/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  : [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]

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


### 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]

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


### 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+1,A=E,B>=0,A>=B+1] 

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

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

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


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

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

* Chain [[11],12]: 2*it(11)+1*s(3)+0
  Such that:aux(4) =< A
it(11) =< aux(4)
s(3) =< it(11)*aux(4)

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

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

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

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


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

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

  with precondition: [A>=1] 

* Chain [14]: 2*s(13)+1*s(14)+0
  Such that:s(12) =< A
s(13) =< s(12)
s(14) =< s(13)*s(12)

  with precondition: [A>=2] 


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

### Maximum cost of start(A,B,C): nat(A)*nat(A)+nat(A)*2 
Asymptotic class: n^2 
* Total analysis performed in 109 ms.