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


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_perfectg_bb3_in/4,eval_perfectg_bb5_in/4]
1. recursive  : [eval_perfectg_10/14,eval_perfectg_9/14,eval_perfectg_bb1_in/14,eval_perfectg_bb3_in_loop_cont/15,eval_perfectg_bb4_in/14]
2. non_recursive  : [eval_perfectg_stop/9]
3. non_recursive  : [eval_perfectg_bb2_in/9]
4. non_recursive  : [exit_location/1]
5. non_recursive  : [eval_perfectg_bb1_in_loop_cont/10]
6. non_recursive  : [eval_perfectg_3/9]
7. non_recursive  : [eval_perfectg_2/9]
8. non_recursive  : [eval_perfectg_1/9]
9. non_recursive  : [eval_perfectg_bb0_in/9]
10. non_recursive  : [eval_perfectg_start/9]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_perfectg_bb3_in/4
1. SCC is partially evaluated into eval_perfectg_bb1_in/14
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into eval_perfectg_bb2_in/9
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval_perfectg_bb1_in_loop_cont/10
6. SCC is partially evaluated into eval_perfectg_3/9
7. SCC is completely evaluated into other SCCs
8. SCC is completely evaluated into other SCCs
9. SCC is completely evaluated into other SCCs
10. SCC is partially evaluated into eval_perfectg_start/9

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

### Specialization of cost equations eval_perfectg_bb3_in/4 
* CE 21 is refined into CE [22] 
* CE 20 is refined into CE [23] 
* CE 19 is refined into CE [24] 


### Cost equations --> "Loop" of eval_perfectg_bb3_in/4 
* CEs [24] --> Loop 22 
* CEs [22] --> Loop 23 
* CEs [23] --> Loop 24 

### Ranking functions of CR eval_perfectg_bb3_in(V_2,V_y2_1,B,C) 
* RF of phase [22]: [-V_2+V_y2_1+1,V_y2_1]

#### Partial ranking functions of CR eval_perfectg_bb3_in(V_2,V_y2_1,B,C) 
* Partial RF of phase [22]:
  - RF of loop [22:1]:
    -V_2+V_y2_1+1
    V_y2_1


### Specialization of cost equations eval_perfectg_bb1_in/14 
* CE 13 is refined into CE [25,26] 
* CE 14 is discarded (unfeasible) 
* CE 16 is refined into CE [27] 
* CE 15 is refined into CE [28] 
* CE 9 is refined into CE [29] 
* CE 11 is discarded (unfeasible) 
* CE 10 is discarded (unfeasible) 
* CE 12 is discarded (unfeasible) 
* CE 7 is refined into CE [30] 
* CE 8 is discarded (unfeasible) 


### Cost equations --> "Loop" of eval_perfectg_bb1_in/14 
* CEs [29] --> Loop 25 
* CEs [30] --> Loop 26 
* CEs [25,26] --> Loop 27 
* CEs [27] --> Loop 28 
* CEs [28] --> Loop 29 

### Ranking functions of CR eval_perfectg_bb1_in(V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B,C,D,E,F,G,H) 
* RF of phase [25,26]: [V_y1_0-1]

#### Partial ranking functions of CR eval_perfectg_bb1_in(V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B,C,D,E,F,G,H) 
* Partial RF of phase [25,26]:
  - RF of loop [25:1]:
    V_y1_0-2
  - RF of loop [26:1]:
    V_y1_0-1


### Specialization of cost equations eval_perfectg_bb2_in/9 
* CE 5 is refined into CE [31] 
* CE 4 is refined into CE [32] 
* CE 6 is refined into CE [33] 


### Cost equations --> "Loop" of eval_perfectg_bb2_in/9 
* CEs [31] --> Loop 30 
* CEs [32] --> Loop 31 
* CEs [33] --> Loop 32 

### Ranking functions of CR eval_perfectg_bb2_in(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 

#### Partial ranking functions of CR eval_perfectg_bb2_in(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 


### Specialization of cost equations eval_perfectg_bb1_in_loop_cont/10 
* CE 17 is refined into CE [34,35,36] 
* CE 18 is refined into CE [37] 


### Cost equations --> "Loop" of eval_perfectg_bb1_in_loop_cont/10 
* CEs [36] --> Loop 33 
* CEs [35] --> Loop 34 
* CEs [34] --> Loop 35 
* CEs [37] --> Loop 36 

### Ranking functions of CR eval_perfectg_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 

#### Partial ranking functions of CR eval_perfectg_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 


### Specialization of cost equations eval_perfectg_3/9 
* CE 3 is refined into CE [38,39,40,41,42,43] 
* CE 2 is refined into CE [44,45,46] 


### Cost equations --> "Loop" of eval_perfectg_3/9 
* CEs [40] --> Loop 37 
* CEs [38,39,41,42,43] --> Loop 38 
* CEs [46] --> Loop 39 
* CEs [45] --> Loop 40 
* CEs [44] --> Loop 41 

### Ranking functions of CR eval_perfectg_3(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 

#### Partial ranking functions of CR eval_perfectg_3(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 


### Specialization of cost equations eval_perfectg_start/9 
* CE 1 is refined into CE [47,48,49,50,51] 


### Cost equations --> "Loop" of eval_perfectg_start/9 
* CEs [51] --> Loop 42 
* CEs [50] --> Loop 43 
* CEs [47,48,49] --> Loop 44 

