/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_perfect_bb2_in/4,eval_perfect_bb3_in/4]
1. recursive  : [eval_perfect_10/14,eval_perfect_11/14,eval_perfect_7/14,eval_perfect_8/14,eval_perfect_9/14,eval_perfect_bb1_in/14,eval_perfect_bb2_in_loop_cont/15,eval_perfect_bb4_in/14]
2. non_recursive  : [eval_perfect_stop/8]
3. non_recursive  : [eval_perfect_bb6_in/8]
4. non_recursive  : [eval_perfect_bb5_in/8]
5. non_recursive  : [exit_location/1]
6. non_recursive  : [eval_perfect_bb1_in_loop_cont/9]
7. non_recursive  : [eval_perfect_1/8]
8. non_recursive  : [eval_perfect_0/8]
9. non_recursive  : [eval_perfect_bb0_in/8]
10. non_recursive  : [eval_perfect_start/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_perfect_bb2_in/4
1. SCC is partially evaluated into eval_perfect_bb1_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_perfect_bb5_in/8
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into eval_perfect_bb1_in_loop_cont/9
7. SCC is partially evaluated into eval_perfect_1/8
8. SCC is completely evaluated into other SCCs
9. SCC is completely evaluated into other SCCs
10. SCC is partially evaluated into eval_perfect_start/8

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

### Specialization of cost equations eval_perfect_bb2_in/4 
* CE 14 is refined into CE [18] 
* CE 13 is refined into CE [19] 
* CE 12 is refined into CE [20] 


### Cost equations --> "Loop" of eval_perfect_bb2_in/4 
* CEs [20] --> Loop 18 
* CEs [18] --> Loop 19 
* CEs [19] --> Loop 20 

### Ranking functions of CR eval_perfect_bb2_in(V_1,V_y2_1,B,C) 
* RF of phase [18]: [-V_1+V_y2_1+1,V_y2_1]

#### Partial ranking functions of CR eval_perfect_bb2_in(V_1,V_y2_1,B,C) 
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    -V_1+V_y2_1+1
    V_y2_1


### Specialization of cost equations eval_perfect_bb1_in/14 
* CE 8 is refined into CE [21] 
* CE 7 is refined into CE [22,23] 
* CE 9 is refined into CE [24] 
* CE 6 is refined into CE [25] 
* CE 5 is discarded (unfeasible) 
* CE 4 is refined into CE [26] 


### Cost equations --> "Loop" of eval_perfect_bb1_in/14 
* CEs [25] --> Loop 21 
* CEs [26] --> Loop 22 
* CEs [21] --> Loop 23 
* CEs [22,23] --> Loop 24 
* CEs [24] --> Loop 25 

### Ranking functions of CR eval_perfect_bb1_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B,C,D,E,F,G,H) 
* RF of phase [21,22]: [V_y1_0_sink-1]

#### Partial ranking functions of CR eval_perfect_bb1_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B,C,D,E,F,G,H) 
* Partial RF of phase [21,22]:
  - RF of loop [21:1]:
    V_y1_0_sink-2
  - RF of loop [22:1]:
    V_y1_0_sink-1


### Specialization of cost equations eval_perfect_bb5_in/8 
* CE 16 is refined into CE [27] 
* CE 15 is refined into CE [28] 
* CE 17 is refined into CE [29] 


### Cost equations --> "Loop" of eval_perfect_bb5_in/8 
* CEs [27] --> Loop 26 
* CEs [28] --> Loop 27 
* CEs [29] --> Loop 28 

### Ranking functions of CR eval_perfect_bb5_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 

#### Partial ranking functions of CR eval_perfect_bb5_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 


### Specialization of cost equations eval_perfect_bb1_in_loop_cont/9 
* CE 10 is refined into CE [30,31,32] 
* CE 11 is refined into CE [33] 


### Cost equations --> "Loop" of eval_perfect_bb1_in_loop_cont/9 
* CEs [32] --> Loop 29 
* CEs [31] --> Loop 30 
* CEs [30] --> Loop 31 
* CEs [33] --> Loop 32 

### Ranking functions of CR eval_perfect_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR eval_perfect_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations eval_perfect_1/8 
* CE 3 is refined into CE [34,35,36,37,38,39] 
* CE 2 is refined into CE [40] 


