/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^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval2/6]
1. recursive  : [eval1/4,eval2_loop_cont/5]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [eval1_loop_cont/2]
4. non_recursive  : [start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval2/6
1. SCC is partially evaluated into eval1/4
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into start/4

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

### Specialization of cost equations eval2/6 
* 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 eval2/6 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

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

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


### Specialization of cost equations eval1/4 
* 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 eval1/4 
* CEs [14] --> Loop 11 
* CEs [11,12] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR eval1(A,B,C,D) 

#### Partial ranking functions of CR eval1(A,B,C,D) 


### Specialization of cost equations start/4 
* CE 1 is refined into CE [15,16] 


### Cost equations --> "Loop" of start/4 
* CEs [16] --> Loop 14 
* CEs [15] --> Loop 15 

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

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


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

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

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

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

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

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


#### Cost of chains of eval1(A,B,C,D):
* Chain [13]: 0
  with precondition: [D=3] 

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

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

* Chain [11,13]: 1*s(2)+1
  Such that:s(2) =< A-B

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


#### Cost of chains of start(A,B,C,D):
* Chain [15]: 0
  with precondition: [] 

* Chain [14]: 2*s(6)+1
  Such that:s(5) =< A-B
s(6) =< s(5)

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


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

### Maximum cost of start(A,B,C,D): nat(A-B)*2+1 
Asymptotic class: n 
* Total analysis performed in 109 ms.