/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  : [eval2/5]
1. recursive  : [eval1/3,eval2_loop_cont/4]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [eval1_loop_cont/2]
4. non_recursive  : [start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval2/5
1. SCC is partially evaluated into eval1/3
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into start/3

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

### Specialization of cost equations eval2/5 
* CE 7 is refined into CE [8] 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 


### Cost equations --> "Loop" of eval2/5 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval2(A,B,C,D,E) 
* RF of phase [8]: [A-B+1]

#### Partial ranking functions of CR eval2(A,B,C,D,E) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    A-B+1


### Specialization of cost equations eval1/3 
* CE 2 is refined into CE [11,12] 
* CE 4 is refined into CE [13] 
* CE 3 is refined into CE [14] 


### Cost equations --> "Loop" of eval1/3 
* CEs [14] --> Loop 11 
* CEs [11,12] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR eval1(A,B,C) 
* RF of phase [11]: [A+1]

#### Partial ranking functions of CR eval1(A,B,C) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    A+1


### Specialization of cost equations start/3 
* CE 1 is refined into CE [15,16,17] 


### Cost equations --> "Loop" of start/3 
* CEs [17] --> Loop 14 
* CEs [16] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR start(A,B,C) 

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


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

#### Cost of chains of eval2(A,B,C,D,E):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< -B+E

  with precondition: [C=2,A=D+2,A+1=E,B>=1,A>=B] 

* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< A-B+1

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

* Chain [9]: 0
  with precondition: [C=3,A>=1,B>=1] 


#### Cost of chains of eval1(A,B,C):
* Chain [[11],13]: 1*it(11)+1*s(3)+0
  Such that:it(11) =< A+1
aux(1) =< A+2
s(3) =< it(11)*aux(1)

  with precondition: [C=3,A>=0] 

* Chain [[11],12]: 2*it(11)+1*s(3)+0
  Such that:aux(1) =< A+2
aux(2) =< A
aux(3) =< A+1
it(11) =< aux(2)
it(11) =< aux(3)
s(3) =< it(11)*aux(1)

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

* Chain [13]: 0
  with precondition: [C=3] 

* Chain [12]: 1*s(4)+0
  Such that:s(4) =< A+1

  with precondition: [C=3,A>=0] 


#### Cost of chains of start(A,B,C):
* Chain [16]: 0
  with precondition: [] 

* Chain [15]: 2*s(11)+1*s(12)+0
  Such that:s(10) =< A+1
s(9) =< A+2
s(11) =< s(10)
s(12) =< s(11)*s(9)

  with precondition: [A>=0] 

* Chain [14]: 2*s(16)+1*s(17)+0
  Such that:s(14) =< A
s(15) =< A+1
s(13) =< A+2
s(16) =< s(14)
s(16) =< s(15)
s(17) =< s(16)*s(13)

  with precondition: [A>=1] 


Closed-form bounds of start(A,B,C): 
-------------------------------------
* Chain [16] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [A>=0] 
    - Upper bound: 2*A+2+(A+2)*(A+1) 
    - Complexity: n^2 
* Chain [14] with precondition: [A>=1] 
    - Upper bound: (A+2)*A+2*A 
    - Complexity: n^2 

### Maximum cost of start(A,B,C): max([nat(A+2)*nat(A)+nat(A)*2,nat(A+2)*nat(A+1)+nat(A+1)*2]) 
Asymptotic class: n^2 
* Total analysis performed in 112 ms.