### Cost equations --> "Loop" of eval_perfect_1/8 
* CEs [36] --> Loop 33 
* CEs [34,35,37,38,39] --> Loop 34 
* CEs [40] --> Loop 35 

### Ranking functions of CR eval_perfect_1(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 

#### Partial ranking functions of CR eval_perfect_1(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 


### Specialization of cost equations eval_perfect_start/8 
* CE 1 is refined into CE [41,42,43] 


### Cost equations --> "Loop" of eval_perfect_start/8 
* CEs [43] --> Loop 36 
* CEs [42] --> Loop 37 
* CEs [41] --> Loop 38 

### Ranking functions of CR eval_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 

#### Partial ranking functions of CR eval_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 


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

#### Cost of chains of eval_perfect_bb2_in(V_1,V_y2_1,B,C):
* Chain [[18],20]: 1*it(18)+0
  Such that:it(18) =< -V_1+V_y2_1+1

  with precondition: [B=2,C>=0,V_1>=C+1,V_y2_1>=V_1+C] 

* Chain [[18],19]: 1*it(18)+0
  Such that:it(18) =< -V_1+V_y2_1+1

  with precondition: [B=3,V_1>=1,V_y2_1>=V_1] 

* Chain [19]: 0
  with precondition: [B=3,V_1>=1] 


#### Cost of chains of eval_perfect_bb1_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B,C,D,E,F,G,H):
* Chain [[21,22],25]: 2*it(21)+1*s(5)+1*s(6)+0
  Such that:aux(1) =< V_x
aux(5) =< V_y1_0_sink
it(21) =< aux(5)
aux(2) =< aux(1)
s(5) =< it(21)*aux(1)
s(6) =< it(21)*aux(2)

  with precondition: [B=3,V_y1_0_sink>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0] 

* Chain [[21,22],24]: 2*it(21)+1*s(5)+1*s(6)+1*s(7)+0
  Such that:aux(6) =< V_x
aux(7) =< V_y1_0_sink
s(7) =< aux(6)
it(21) =< aux(7)
aux(2) =< aux(6)
s(5) =< it(21)*aux(6)
s(6) =< it(21)*aux(2)

  with precondition: [B=3,V_y1_0_sink>=3,V_x>=V_y1_0_sink,V_x>=V_y3_0] 

* Chain [[21,22],23]: 2*it(21)+1*s(5)+1*s(6)+0
  Such that:aux(1) =< V_x
aux(8) =< V_y1_0_sink
it(21) =< aux(8)
aux(2) =< aux(1)
s(5) =< it(21)*aux(1)
s(6) =< it(21)*aux(2)

  with precondition: [B=4,D=1,F=1,G=0,C=E,C=H,V_y1_0_sink>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0,V_y3_0>=C+1] 

* Chain [25]: 0
  with precondition: [B=3,V_x>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0,V_x+V_y1_0_sink>=V_y3_0+2] 

* Chain [24]: 1*s(7)+0
  Such that:s(7) =< V_x-V_y1_0_sink+2

  with precondition: [B=3,V_y1_0_sink>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0] 


#### Cost of chains of eval_perfect_bb5_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B):
* Chain [28]: 0
  with precondition: [V_y3_0=0,V_x>=2] 

* Chain [27]: 0
  with precondition: [0>=V_y3_0+1,V_x>=2] 

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


#### Cost of chains of eval_perfect_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [32]: 0
  with precondition: [A=3,E>=2] 

* Chain [31]: 0
  with precondition: [A=4,H=0,E>=2] 

* Chain [30]: 0
  with precondition: [A=4,0>=H+1,E>=2] 

* Chain [29]: 0
  with precondition: [A=4,E>=2,H>=1] 


#### Cost of chains of eval_perfect_1(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B):
* Chain [35]: 0
  with precondition: [1>=V_x] 

* Chain [34]: 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 [33]: 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_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B):
* Chain [38]: 0
  with precondition: [1>=V_x] 

* Chain [37]: 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 [36]: 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_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B): 
-------------------------------------
* Chain [38] with precondition: [1>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [37] with precondition: [V_x>=2] 
    - Upper bound: 8*V_x+2+8*V_x*V_x 
    - Complexity: n^2 
* Chain [36] with precondition: [V_x>=3] 
    - Upper bound: 2*V_x*V_x+3*V_x 
    - Complexity: n^2 

### Maximum cost of eval_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,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 556 ms.