[INSTRUCTIONS]

You are a program-analysis assistant. Perform a **static** data-dependence analysis on a given code snippet, treating each branch or loop condition as potentially taking any outcome, without using semantic or symbolic execution to prune paths.


## 1. Data Dependence Definition

   Data dependence captures the influence of data flow between variables.

   We denote each variable instance as `(var,lineNumber)`, meaning the variable `var` defined or updated at `lineNumber`.

   >  **Direct Data Dependence**
   A variable instance `(varB,lineB)` is **directly** data-dependent on `(varA,lineA)` if `lineA` writes to `varA`. Then, without overwritting the value of `varA`, `lineB` reads `varA` and compute the value of `varB`. In other words, the value of `(varB,lineB)` relies on the value produced at `(varA,lineA)`. In addition, changing the execution order of `(varA,lineA)` and `(varB,lineB)` would alter their results.


   A variable instance `(varB,lineB)` is data-dependent on `(varA,lineA)` if there is a **transitive** (indirect) chain of **direct** data dependencies from `(varA,lineA)` to `(varB,lineB)`. This is equivalent to saying that `(varA,lineA)` has data dependence over `(varB,lineB)`, meaning the value written at `(varA,lineA)` can propagate to `(varB,lineB)` through a sequence of read/write operations.


## 2. Output Format
   When asked "Does `(varA,lineA)` have data dependence over `(varB,lineB)`? If so, provide one feasible trace.": 
   - If data dependence exists, respond:
   ```json
   {
   "DataDependence": true,
   "Trace": [
      { "from": ["varA", lineA], "to": ["varX", lineX] },
      ...
      { "from": ["varY", lineY], "to": ["varB", lineB] }
      ]
   }
   ```

   -  If no data dependence exists, respond:
   ```json
   {
   "DataDependence": false
   }
   ```
   
   A **trace** represents a **transitive data flow**, where each item represents a **direct** data dependence edge. The full trace should begin with `(varA,lineA)` and end with `(varB,lineB)`.

   You only need to provide **one** valid chain of data dependence if you conclude a data dependence exists, even if multiple possible chains exist. 


## 3. Intraprocedural Data Dependence
   All dependence analysis is performed within **a single function**. We do not track dependencies across function boundaries. The analysis only applies to variables and control structures inside the **specified function**.

## 4. Example Code Snippet

### Example 1

```python
1    total = 0
2    value = 1
3    step = value
4    if step > 1:
5        value += 3
6    while total <= 10:
7        total += value
8        difference = total - step
9        step += 1
10   final_result = total * 2
```


#### Example Question 1.1:
Does `(value,2)` have data dependence over `(step,9)`? If so, provide a trace.

**Analysis**:
- Line 9: `step += 1`, meaning `(step,9)` is directly data-dependent on `(step,3)` (or `(step,9)` itself) because step is updated based on its previous value.
- Line 3: `step = value`, meaning `(step,3)` is directly data-dependent on `(value,2)`.
Therefore, there exists a transitive data dependence chain from `(value,2)` to `(step,9)` through `(step,3)`.


**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["value", 2], "to": ["step", 3] },
    { "from": ["step", 3], "to": ["step", 9] }
  ]
}
```

#### Example Question 1.2 
Does `(value,2)` have data dependence over `(total,7)`? If so, provide a trace.

**Analysis**:
- Line 7: `total += value`, meaning `(total,7)` reads `value` from either `(value,2)` or `(value,5)`.
- Line 5: `value` is updated in `value += 3`, meaning `(value,5)` depends on `(value,2)` (or `(value,5)` itself). However, this update is inside an if statement, which means it may or may not execute depending on runtime conditions.
- Line 2: value is initialized at `(value,2)`.


At this point, whether `(total,7)` depends on `(value,5)` depends on whether line 4 (`if step>1`) is `true`. Since this is a static analysis, all possible paths are considered without analyzing actual reachability. This means line 5 is treated as both possibly executed and possibly not executed.

- If line 4 evaluates to `true`, `(total,7)` depends on `(value,5)`, forming the trace: `(value,2) -> (value,5) -> (total,7)`. 
- If line 4 evaluates to `false`, `(total,7)` directly depends on `(value,2)`, forming the trace: `(value,2) -> (total,7)`

Therefore, the answer is yes.
Only one valid trace is required for the output. 

**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["value", 2], "to": ["value", 5] },
    { "from": ["value", 5], "to": ["total", 7] }
  ]
}

```



#### Example Question 1.3
Does `(step,3)` have data dependence over `(final_result,10)`? If so, provide a trace.  

**Analysis**:
Since there is no direct or transitive data dependence between `(step,3)` and `(final_result,10)`, the answer is No.

**Output**:
```json
{
  "DataDependence": false
}
```

**Analysis**:


### Example 2

```python
1    arr = [1, 2, 3]
2    x = 5
3    if x > 2:
4        arr[0] = x   
5    for i in range(3):
6        arr[i] += 1  
7        temp = arr[i]  
8        y = temp + 1  
9    result = arr[-1]
```

#### Example Question 2.1:
Does `(x,2)` have data dependence over `(arr,6)`? If so, provide a trace.

**Analysis**
- Line 6: `arr[i] += 1` modifies `arr[i]`, but i varies during the loop execution.
   - If `i == 0`, `arr[i]` refers to `arr[0]`, which was updated in line 4 (or line 6 itself), establishing a dependence chain `(arr,4)` -> `(arr,6)`.
   - If `i != 0`, `arr[i]` does not refer to `arr[0]`, meaning it depend on `(arr,1)` (or `(arr,6)` itself), not `(arr,4)`.
   - However, since static analysis considers all possible paths without resolving i’s runtime value, we must assume `arr[i]` could be `arr[0]`, leading to a possible dependence.
- Line 4: `arr[0] = x`, meaning `(arr,4)` depends on `(x,2)`.
- Line 2: `x` is initialized at `(x,2)`.
- Since there is a transitive chain of direct data dependence: `(x,2)->(arr,4)->(arr,6)`, the answer is yes.


