/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  : [evalrealselectbb1in/4,evalrealselectbb4in/4]
1. recursive  : [evalrealselectbb4in_loop_cont/7,evalrealselectbb5in/6,evalrealselectbb6in/6,evalrealselectbbin/6]
2. non_recursive  : [evalrealselectstop/4]
3. non_recursive  : [evalrealselectreturnin/4]
4. non_recursive  : [exit_location/1]
5. non_recursive  : [evalrealselectbb6in_loop_cont/5]
6. non_recursive  : [evalrealselectentryin/4]
7. non_recursive  : [evalrealselectstart/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into evalrealselectbb4in/4
1. SCC is partially evaluated into evalrealselectbb6in/6
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 evalrealselectbb6in_loop_cont/5
6. SCC is partially evaluated into evalrealselectentryin/4
7. SCC is partially evaluated into evalrealselectstart/4

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

### Specialization of cost equations evalrealselectbb4in/4 
* CE 11 is refined into CE [12] 
* CE 10 is refined into CE [13] 
* CE 9 is refined into CE [14] 


### Cost equations --> "Loop" of evalrealselectbb4in/4 
* CEs [14] --> Loop 12 
* CEs [12] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR evalrealselectbb4in(B,C,F,G) 
* RF of phase [12]: [B-C]

#### Partial ranking functions of CR evalrealselectbb4in(B,C,F,G) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    B-C


### Specialization of cost equations evalrealselectbb6in/6 
* CE 5 is refined into CE [15] 
* CE 3 is refined into CE [16,17] 
* CE 6 is refined into CE [18] 
* CE 4 is refined into CE [19] 


### Cost equations --> "Loop" of evalrealselectbb6in/6 
* CEs [19] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [16,17] --> Loop 17 
* CEs [18] --> Loop 18 

### Ranking functions of CR evalrealselectbb6in(A,B,C,F,G,H) 
* RF of phase [15]: [-A+B-1]

#### Partial ranking functions of CR evalrealselectbb6in(A,B,C,F,G,H) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    -A+B-1


### Specialization of cost equations evalrealselectbb6in_loop_cont/5 
* CE 7 is refined into CE [20] 
* CE 8 is refined into CE [21] 


### Cost equations --> "Loop" of evalrealselectbb6in_loop_cont/5 
* CEs [20] --> Loop 19 
* CEs [21] --> Loop 20 

### Ranking functions of CR evalrealselectbb6in_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR evalrealselectbb6in_loop_cont(A,B,C,D,E) 


### Specialization of cost equations evalrealselectentryin/4 
* CE 2 is refined into CE [22,23,24,25,26] 


### Cost equations --> "Loop" of evalrealselectentryin/4 
* CEs [24] --> Loop 21 
* CEs [23,26] --> Loop 22 
* CEs [25] --> Loop 23 
* CEs [22] --> Loop 24 

### Ranking functions of CR evalrealselectentryin(A,B,C,F) 

#### Partial ranking functions of CR evalrealselectentryin(A,B,C,F) 


### Specialization of cost equations evalrealselectstart/4 
* CE 1 is refined into CE [27,28,29,30] 


### Cost equations --> "Loop" of evalrealselectstart/4 
* CEs [30] --> Loop 25 
* CEs [29] --> Loop 26 
* CEs [28] --> Loop 27 
* CEs [27] --> Loop 28 

### Ranking functions of CR evalrealselectstart(A,B,C,F) 

#### Partial ranking functions of CR evalrealselectstart(A,B,C,F) 


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

#### Cost of chains of evalrealselectbb4in(B,C,F,G):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< -C+G

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

* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< B-C

  with precondition: [F=3,C>=1,B>=C+1] 

* Chain [13]: 0
  with precondition: [F=3,B>=2,C>=1,B>=C] 


#### Cost of chains of evalrealselectbb6in(A,B,C,F,G,H):
* Chain [[15],18]: 1*it(15)+1*s(3)+0
  Such that:aux(1) =< B
aux(3) =< -A+B
it(15) =< aux(3)
aux(1) =< aux(3)
s(3) =< it(15)*aux(1)

  with precondition: [F=3,A>=0,B>=A+2] 

* Chain [[15],17]: 2*it(15)+1*s(3)+0
  Such that:aux(1) =< B
aux(4) =< -A+B
it(15) =< aux(4)
aux(1) =< aux(4)
s(3) =< it(15)*aux(1)

  with precondition: [F=3,A>=0,B>=A+3] 

* Chain [[15],16]: 1*it(15)+1*s(3)+0
  Such that:it(15) =< -A+G
aux(2) =< -A+G+1
aux(1) =< G+1
aux(1) =< aux(2)
it(15) =< aux(2)
s(3) =< it(15)*aux(1)

  with precondition: [F=4,B=G+1,B=H,A>=0,B>=A+2] 

* Chain [18]: 0
  with precondition: [F=3,A>=0] 

* Chain [17]: 1*s(4)+0
  Such that:s(4) =< -A+B

  with precondition: [F=3,A>=0,B>=A+2] 

* Chain [16]: 0
  with precondition: [F=4,H=C,A=G,A>=0,A+1>=B] 


#### Cost of chains of evalrealselectbb6in_loop_cont(A,B,C,D,E):
* Chain [20]: 0
  with precondition: [A=3] 

* Chain [19]: 0
  with precondition: [A=4] 


#### Cost of chains of evalrealselectentryin(A,B,C,F):
* Chain [24]: 0
  with precondition: [] 

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

* Chain [22]: 3*s(12)+2*s(13)+0
  Such that:aux(8) =< B
s(12) =< aux(8)
s(13) =< s(12)*aux(8)

  with precondition: [B>=2] 

* Chain [21]: 2*s(20)+1*s(21)+0
  Such that:aux(9) =< B
s(20) =< aux(9)
s(21) =< s(20)*aux(9)

  with precondition: [B>=3] 


#### Cost of chains of evalrealselectstart(A,B,C,F):
* Chain [28]: 0
  with precondition: [] 

* Chain [27]: 0
  with precondition: [1>=B] 

* Chain [26]: 3*s(23)+2*s(24)+0
  Such that:s(22) =< B
s(23) =< s(22)
s(24) =< s(23)*s(22)

  with precondition: [B>=2] 

* Chain [25]: 2*s(26)+1*s(27)+0
  Such that:s(25) =< B
s(26) =< s(25)
s(27) =< s(26)*s(25)

  with precondition: [B>=3] 


Closed-form bounds of evalrealselectstart(A,B,C,F): 
-------------------------------------
* Chain [28] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [27] with precondition: [1>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [26] with precondition: [B>=2] 
    - Upper bound: 2*B*B+3*B 
    - Complexity: n^2 
* Chain [25] with precondition: [B>=3] 
    - Upper bound: 2*B+B*B 
    - Complexity: n^2 

### Maximum cost of evalrealselectstart(A,B,C,F): nat(B)*nat(B)+nat(B)*2+(nat(B)*nat(B)+nat(B)) 
Asymptotic class: n^2 
* Total analysis performed in 193 ms.