/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  : [evalfbb1in/7,evalfbb2in/7,evalfbb3in/7,evalfbb4in/7,evalfbbin/7]
1. non_recursive  : [evalfstop/5]
2. non_recursive  : [evalfreturnin/5]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [evalfbb3in_loop_cont/6]
5. non_recursive  : [evalfentryin/5]
6. non_recursive  : [evalfstart/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into evalfbb3in/7
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into evalfbb3in_loop_cont/6
5. SCC is partially evaluated into evalfentryin/5
6. SCC is partially evaluated into evalfstart/5

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

### Specialization of cost equations evalfbb3in/7 
* CE 7 is refined into CE [10] 
* CE 3 is refined into CE [11] 
* CE 6 is refined into CE [12] 
* CE 5 is refined into CE [13] 
* CE 4 is refined into CE [14] 


### Cost equations --> "Loop" of evalfbb3in/7 
* CEs [13] --> Loop 10 
* CEs [14] --> Loop 11 
* CEs [10] --> Loop 12 
* CEs [12] --> Loop 13 
* CEs [11] --> Loop 14 

### Ranking functions of CR evalfbb3in(A,B,C,D,F,G,H) 

#### Partial ranking functions of CR evalfbb3in(A,B,C,D,F,G,H) 
* Partial RF of phase [10,11]:
  - RF of loop [10:1]:
    A-C depends on loops [11:1] 
    B-C-1 depends on loops [11:1] 
  - RF of loop [11:1]:
    -A+C+1 depends on loops [10:1] 
    B-D
    C depends on loops [10:1] 


### Specialization of cost equations evalfbb3in_loop_cont/6 
* CE 9 is refined into CE [15] 
* CE 8 is refined into CE [16] 


### Cost equations --> "Loop" of evalfbb3in_loop_cont/6 
* CEs [15] --> Loop 15 
* CEs [16] --> Loop 16 

### Ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations evalfentryin/5 
* CE 2 is refined into CE [17,18,19,20,21] 


### Cost equations --> "Loop" of evalfentryin/5 
* CEs [17,18,19,20,21] --> Loop 17 

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

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


### Specialization of cost equations evalfstart/5 
* CE 1 is refined into CE [22] 


### Cost equations --> "Loop" of evalfstart/5 
* CEs [22] --> Loop 18 

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

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


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

#### Cost of chains of evalfbb3in(A,B,C,D,F,G,H):
* Chain [[10,11],14]: 1*it(10)+1*it(11)+0
  Such that:aux(19) =< B
aux(4) =< B-C
it(11) =< -D+H
aux(3) =< it(11)*aux(19)
it(10) =< aux(3)+aux(4)

  with precondition: [F=2,A>=1,C>=0,D>=0,B>=A+1,H>=D,A>=G,B>=H+1,G+H>=D+1] 

* Chain [[10,11],13]: 1*it(10)+1*it(11)+0
  Such that:aux(19) =< B
aux(4) =< B-C
it(11) =< B-D
aux(3) =< it(11)*aux(19)
it(10) =< aux(3)+aux(4)

  with precondition: [F=2,G=0,B=H,A>=1,C>=0,D>=0,B>=A+1,B>=D+1] 

* Chain [[10,11],12]: 1*it(10)+1*it(11)+0
  Such that:aux(19) =< B
aux(4) =< B-C
it(11) =< B-D
aux(3) =< it(11)*aux(19)
it(10) =< aux(3)+aux(4)

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

* Chain [14]: 0
  with precondition: [F=2,C=G,D=H,A>=1,C>=0,D>=0,B>=A+1,B>=D+1] 

* Chain [12]: 0
  with precondition: [F=3,A>=1,C>=0,D>=0,B>=A+1] 


#### Cost of chains of evalfbb3in_loop_cont(A,B,C,D,E,F):
* Chain [16]: 0
  with precondition: [A=2,B>=1,C>=B+1] 

* Chain [15]: 0
  with precondition: [A=3,B>=1,C>=B+1] 


#### Cost of chains of evalfentryin(A,B,C,D,F):
* Chain [17]: 3*s(3)+3*s(5)+0
  Such that:aux(25) =< B
s(3) =< aux(25)
s(4) =< s(3)*aux(25)
s(5) =< s(4)+aux(25)

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


#### Cost of chains of evalfstart(A,B,C,D,F):
* Chain [18]: 3*s(17)+3*s(19)+0
  Such that:s(16) =< B
s(17) =< s(16)
s(18) =< s(17)*s(16)
s(19) =< s(18)+s(16)

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


Closed-form bounds of evalfstart(A,B,C,D,F): 
-------------------------------------
* Chain [18] with precondition: [A>=1,B>=A+1] 
    - Upper bound: 3*B*B+6*B 
    - Complexity: n^2 

### Maximum cost of evalfstart(A,B,C,D,F): 3*B*B+6*B 
Asymptotic class: n^2 
* Total analysis performed in 297 ms.