/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 4 is refined into CE [5] 
* CE 2 is refined into CE [6] 
* CE 3 is refined into CE [7] 


### Cost equations --> "Loop" of eval/3 
* CEs [6] --> Loop 5 
* CEs [7] --> Loop 6 
* CEs [5] --> Loop 7 

### Ranking functions of CR eval(A,B,C) 
* RF of phase [5,6]: [A+B-2]

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


### Specialization of cost equations start/3 
* CE 1 is refined into CE [8,9] 


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

### 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 [[5,6],7]: 1*it(5)+1*it(6)+0
  Such that:aux(4) =< -A+B
aux(2) =< A-B
aux(1) =< 2*A+B
aux(14) =< A
aux(15) =< A+B
aux(16) =< A+2*B
aux(17) =< B
aux(3) =< aux(14)
it(5) =< aux(14)
aux(1) =< aux(15)
aux(3) =< aux(15)
it(5) =< aux(15)
it(6) =< aux(15)
aux(1) =< aux(16)
aux(3) =< aux(16)
aux(1) =< aux(17)
it(6) =< aux(17)
it(6) =< aux(3)+aux(4)
aux(1) =< it(6)*aux(17)
it(5) =< aux(1)+aux(2)

  with precondition: [C=2,A>=1,B>=1,A+B>=3] 

* Chain [7]: 0
  with precondition: [C=2] 


#### Cost of chains of start(A,B,C):
* Chain [9]: 0
  with precondition: [] 

* Chain [8]: 1*s(9)+1*s(10)+0
  Such that:s(1) =< -A+B
s(4) =< A
s(2) =< A-B
s(5) =< A+B
s(6) =< A+2*B
s(3) =< 2*A+B
aux(18) =< B
s(1) =< aux(18)
s(8) =< s(4)
s(9) =< s(4)
s(3) =< s(5)
s(8) =< s(5)
s(9) =< s(5)
s(10) =< s(5)
s(3) =< s(6)
s(8) =< s(6)
s(3) =< aux(18)
s(10) =< aux(18)
s(10) =< s(8)+s(1)
s(3) =< s(10)*aux(18)
s(9) =< s(3)+s(2)

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


Closed-form bounds of start(A,B,C): 
-------------------------------------
* Chain [9] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [8] with precondition: [A>=1,B>=1,A+B>=3] 
    - Upper bound: 2*A+B 
    - Complexity: n 

### Maximum cost of start(A,B,C): nat(A+B)+nat(A) 
Asymptotic class: n 
* Total analysis performed in 116 ms.