/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  : [evalsipmabubblebb1in/4,evalsipmabubblebb2in/4,evalsipmabubblebb3in/4,evalsipmabubblebb4in/4]
1. recursive  : [evalsipmabubblebb4in_loop_cont/6,evalsipmabubblebb5in/5,evalsipmabubblebb6in/5]
2. non_recursive  : [evalsipmabubblestop/3]
3. non_recursive  : [evalsipmabubblereturnin/3]
4. non_recursive  : [exit_location/1]
5. non_recursive  : [evalsipmabubblebb6in_loop_cont/4]
6. non_recursive  : [evalsipmabubbleentryin/3]
7. non_recursive  : [evalsipmabubblestart/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into evalsipmabubblebb4in/4
1. SCC is partially evaluated into evalsipmabubblebb6in/5
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 evalsipmabubblebb6in_loop_cont/4
6. SCC is partially evaluated into evalsipmabubbleentryin/3
7. SCC is partially evaluated into evalsipmabubblestart/3

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

### Specialization of cost equations evalsipmabubblebb4in/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 evalsipmabubblebb4in/4 
* CEs [14] --> Loop 12 
* CEs [12] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR evalsipmabubblebb4in(A,B,E,F) 
* RF of phase [12]: [A-B]

#### Partial ranking functions of CR evalsipmabubblebb4in(A,B,E,F) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    A-B


### Specialization of cost equations evalsipmabubblebb6in/5 
* 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 [19,20] 


### Cost equations --> "Loop" of evalsipmabubblebb6in/5 
* CEs [20] --> Loop 15 
* CEs [19] --> Loop 16 
* CEs [15] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [16] --> Loop 19 
* CEs [18] --> Loop 20 

### Ranking functions of CR evalsipmabubblebb6in(A,B,E,F,G) 
* RF of phase [15]: [A]

#### Partial ranking functions of CR evalsipmabubblebb6in(A,B,E,F,G) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    A


### Specialization of cost equations evalsipmabubblebb6in_loop_cont/4 
* CE 7 is refined into CE [21] 
* CE 8 is refined into CE [22] 


### Cost equations --> "Loop" of evalsipmabubblebb6in_loop_cont/4 
* CEs [21] --> Loop 21 
* CEs [22] --> Loop 22 

### Ranking functions of CR evalsipmabubblebb6in_loop_cont(A,B,C,D) 

#### Partial ranking functions of CR evalsipmabubblebb6in_loop_cont(A,B,C,D) 


### Specialization of cost equations evalsipmabubbleentryin/3 
* CE 2 is refined into CE [23,24,25,26,27,28,29,30] 


### Cost equations --> "Loop" of evalsipmabubbleentryin/3 
* CEs [28] --> Loop 23 
* CEs [27,29] --> Loop 24 
* CEs [26] --> Loop 25 
* CEs [30] --> Loop 26 
* CEs [23,24] --> Loop 27 
* CEs [25] --> Loop 28 

### Ranking functions of CR evalsipmabubbleentryin(A,B,E) 

#### Partial ranking functions of CR evalsipmabubbleentryin(A,B,E) 


### Specialization of cost equations evalsipmabubblestart/3 
* CE 1 is refined into CE [31,32,33,34,35,36] 


### Cost equations --> "Loop" of evalsipmabubblestart/3 
* CEs [36] --> Loop 29 
* CEs [35] --> Loop 30 
* CEs [34] --> Loop 31 
* CEs [33] --> Loop 32 
* CEs [32] --> Loop 33 
* CEs [31] --> Loop 34 

### Ranking functions of CR evalsipmabubblestart(A,B,E) 

#### Partial ranking functions of CR evalsipmabubblestart(A,B,E) 


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

#### Cost of chains of evalsipmabubblebb4in(A,B,E,F):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< -B+F

  with precondition: [E=2,A=F,B>=0,A>=B+1] 

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

  with precondition: [E=3,B>=0,A>=B+1] 

* Chain [14]: 0
  with precondition: [E=2,B=A,B=F,B>=0] 

* Chain [13]: 0
  with precondition: [E=3,B>=0,A>=B] 