### Ranking functions of CR eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 

#### Partial ranking functions of CR eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 


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

#### Cost of chains of eval_perfectg_bb3_in(V_2,V_y2_1,B,C):
* Chain [[22],24]: 1*it(22)+0
  Such that:it(22) =< -V_2+V_y2_1+1

  with precondition: [B=2,C>=0,V_2>=C+1,V_y2_1>=V_2+C] 

* Chain [[22],23]: 1*it(22)+0
  Such that:it(22) =< -V_2+V_y2_1+1

  with precondition: [B=3,V_2>=1,V_y2_1>=V_2] 

* Chain [23]: 0
  with precondition: [B=3,V_2>=1] 


#### Cost of chains of eval_perfectg_bb1_in(V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B,C,D,E,F,G,H):
* Chain [[25,26],29]: 2*it(25)+1*s(5)+1*s(6)+0
  Such that:aux(1) =< V_x
aux(5) =< V_y1_0
it(25) =< aux(5)
aux(2) =< aux(1)
s(5) =< it(25)*aux(1)
s(6) =< it(25)*aux(2)

  with precondition: [B=4,C=1,E=1,F=0,D=G,D=H,V_y1_0>=2,V_x>=V_y1_0,V_x>=V_y3_0,V_y3_0>=D+1] 

* Chain [[25,26],28]: 2*it(25)+1*s(5)+1*s(6)+0
  Such that:aux(1) =< V_x
aux(6) =< V_y1_0
it(25) =< aux(6)
aux(2) =< aux(1)
s(5) =< it(25)*aux(1)
s(6) =< it(25)*aux(2)

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

* Chain [[25,26],27]: 2*it(25)+1*s(5)+1*s(6)+1*s(7)+0
  Such that:aux(7) =< V_x
aux(8) =< V_y1_0
s(7) =< aux(7)
it(25) =< aux(8)
aux(2) =< aux(7)
s(5) =< it(25)*aux(7)
s(6) =< it(25)*aux(2)

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

* Chain [28]: 0
  with precondition: [B=3,V_x>=2,V_x>=V_y1_0,V_x>=V_y3_0,V_x+V_y1_0>=V_y3_0+2] 

* Chain [27]: 1*s(7)+0
  Such that:s(7) =< V_x-V_y1_0+2

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


#### Cost of chains of eval_perfectg_bb2_in(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B):
* Chain [32]: 0
  with precondition: [V_y3_2=0] 

* Chain [31]: 0
  with precondition: [0>=V_y3_2+1] 

* Chain [30]: 0
  with precondition: [V_y3_2>=1] 


#### Cost of chains of eval_perfectg_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J):
* Chain [36]: 0
  with precondition: [A=3,E>=2] 

* Chain [35]: 0
  with precondition: [A=4,I=0,E>=2] 

* Chain [34]: 0
  with precondition: [A=4,0>=I+1,E>=2] 

* Chain [33]: 0
  with precondition: [A=4,E>=2,I>=1] 


#### Cost of chains of eval_perfectg_3(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B):
* Chain [41]: 0
  with precondition: [V_0=0,1>=V_x] 

* Chain [40]: 0
  with precondition: [0>=V_0+1,1>=V_x] 

* Chain [39]: 0
  with precondition: [1>=V_x,V_0>=1] 

* Chain [38]: 1*s(16)+8*s(18)+4*s(20)+4*s(21)+0
  Such that:s(16) =< 2
aux(13) =< V_x
s(18) =< aux(13)
s(19) =< aux(13)
s(20) =< s(18)*aux(13)
s(21) =< s(18)*s(19)

  with precondition: [V_x>=2] 

* Chain [37]: 3*s(42)+1*s(45)+1*s(46)+0
  Such that:aux(14) =< V_x
s(42) =< aux(14)
s(44) =< aux(14)
s(45) =< s(42)*aux(14)
s(46) =< s(42)*s(44)

  with precondition: [V_x>=3] 


#### Cost of chains of eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B):
* Chain [44]: 0
  with precondition: [1>=V_x] 

* Chain [43]: 1*s(47)+8*s(49)+4*s(51)+4*s(52)+0
  Such that:s(47) =< 2
s(48) =< V_x
s(49) =< s(48)
s(50) =< s(48)
s(51) =< s(49)*s(48)
s(52) =< s(49)*s(50)

  with precondition: [V_x>=2] 

* Chain [42]: 3*s(54)+1*s(56)+1*s(57)+0
  Such that:s(53) =< V_x
s(54) =< s(53)
s(55) =< s(53)
s(56) =< s(54)*s(53)
s(57) =< s(54)*s(55)

  with precondition: [V_x>=3] 


Closed-form bounds of eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B): 
-------------------------------------
* Chain [44] with precondition: [1>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [43] with precondition: [V_x>=2] 
    - Upper bound: 8*V_x+2+8*V_x*V_x 
    - Complexity: n^2 
* Chain [42] with precondition: [V_x>=3] 
    - Upper bound: 2*V_x*V_x+3*V_x 
    - Complexity: n^2 

### Maximum cost of eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,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 646 ms.