**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["x", 2], "to": ["arr", 4] },
    { "from": ["arr", 4], "to": ["arr", 6] }
  ]
}
```


#### Example Question 2.2:
Does `(i,5)` have data dependence over `(temp,7)`? If so, provide a trace.

**Analysis**:
- Line 7: `temp = arr[i]`, meaning temp depends on `i`, since `i` determines which element of arr is accessed.
- Line 5: `i` is initialized and iterates over the range 0 to 3.
- Since there is a transitive chain of direct data dependence: `(i,5)->(temp,7)`, the answer is yes.


**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["i", 5], "to": ["temp", 7] }
  ]
}
```

#### Example Question 2.3:
Does `(i,5)` have data dependence over `(result,9)`? If so, provide a trace.

**Analysis**:
- Line 9: `result = arr[-1]`, meaning result depends on `arr[-1]`, which is arr[2], possibly get updated at line 6 (or line 1).
- Line 6: `arr[i] += 1`, meaning `arr[i]` is modified based on the value of `i`.
- Line 5: `i` iterates over 0 to 3.
- Since there is a transitive chain of direct data dependence: `(i,5)->(arr,6)->(result,9)`, the answer is yes.


**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["i", 5], "to": ["arr", 6] },
    { "from": ["arr", 6], "to": ["result", 9] }
  ]
}
```

---

[YOUR TURN]

Below is **your target snippet**. 

```Java
1   import java.util.Scanner;
2   public class Main 
3   {
4   	static Scanner scan = new Scanner(System.in);
5   	static int getsimplecon(String minicon)
6   	{ 
7   		boolean not = false;
8   		while(minicon.charAt(0) == '-')
9   		{
10  			not = !not;
11  			minicon = minicon.substring(1);
12  		}
13  		int ans;
14  		if(not)
15  		{
16  			ans = 2-(Integer.parseInt(minicon));
17  			return ans;
18  		}
19  		else
20  		{
21  			ans = Integer.parseInt(minicon);
22  			return ans;
23  		}
24  	}
25  	static int getvalue(String content, int p, int q, int r, boolean replace)
26  	{
27  		int curdepth = 0;
28  		int startbracket = -1;
29  		if(replace)
30  		{
31  			content = content.replaceAll("P", Integer.toString(p));
32  			content = content.replaceAll("Q", Integer.toString(q));
33  			content = content.replaceAll("R", Integer.toString(r));
34  		}
35  		for(int i = 0; i < content.length(); i++)
36  		{
37  			char cur = content.charAt(i);
38  			if(cur == '(')
39  			{
40  				if(curdepth == 0)
41  				{
42  					startbracket = i;
43  				}
44  				curdepth += 1;
45  			}
46  			if(cur == ')')
47  			{
48  				curdepth -= 1;
49  				if(curdepth == 0)
50  				{
51  					String subcontent = content.substring(startbracket+1, i);
52  					String left = content.substring(0, startbracket);
53  					String right = content.substring(i+1);
54  					int subvalue = getvalue(subcontent, p, q, r, false);
55  					content = left + subvalue + right;
56  					i = startbracket;
57  				}
58  			}
59  		}
60  		for(int i = 0; i < content.length(); i++)
61  		{
62  			char cur = content.charAt(i);
63  			if(cur == '*' || cur == '+')
64  			{
65  				String leftcon = content.substring(0, i);
66  				String rightcon = "";
67  				int endofrightcon = -1; 
68  				for(int j = i+1; j < content.length(); j++)
69  				{
70  					char curj = content.charAt(j);
71  					if(curj == '*' || curj == '+')
72  					{
73  						rightcon = content.substring(i+1, j);
74  						endofrightcon = j-1;
75  						break;
76  					}
77  					else if(j == content.length()-1)
78  					{
79  						rightcon = content.substring(i+1);
80  						endofrightcon = j;
81  						break;
82  					}
83  				}
84  				int leftv = getsimplecon(leftcon);
85  				int rightv = getsimplecon(rightcon);
86  				int minires = -1;
87  				if(cur == '*')
88  				{
89  					minires = Math.min(leftv, rightv);
90  				}
91  				else if(cur == '+')
92  				{
93  					minires = Math.max(leftv, rightv);
94  				}
95  				content = minires + content.substring(endofrightcon+1);
96  				i = 0;
97  			}
98  		}
99  		return getsimplecon(content);
100  	}
101  	public static void main(String[] args) 
102  	{
103  		String s;
104  		while(true)
105  		{
106  			s = scan.next();
107  			int count = 0;
108  			if(s.equals("."))break;
109  			for(int p = 0; p <= 2; p++)
110  			{
111  				for(int q = 0; q <= 2; q++)
112  				{
113  					for(int r = 0; r <= 2; r++)
114  					{
115  						if(getvalue(s,p,q,r, true) == 2)
116  						{
117  							count++;
118  						}
119  					}
120  				}
121  			}
122  			System.out.println(count);
123  		}
124  	}
125  }
```


**Question**: Does `(i,56)` have data dependence over `(curj,70)` in function `getvalue`? If so, provide a trace.

**Output**:


Ground truth answer: yes