#### Cost of chains of evalsipmabubblebb6in(A,B,E,F,G):
* Chain [[15],20]: 1*it(15)+1*s(3)+0
  Such that:aux(3) =< A
it(15) =< aux(3)
s(3) =< it(15)*aux(3)

  with precondition: [E=3,A>=1] 

* Chain [[15],19]: 1*it(15)+1*s(3)+0
  Such that:aux(4) =< A
it(15) =< aux(4)
s(3) =< it(15)*aux(4)

  with precondition: [E=3,A>=1] 

* Chain [[15],18]: 2*it(15)+1*s(3)+0
  Such that:aux(5) =< A
it(15) =< aux(5)
s(3) =< it(15)*aux(5)

  with precondition: [E=3,A>=2] 

* Chain [[15],16,20]: 1*it(15)+1*s(3)+1
  Such that:aux(6) =< A
it(15) =< aux(6)
s(3) =< it(15)*aux(6)

  with precondition: [E=3,A>=1] 

* Chain [[15],16,17]: 1*it(15)+1*s(3)+1
  Such that:aux(7) =< A
it(15) =< aux(7)
s(3) =< it(15)*aux(7)

  with precondition: [E=4,F+1=0,G=0,A>=1] 

* Chain [20]: 0
  with precondition: [E=3] 

* Chain [19]: 0
  with precondition: [E=3,A>=0] 

* Chain [18]: 1*s(4)+0
  Such that:s(4) =< A

  with precondition: [E=3,A>=1] 

* Chain [17]: 0
  with precondition: [E=4,G=B,A=F,0>=A+1] 

* Chain [16,20]: 1
  with precondition: [A=0,E=3] 

* Chain [16,17]: 1
  with precondition: [A=0,E=4,F+1=0,G=0] 


#### Cost of chains of evalsipmabubblebb6in_loop_cont(A,B,C,D):
* Chain [22]: 0
  with precondition: [A=3] 

* Chain [21]: 0
  with precondition: [A=4] 


#### Cost of chains of evalsipmabubbleentryin(A,B,E):
* Chain [28]: 0
  with precondition: [] 

* Chain [27]: 1
  with precondition: [A=0] 

* Chain [26]: 0
  with precondition: [0>=A+1] 

* Chain [25]: 0
  with precondition: [A>=0] 

* Chain [24]: 5*s(16)+4*s(17)+1
  Such that:aux(9) =< A
s(16) =< aux(9)
s(17) =< s(16)*aux(9)

  with precondition: [A>=1] 

* Chain [23]: 2*s(22)+1*s(23)+0
  Such that:s(21) =< A
s(22) =< s(21)
s(23) =< s(22)*s(21)

  with precondition: [A>=2] 


#### Cost of chains of evalsipmabubblestart(A,B,E):
* Chain [34]: 0
  with precondition: [] 

* Chain [33]: 1
  with precondition: [A=0] 

* Chain [32]: 0
  with precondition: [0>=A+1] 

* Chain [31]: 0
  with precondition: [A>=0] 

* Chain [30]: 5*s(25)+4*s(26)+1
  Such that:s(24) =< A
s(25) =< s(24)
s(26) =< s(25)*s(24)

  with precondition: [A>=1] 

* Chain [29]: 2*s(28)+1*s(29)+0
  Such that:s(27) =< A
s(28) =< s(27)
s(29) =< s(28)*s(27)

  with precondition: [A>=2] 


Closed-form bounds of evalsipmabubblestart(A,B,E): 
-------------------------------------
* Chain [34] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [A=0] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [32] with precondition: [0>=A+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [31] with precondition: [A>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [30] with precondition: [A>=1] 
    - Upper bound: 5*A+1+4*A*A 
    - Complexity: n^2 
* Chain [29] with precondition: [A>=2] 
    - Upper bound: 2*A+A*A 
    - Complexity: n^2 

### Maximum cost of evalsipmabubblestart(A,B,E): max([1,nat(A)*3+1+nat(A)*3*nat(A)+(nat(A)*nat(A)+nat(A)*2)]) 
Asymptotic class: n^2 
* Total analysis performed in 199 ms.