/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,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 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 
* CE 3 is refined into CE [11] 
* CE 4 is refined into CE [12] 


### Cost equations --> "Loop" of evalfbb3in/7 
* CEs [11] --> Loop 9 
* CEs [12] --> Loop 10 
* CEs [9] --> Loop 11 
* CEs [10] --> Loop 12 

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

#### Partial ranking functions of CR evalfbb3in(A,B,C,D,E,F,G) 
* Partial RF of phase [9,10]:
  - RF of loop [9:1]:
    -A+D depends on loops [10:1] 
  - RF of loop [10:1]:
    -B+C


### Specialization of cost equations evalfbb3in_loop_cont/6 
* CE 8 is refined into CE [13] 
* CE 7 is refined into CE [14] 


### Cost equations --> "Loop" of evalfbb3in_loop_cont/6 
* CEs [13] --> Loop 13 
* CEs [14] --> Loop 14 

### 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 [15,16,17,18] 


### Cost equations --> "Loop" of evalfentryin/5 
* CEs [15,18] --> Loop 15 
* CEs [16] --> Loop 16 
* CEs [17] --> Loop 17 

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

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


### Specialization of cost equations evalfstart/5 
* CE 1 is refined into CE [19,20,21] 


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

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

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


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

#### Cost of chains of evalfbb3in(A,B,C,D,E,F,G):
* Chain [[9,10],12]: 1*it(9)+1*it(10)+0
  Such that:aux(2) =< -A+D
it(10) =< -B+C
aux(11) =< D
aux(1) =< it(10)*aux(11)
it(9) =< aux(1)+aux(2)

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

* Chain [[9,10],11]: 1*it(9)+1*it(10)+0
  Such that:aux(2) =< -A+D
it(10) =< -B+C
aux(11) =< D
aux(1) =< it(10)*aux(11)
it(9) =< aux(1)+aux(2)

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

* Chain [12]: 0
  with precondition: [E=2,A=F,B=G,A>=0,B>=0,B>=C] 

* Chain [11]: 0
  with precondition: [E=3,A>=0,B>=0] 


#### Cost of chains of evalfbb3in_loop_cont(A,B,C,D,E,F):
* Chain [14]: 0
  with precondition: [A=2] 

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


#### Cost of chains of evalfentryin(A,B,C,D,E):
* Chain [17]: 0
  with precondition: [] 

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

* Chain [15]: 2*s(2)+2*s(5)+0
  Such that:aux(16) =< C
aux(17) =< D
s(2) =< aux(16)
s(4) =< s(2)*aux(17)
s(5) =< s(4)+aux(17)

  with precondition: [C>=1] 


#### Cost of chains of evalfstart(A,B,C,D,E):
* Chain [20]: 0
  with precondition: [] 

* Chain [19]: 0
  with precondition: [0>=C] 

* Chain [18]: 2*s(13)+2*s(15)+0
  Such that:s(11) =< C
s(12) =< D
s(13) =< s(11)
s(14) =< s(13)*s(12)
s(15) =< s(14)+s(12)

  with precondition: [C>=1] 


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

### Maximum cost of evalfstart(A,B,C,D,E): nat(C)*2*nat(D)+nat(C)*2+nat(D)*2 
Asymptotic class: n^2 
* Total analysis performed in 188 ms.