/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. non_recursive  : [f1/6]
1. recursive  : [f300/7]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f300_loop_cont/7]
4. non_recursive  : [f2/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is completely evaluated into other SCCs
1. SCC is partially evaluated into f300/7
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f300_loop_cont/7
4. SCC is partially evaluated into f2/6

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

### Specialization of cost equations f300/7 
* CE 6 is refined into CE [9] 
* CE 3 is refined into CE [10] 
* CE 4 is refined into CE [11] 
* CE 5 is refined into CE [12] 


### Cost equations --> "Loop" of f300/7 
* CEs [11] --> Loop 9 
* CEs [12] --> Loop 10 
* CEs [9] --> Loop 11 
* CEs [10] --> Loop 12 

### Ranking functions of CR f300(B,D,E,G,H,I,J) 
* RF of phase [9]: [-D-1]
* RF of phase [10]: [-D-1,-E-1]

#### Partial ranking functions of CR f300(B,D,E,G,H,I,J) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    -D-1
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    -D-1
    -E-1


### Specialization of cost equations f300_loop_cont/7 
* CE 8 is refined into CE [13] 
* CE 7 is refined into CE [14] 


### Cost equations --> "Loop" of f300_loop_cont/7 
* CEs [13] --> Loop 13 
* CEs [14] --> Loop 14 

### Ranking functions of CR f300_loop_cont(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR f300_loop_cont(A,B,C,D,E,F,G) 


### Specialization of cost equations f2/6 
* CE 2 is refined into CE [15,16,17,18,19,20] 
* CE 1 is refined into CE [21] 


### Cost equations --> "Loop" of f2/6 
* CEs [17] --> Loop 15 
* CEs [18] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [15,20] --> Loop 18 
* CEs [19] --> Loop 19 
* CEs [21] --> Loop 20 

### Ranking functions of CR f2(A,B,C,D,E,G) 

#### Partial ranking functions of CR f2(A,B,C,D,E,G) 


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

#### Cost of chains of f300(B,D,E,G,H,I,J):
* Chain [[10],12]: 1*it(10)+0
  Such that:it(10) =< -E+J

  with precondition: [G=2,I+1=0,D+J+1=E,0>=D+2,D>=E] 

* Chain [[10],11]: 1*it(10)+0
  Such that:it(10) =< -D
it(10) =< -E

  with precondition: [G=3,0>=D+2,0>=E+2] 

* Chain [[9],12]: 1*it(9)+0
  Such that:it(9) =< -E+J

  with precondition: [G=2,I+1=0,D+J+1=E,0>=D+2,E>=0] 

* Chain [[9],11]: 1*it(9)+0
  Such that:it(9) =< -D

  with precondition: [G=3,0>=D+2,E>=0] 

* Chain [12]: 0
  with precondition: [G=2,J=E,D=I,D+1>=0] 

* Chain [11]: 0
  with precondition: [G=3] 


#### Cost of chains of f300_loop_cont(A,B,C,D,E,F,G):
* Chain [14]: 0
  with precondition: [A=2,B>=2,D>=2] 

* Chain [13]: 0
  with precondition: [A=3,B>=2,D>=2] 


#### Cost of chains of f2(A,B,C,D,E,G):
* Chain [20]: 0
  with precondition: [1>=A] 

* Chain [19]: 1*s(1)+0
  Such that:s(1) =< -D
s(1) =< -E

  with precondition: [0>=D+2,0>=E+2,A>=2,C>=2] 

* Chain [18]: 2*s(2)+0
  Such that:aux(1) =< -D
s(2) =< aux(1)

  with precondition: [0>=D+2,A>=2,C>=2,E>=0] 

* Chain [17]: 1*s(4)+0
  Such that:s(4) =< -D

  with precondition: [0>=D+2,A>=2,C>=2,D>=E] 

* Chain [16]: 0
  with precondition: [A>=2,C>=2] 

* Chain [15]: 0
  with precondition: [A>=2,C>=2,D+1>=0] 


Closed-form bounds of f2(A,B,C,D,E,G): 
-------------------------------------
* Chain [20] with precondition: [1>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [19] with precondition: [0>=D+2,0>=E+2,A>=2,C>=2] 
    - Upper bound: -D 
    - Complexity: n 
* Chain [18] with precondition: [0>=D+2,A>=2,C>=2,E>=0] 
    - Upper bound: -2*D 
    - Complexity: n 
* Chain [17] with precondition: [0>=D+2,A>=2,C>=2,D>=E] 
    - Upper bound: -D 
    - Complexity: n 
* Chain [16] with precondition: [A>=2,C>=2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [A>=2,C>=2,D+1>=0] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of f2(A,B,C,D,E,G): nat(-D)*2 
Asymptotic class: n 
* Total analysis performed in 152 ms.