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


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


WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [l2/9]
1. recursive  : [l1/5,l2_loop_cont/6]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [l1_loop_cont/2]
4. non_recursive  : [l0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l2/9
1. SCC is partially evaluated into l1/5
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into l0/5

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

### Specialization of cost equations l2/9 
* 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 l2/9 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR l2(A,B,C,D,E,F,G,H,I) 
* RF of phase [8]: [B-C]

#### Partial ranking functions of CR l2(A,B,C,D,E,F,G,H,I) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    B-C


### Specialization of cost equations l1/5 
* 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 l1/5 
* CEs [14] --> Loop 11 
* CEs [11,12] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR l1(A,B,C,D,E) 
* RF of phase [11]: [B]

#### Partial ranking functions of CR l1(A,B,C,D,E) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    B


### Specialization of cost equations l0/5 
* CE 1 is refined into CE [15,16,17] 


### Cost equations --> "Loop" of l0/5 
* CEs [17] --> Loop 14 
* CEs [16] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR l0(A,B,C,D,E) 

#### Partial ranking functions of CR l0(A,B,C,D,E) 


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

#### Cost of chains of l2(A,B,C,D,E,F,G,H,I):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< B-C

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

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

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

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


#### Cost of chains of l1(A,B,C,D,E):
* Chain [[11],13]: 1*it(11)+1*s(3)+0
  Such that:aux(3) =< B
it(11) =< aux(3)
s(3) =< it(11)*aux(3)

  with precondition: [E=3,B>=1] 

* Chain [[11],12]: 2*it(11)+1*s(3)+0
  Such that:aux(4) =< B
it(11) =< aux(4)
s(3) =< it(11)*aux(4)

  with precondition: [E=3,B>=2] 

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

* Chain [12]: 1*s(4)+0
  Such that:s(4) =< B

  with precondition: [E=3,B>=1] 


#### Cost of chains of l0(A,B,C,D,E):
* Chain [16]: 0
  with precondition: [] 

* Chain [15]: 2*s(10)+1*s(11)+0
  Such that:s(9) =< B
s(10) =< s(9)
s(11) =< s(10)*s(9)

  with precondition: [B>=1] 

* Chain [14]: 2*s(13)+1*s(14)+0
  Such that:s(12) =< B
s(13) =< s(12)
s(14) =< s(13)*s(12)

  with precondition: [B>=2] 


Closed-form bounds of l0(A,B,C,D,E): 
-------------------------------------
* Chain [16] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [B>=1] 
    - Upper bound: 2*B+B*B 
    - Complexity: n^2 
* Chain [14] with precondition: [B>=2] 
    - Upper bound: 2*B+B*B 
    - Complexity: n^2 

### Maximum cost of l0(A,B,C,D,E): nat(B)*nat(B)+nat(B)*2 
Asymptotic class: n^2 
* Total analysis performed in 147 ms.