/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_perfect1_bb3_in/4,eval_perfect1_bb4_in/4]
1. recursive  : [eval_perfect1_12/14,eval_perfect1_13/14,eval_perfect1_14/14,eval_perfect1_15/14,eval_perfect1_16/14,eval_perfect1_17/14,eval_perfect1_bb2_in/14,eval_perfect1_bb3_in_loop_cont/15,eval_perfect1_bb5_in/14]
2. non_recursive  : [eval_perfect1_stop/9]
3. non_recursive  : [eval_perfect1_bb7_in/9]
4. non_recursive  : [eval_perfect1_bb6_in/9]
5. non_recursive  : [exit_location/1]
6. non_recursive  : [eval_perfect1_bb2_in_loop_cont/10]
7. non_recursive  : [eval_perfect1_8/9]
8. non_recursive  : [eval_perfect1_7/9]
9. non_recursive  : [eval_perfect1_6/9]
10. non_recursive  : [eval_perfect1_5/9]
11. non_recursive  : [eval_perfect1_4/9]
12. non_recursive  : [eval_perfect1_3/9]
13. non_recursive  : [eval_perfect1_2/9]
14. non_recursive  : [eval_perfect1_bb1_in/9]
15. non_recursive  : [eval_perfect1_1/9]
16. non_recursive  : [eval_perfect1_0/9]
17. non_recursive  : [eval_perfect1_bb0_in/9]
18. non_recursive  : [eval_perfect1_start/9]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_perfect1_bb3_in/4
1. SCC is partially evaluated into eval_perfect1_bb2_in/14
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into eval_perfect1_bb6_in/9
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into eval_perfect1_bb2_in_loop_cont/10
7. SCC is partially evaluated into eval_perfect1_8/9
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 completely evaluated into other SCCs
13. SCC is completely evaluated into other SCCs
14. SCC is completely evaluated into other SCCs
15. SCC is partially evaluated into eval_perfect1_1/9
16. SCC is completely evaluated into other SCCs
17. SCC is completely evaluated into other SCCs
18. SCC is partially evaluated into eval_perfect1_start/9

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

### Specialization of cost equations eval_perfect1_bb3_in/4 
* CE 15 is refined into CE [19] 
* CE 14 is refined into CE [20] 
* CE 13 is refined into CE [21] 


### Cost equations --> "Loop" of eval_perfect1_bb3_in/4 
* CEs [21] --> Loop 19 
* CEs [19] --> Loop 20 
* CEs [20] --> Loop 21 

### Ranking functions of CR eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C) 
* RF of phase [19]: [-V_y1_0+V_y2_1+1,V_y2_1]

#### Partial ranking functions of CR eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C) 
* Partial RF of phase [19]:
  - RF of loop [19:1]:
    -V_y1_0+V_y2_1+1
    V_y2_1


### Specialization of cost equations eval_perfect1_bb2_in/14 
* CE 9 is refined into CE [22] 
* CE 8 is refined into CE [23,24] 
* CE 10 is refined into CE [25] 
* CE 7 is refined into CE [26] 
* CE 6 is discarded (unfeasible) 
* CE 5 is refined into CE [27] 


### Cost equations --> "Loop" of eval_perfect1_bb2_in/14 
* CEs [26] --> Loop 22 
* CEs [27] --> Loop 23 
* CEs [22] --> Loop 24 
* CEs [23,24] --> Loop 25 
* CEs [25] --> Loop 26 

### Ranking functions of CR eval_perfect1_bb2_in(V__y3_0,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B,C,D,E,F,G,H) 
* RF of phase [22,23]: [V_y1_0]

#### Partial ranking functions of CR eval_perfect1_bb2_in(V__y3_0,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B,C,D,E,F,G,H) 
* Partial RF of phase [22,23]:
  - RF of loop [22:1]:
    V_y1_0-1
  - RF of loop [23:1]:
    V_y1_0


### Specialization of cost equations eval_perfect1_bb6_in/9 
* CE 17 is refined into CE [28] 
* CE 16 is refined into CE [29] 
* CE 18 is refined into CE [30] 


### Cost equations --> "Loop" of eval_perfect1_bb6_in/9 
* CEs [28] --> Loop 27 
* CEs [29] --> Loop 28 
* CEs [30] --> Loop 29 

