/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^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval/3]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [eval_loop_cont/2]
3. non_recursive  : [start/3]

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

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

### Specialization of cost equations eval/3 
* CE 5 is refined into CE [6] 
* CE 2 is refined into CE [7] 
* CE 4 is refined into CE [8] 
* CE 3 is refined into CE [9] 


### Cost equations --> "Loop" of eval/3 
* CEs [7] --> Loop 6 
* CEs [8] --> Loop 7 
* CEs [9] --> Loop 8 
* CEs [6] --> Loop 9 

### Ranking functions of CR eval(A,B,C) 
* RF of phase [6]: [A,A-B,A+B]
* RF of phase [7,8]: [A+B]

#### Partial ranking functions of CR eval(A,B,C) 
* Partial RF of phase [6]:
  - RF of loop [6:1]:
    A
    A-B
    A+B
* Partial RF of phase [7,8]:
  - RF of loop [7:1]:
    -A+B depends on loops [8:1] 
    A+B
    B
  - RF of loop [8:1]:
    A+1
    A-B+1 depends on loops [7:1] 


### Specialization of cost equations start/3 
* CE 1 is refined into CE [10,11,12,13] 


### Cost equations --> "Loop" of start/3 
* CEs [13] --> Loop 10 
* CEs [12] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [10] --> Loop 13 

### Ranking functions of CR start(A,B,C) 

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


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

#### Cost of chains of eval(A,B,C):
* Chain [[7,8],9]: 1*it(7)+1*it(8)+0
  Such that:it(8) =< A+1
it(7) =< B
aux(7) =< A+B
it(7) =< aux(7)
it(8) =< aux(7)

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

* Chain [[6],[7,8],9]: 1*it(6)+1*it(7)+1*it(8)+0
  Such that:it(6) =< A-B
it(7) =< B
it(8) =< B+1
aux(7) =< 2*B
it(7) =< aux(7)
it(8) =< aux(7)

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

* Chain [[6],9]: 1*it(6)+0
  Such that:it(6) =< A-B
it(6) =< A+B

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

* Chain [9]: 0
  with precondition: [C=2] 


#### Cost of chains of start(A,B,C):
* Chain [13]: 0
  with precondition: [] 

* Chain [12]: 1*s(1)+1*s(2)+1*s(3)+0
  Such that:s(1) =< A-B
s(2) =< B
s(3) =< B+1
s(4) =< 2*B
s(2) =< s(4)
s(3) =< s(4)

  with precondition: [2*B>=1,A>=B+1] 

* Chain [11]: 1*s(5)+1*s(6)+0
  Such that:s(5) =< A+1
s(7) =< A+B
s(6) =< B
s(5) =< B+1
s(6) =< s(7)
s(5) =< s(7)

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

* Chain [10]: 1*s(8)+0
  Such that:s(8) =< A-B
s(8) =< A+B

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


Closed-form bounds of start(A,B,C): 
-------------------------------------
* Chain [13] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [12] with precondition: [2*B>=1,A>=B+1] 
    - Upper bound: A+B+1 
    - Complexity: n 
* Chain [11] with precondition: [B>=A,A+B>=1] 
    - Upper bound: nat(A+1)+B 
    - Complexity: n 
* Chain [10] with precondition: [A>=B+1,A+B>=1] 
    - Upper bound: A-B 
    - Complexity: n 

### Maximum cost of start(A,B,C): max([nat(A-B),nat(B)+max([nat(A+1),nat(A-B)+nat(B+1)])]) 
Asymptotic class: n 
* Total analysis performed in 110 ms.