Binary Search into a sorted array

### Program Information

Name: Binary Search into a sorted array
Domain: Algorithm
Functionality: Perform binary search on a sorted array
Input: $A$ is a sorted array of small integers;
Output: $p$ is expected to implement a function which is invariant to any increasing function of its arguments.k is the value of output.

#### Reference

Automated Metamorphic Testing https://doi.org/10.1109/CMPSAC.2003.1245319

### MR Information

#### MR1------

Description:
Property: $\left\{ \begin{array}{l} I_1=(A,x) \\ I_2=(A',x') \\ \end{array} \right. \Rightarrow p(I_2) = p(I_1)$ where $A'$ and $x'$ are defined as $(A'[i]=f(A[i]))_{\forall i \in \{0,\dots 99\}}$ and $x'=f(x)$ for any increasing function $f$ over $N^*$
Source input: $I_1=(A,x)$
Source output: $k_1=p(I_1)$
Follow-up input: $I_2=(A',x')$
Follow-up output: $k_2=p(I_2)$
Input relation: $(A,x) \Rightarrow (A',x')$ where $A'$ and $x'$ are defined as $(A'[i]=f(A[i]))_{\forall i \in \{0,\dots 99\}}$ and $x'=f(x)$ for any increasing function $f$ over $N^*$
Output relation: $k_1=k_2$
Pattern:
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