### Ranking functions of CR eval_perfect1_bb6_in(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 

#### Partial ranking functions of CR eval_perfect1_bb6_in(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 


### Specialization of cost equations eval_perfect1_bb2_in_loop_cont/10 
* CE 11 is refined into CE [31,32,33] 
* CE 12 is refined into CE [34] 


### Cost equations --> "Loop" of eval_perfect1_bb2_in_loop_cont/10 
* CEs [33] --> Loop 30 
* CEs [32] --> Loop 31 
* CEs [31] --> Loop 32 
* CEs [34] --> Loop 33 

### Ranking functions of CR eval_perfect1_bb2_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 

#### Partial ranking functions of CR eval_perfect1_bb2_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 


### Specialization of cost equations eval_perfect1_8/9 
* CE 4 is refined into CE [35,36,37,38,39,40] 


### Cost equations --> "Loop" of eval_perfect1_8/9 
* CEs [37] --> Loop 34 
* CEs [35,36,38,39,40] --> Loop 35 

### Ranking functions of CR eval_perfect1_8(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 

#### Partial ranking functions of CR eval_perfect1_8(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 


### Specialization of cost equations eval_perfect1_1/9 
* CE 3 is refined into CE [41,42] 
* CE 2 is refined into CE [43] 


### Cost equations --> "Loop" of eval_perfect1_1/9 
* CEs [42] --> Loop 36 
* CEs [41] --> Loop 37 
* CEs [43] --> Loop 38 

### Ranking functions of CR eval_perfect1_1(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 

#### Partial ranking functions of CR eval_perfect1_1(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 


### Specialization of cost equations eval_perfect1_start/9 
* CE 1 is refined into CE [44,45,46] 


### Cost equations --> "Loop" of eval_perfect1_start/9 
* CEs [46] --> Loop 39 
* CEs [45] --> Loop 40 
* CEs [44] --> Loop 41 

### Ranking functions of CR eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 

#### Partial ranking functions of CR eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 


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

#### Cost of chains of eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C):
* Chain [[19],21]: 1*it(19)+0
  Such that:it(19) =< -V_y1_0+V_y2_1+1

  with precondition: [B=2,C>=0,V_y1_0>=C+1,V_y2_1>=V_y1_0+C] 

* Chain [[19],20]: 1*it(19)+0
  Such that:it(19) =< -V_y1_0+V_y2_1+1

  with precondition: [B=3,V_y1_0>=1,V_y2_1>=V_y1_0] 

* Chain [20]: 0
  with precondition: [B=3,V_y1_0>=1] 


#### Cost of chains of eval_perfect1_bb2_in(V__y3_0,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B,C,D,E,F,G,H):
* Chain [[22,23],26]: 2*it(22)+1*s(5)+1*s(6)+0
  Such that:aux(1) =< V_x
aux(5) =< V_y1_0
it(22) =< aux(5)
aux(2) =< aux(1)
s(5) =< it(22)*aux(1)
s(6) =< it(22)*aux(2)

  with precondition: [B=3,V_y1_0>=1,V_x>=V_y1_0+1,V_x>=V_y3_0] 

* Chain [[22,23],25]: 2*it(22)+1*s(5)+1*s(6)+1*s(7)+0
  Such that:aux(6) =< V_x
aux(7) =< V_y1_0
s(7) =< aux(6)
it(22) =< aux(7)
aux(2) =< aux(6)
s(5) =< it(22)*aux(6)
s(6) =< it(22)*aux(2)

  with precondition: [B=3,V_y1_0>=2,V_x>=V_y1_0+1,V_x>=V_y3_0] 

* Chain [[22,23],24]: 2*it(22)+1*s(5)+1*s(6)+0
  Such that:aux(1) =< V_x
aux(8) =< V_y1_0
it(22) =< aux(8)
aux(2) =< aux(1)
s(5) =< it(22)*aux(1)
s(6) =< it(22)*aux(2)

  with precondition: [B=4,E=0,F=0,G=0,C=D,C=H,V_y1_0>=1,V_x>=V_y1_0+1,V_x>=V_y3_0,V_y3_0>=C+1] 

* Chain [26]: 0
  with precondition: [B=3,V_x>=2,V_x>=V_y1_0+1,V_x>=V_y3_0,V_x+V_y1_0>=V_y3_0+1] 

