/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [f2/4,f3/4]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f2_loop_cont/2]
3. non_recursive  : [f1/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/4
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f1/4

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

### Specialization of cost equations f2/4 
* CE 6 is refined into CE [7] 
* CE 3 is refined into CE [8] 
* CE 2 is refined into CE [9] 
* CE 5 is discarded (unfeasible) 
* CE 4 is refined into CE [10] 


### Cost equations --> "Loop" of f2/4 
* CEs [8] --> Loop 7 
* CEs [9] --> Loop 8 
* CEs [10] --> Loop 9 
* CEs [7] --> Loop 10 

### Ranking functions of CR f2(A,B,C,D) 
* RF of phase [7]: [A-C,B-C]
* RF of phase [8]: [A-C+1]

#### Partial ranking functions of CR f2(A,B,C,D) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    A-C
    B-C
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    A-C+1


### Specialization of cost equations f1/4 
* CE 1 is refined into CE [11,12,13] 


### Cost equations --> "Loop" of f1/4 
* CEs [13] --> Loop 11 
* CEs [12] --> Loop 12 
* CEs [11] --> Loop 13 

### Ranking functions of CR f1(A,B,C,D) 

#### Partial ranking functions of CR f1(A,B,C,D) 


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

#### Cost of chains of f2(A,B,C,D):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< A-C+1

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

* Chain [[8],9,[7],10]: 1*it(7)+1*it(8)+1
  Such that:it(8) =< A-C+1
it(7) =< B

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

* Chain [[8],9,10]: 1*it(8)+1
  Such that:it(8) =< A-C+1

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

* Chain [10]: 0
  with precondition: [D=2,B>=1,C>=0,A>=B,A+1>=C] 

* Chain [9,[7],10]: 1*it(7)+1
  Such that:it(7) =< B

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

* Chain [9,10]: 1
  with precondition: [D=2,A+1=C,B>=1,A>=B] 


#### Cost of chains of f1(A,B,C,D):
* Chain [13]: 1*s(6)+1
  Such that:s(6) =< B

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

* Chain [12]: 0
  with precondition: [B>=1,A>=B] 

* Chain [11]: 1*s(7)+3*s(9)+1
  Such that:s(8) =< A-B
s(7) =< B
s(9) =< s(8)

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


Closed-form bounds of f1(A,B,C,D): 
-------------------------------------
* Chain [13] with precondition: [A=B,A>=1] 
    - Upper bound: B+1 
    - Complexity: n 
* Chain [12] with precondition: [B>=1,A>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [11] with precondition: [B>=1,A>=B+1] 
    - Upper bound: 3*A-2*B+1 
    - Complexity: n 

### Maximum cost of f1(A,B,C,D): 3*A-2*B+1 
Asymptotic class: n 
* Total analysis performed in 161 ms.