/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  : [f4/4]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f4_loop_cont/2]
3. non_recursive  : [f0/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f4/4
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f0/4

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

### Specialization of cost equations f4/4 
* CE 4 is refined into CE [5] 
* CE 2 is refined into CE [6] 
* CE 3 is refined into CE [7] 


### Cost equations --> "Loop" of f4/4 
* CEs [6] --> Loop 5 
* CEs [7] --> Loop 6 
* CEs [5] --> Loop 7 

### Ranking functions of CR f4(A,B,C,D) 

#### Partial ranking functions of CR f4(A,B,C,D) 
* Partial RF of phase [5,6]:
  - RF of loop [5:1]:
    A-B depends on loops [6:1] 
    -B+C-1 depends on loops [6:1] 
  - RF of loop [6:1]:
    -A+B+1 depends on loops [5:1] 
    -A+C-1


### Specialization of cost equations f0/4 
* CE 1 is refined into CE [8,9] 


### Cost equations --> "Loop" of f0/4 
* CEs [9] --> Loop 8 
* CEs [8] --> Loop 9 

### Ranking functions of CR f0(A,B,C,D) 

#### Partial ranking functions of CR f0(A,B,C,D) 


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

#### Cost of chains of f4(A,B,C,D):
* Chain [[5,6],7]: 1*it(5)+1*it(6)+0
  Such that:it(6) =< -A+C
aux(8) =< -B+C
aux(25) =< C
aux(26) =< A-B
aux(8) =< aux(26)
aux(21) =< aux(25)
aux(22) =< it(6)*aux(21)
aux(3) =< it(6)*aux(21)
aux(14) =< it(6)*aux(25)
aux(3) =< it(6)*aux(25)
aux(7) =< aux(22)
aux(7) =< aux(14)
it(5) =< aux(3)+aux(26)
it(5) =< aux(7)+aux(8)

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

* Chain [7]: 0
  with precondition: [D=2,B>=0,C>=A+1,A>=B] 


#### Cost of chains of f0(A,B,C,D):
* Chain [9]: 0
  with precondition: [C>=1] 

* Chain [8]: 1*s(1)+1*s(10)+0
  Such that:aux(27) =< C
s(1) =< aux(27)
s(5) =< aux(27)
s(6) =< s(1)*s(5)
s(7) =< s(1)*s(5)
s(8) =< s(1)*aux(27)
s(7) =< s(1)*aux(27)
s(9) =< s(6)
s(9) =< s(8)
s(10) =< s(7)
s(10) =< s(9)

  with precondition: [C>=2] 


Closed-form bounds of f0(A,B,C,D): 
-------------------------------------
* Chain [9] with precondition: [C>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [8] with precondition: [C>=2] 
    - Upper bound: C*C+C 
    - Complexity: n^2 

### Maximum cost of f0(A,B,C,D): C*C+C 
Asymptotic class: n^2 
* Total analysis performed in 128 ms.