
  Such that:aux(3) =< -V_y1_1+111
it(19) =< V_y2_1
it(20) =< it(19)*9+aux(3)

  with precondition: [B=3,V_y2_1>=2] 

* Chain [23]: 0
  with precondition: [B=2,C=V_5,D=V_6,E=V_y1_1,F=V_y1_2,H=V_y2_2,V_y2_1=G,1>=V_y2_1] 

* Chain [22]: 0
  with precondition: [B=3] 

* Chain [21,23]: 1
  with precondition: [V_y2_1=2,B=2,G=1,V_5=C,V_6=D,V_y1_1=E+10,V_y1_2=F,V_y2_2=H,V_y1_1>=111] 

* Chain [21,22]: 1
  with precondition: [V_y2_1=2,B=3,V_y1_1>=111] 


#### Cost of chains of eval_sipma91_bb3_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K):
* Chain [25]: 0
  with precondition: [A=2,100>=D] 

* Chain [24]: 0
  with precondition: [A=3,100>=D] 


#### Cost of chains of eval_sipma91_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K):
* Chain [30]: 0
  with precondition: [A=3,100>=D] 

* Chain [29]: 1
  with precondition: [A=4,I=2,100>=D,F>=111] 

* Chain [28]: 0
  with precondition: [A=4,100>=D] 

* Chain [27]: 0
  with precondition: [A=4,100>=D,1>=I] 

* Chain [26]: 3*s(9)+3*s(10)+1
  Such that:aux(7) =< -F+111
aux(8) =< I
s(9) =< aux(8)
s(10) =< s(9)*9+aux(7)

  with precondition: [A=4,100>=D,I>=2] 


#### Cost of chains of eval_sipma91_3(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B):
* Chain [33]: 1*s(15)+1
  Such that:s(15) =< 1/11

  with precondition: [V_x=100] 

* Chain [32]: 3*s(16)+3*s(21)+3*s(22)+1
  Such that:s(19) =< 10
aux(9) =< -V_x+122
s(20) =< -V_x/11+122/11
aux(10) =< -V_x/11+101/11
s(16) =< aux(10)
s(19) =< aux(9)
s(20) =< aux(9)
s(21) =< s(20)
s(22) =< s(21)*9+s(19)

  with precondition: [100>=V_x] 

* Chain [31]: 0
  with precondition: [V_x>=101] 


#### Cost of chains of eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B):
* Chain [36]: 1*s(23)+1
  Such that:s(23) =< 1/11

  with precondition: [V_x=100] 

* Chain [35]: 3*s(28)+3*s(29)+3*s(30)+1
  Such that:s(24) =< 10
s(25) =< -V_x+122
s(27) =< -V_x/11+101/11
s(26) =< -V_x/11+122/11
s(28) =< s(27)
s(24) =< s(25)
s(26) =< s(25)
s(29) =< s(26)
s(30) =< s(29)*9+s(24)

  with precondition: [100>=V_x] 

* Chain [34]: 0
  with precondition: [V_x>=101] 


Closed-form bounds of eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B): 
-------------------------------------
* Chain [36] with precondition: [V_x=100] 
    - Upper bound: 12/11 
    - Complexity: constant 
* Chain [35] with precondition: [100>=V_x] 
    - Upper bound: -3*V_x+4304/11 
    - Complexity: n 
* Chain [34] with precondition: [V_x>=101] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B): max([12/11,nat(-V_x/11+101/11)*3+31+nat(-V_x/11+122/11)*30]) 
Asymptotic class: n 
* Total analysis performed in 234 ms.