* Chain [25]: 1*s(7)+0
  Such that:s(7) =< V_x-V_y1_0+1

  with precondition: [B=3,V_y1_0>=1,V_x>=V_y1_0+1,V_x>=V_y3_0] 


#### Cost of chains of eval_perfect1_bb6_in(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B):
* Chain [29]: 0
  with precondition: [V_y3_0=0,V_1+1=V_x,V_1>=1] 

* Chain [28]: 0
  with precondition: [V_1+1=V_x,0>=V_y3_0+1,V_1>=1] 

* Chain [27]: 0
  with precondition: [V_1+1=V_x,V_1>=1,V_y3_0>=1] 


#### Cost of chains of eval_perfect1_bb2_in_loop_cont(A,B,C,D,E,F,G,H,I,J):
* Chain [33]: 0
  with precondition: [A=3,F=C+1,F>=2] 

* Chain [32]: 0
  with precondition: [A=4,I=0,F=C+1,F>=2] 

* Chain [31]: 0
  with precondition: [A=4,F=C+1,0>=I+1,F>=2] 

* Chain [30]: 0
  with precondition: [A=4,F=C+1,F>=2,I>=1] 


#### Cost of chains of eval_perfect1_8(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B):
* Chain [35]: 1*s(16)+8*s(18)+4*s(20)+4*s(21)+0
  Such that:s(16) =< 2
aux(9) =< V_1
aux(10) =< V_1+1
s(18) =< aux(9)
s(19) =< aux(10)
s(20) =< s(18)*aux(10)
s(21) =< s(18)*s(19)

  with precondition: [V_x=V_1+1,V_x>=2] 

* Chain [34]: 1*s(42)+2*s(43)+1*s(45)+1*s(46)+0
  Such that:s(41) =< V_1
s(40) =< V_1+1
s(42) =< s(40)
s(43) =< s(41)
s(44) =< s(40)
s(45) =< s(43)*s(40)
s(46) =< s(43)*s(44)

  with precondition: [V_x=V_1+1,V_x>=3] 


#### Cost of chains of eval_perfect1_1(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B):
* Chain [38]: 0
  with precondition: [1>=V_x] 

* Chain [37]: 1*s(47)+8*s(50)+4*s(52)+4*s(53)+0
  Such that:s(47) =< 2
aux(11) =< V_x
s(50) =< aux(11)
s(51) =< aux(11)
s(52) =< s(50)*aux(11)
s(53) =< s(50)*s(51)

  with precondition: [V_x>=2] 

* Chain [36]: 3*s(56)+1*s(59)+1*s(60)+0
  Such that:aux(12) =< V_x
s(56) =< aux(12)
s(58) =< aux(12)
s(59) =< s(56)*aux(12)
s(60) =< s(56)*s(58)

  with precondition: [V_x>=3] 


#### Cost of chains of eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B):
* Chain [41]: 0
  with precondition: [1>=V_x] 

* Chain [40]: 1*s(61)+8*s(63)+4*s(65)+4*s(66)+0
  Such that:s(61) =< 2
s(62) =< V_x
s(63) =< s(62)
s(64) =< s(62)
s(65) =< s(63)*s(62)
s(66) =< s(63)*s(64)

  with precondition: [V_x>=2] 

* Chain [39]: 3*s(68)+1*s(70)+1*s(71)+0
  Such that:s(67) =< V_x
s(68) =< s(67)
s(69) =< s(67)
s(70) =< s(68)*s(67)
s(71) =< s(68)*s(69)

  with precondition: [V_x>=3] 


Closed-form bounds of eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B): 
-------------------------------------
* Chain [41] with precondition: [1>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [40] with precondition: [V_x>=2] 
    - Upper bound: 8*V_x+2+8*V_x*V_x 
    - Complexity: n^2 
* Chain [39] with precondition: [V_x>=3] 
    - Upper bound: 2*V_x*V_x+3*V_x 
    - Complexity: n^2 

### Maximum cost of eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B): nat(V_x)*5+2+nat(V_x)*6*nat(V_x)+(nat(V_x)*2*nat(V_x)+nat(V_x)*3) 
Asymptotic class: n^2 
* Total analysis performed in 642 ms.