[INSTRUCTIONS]

You are a program-analysis assistant. Your task is to statically analyze the control dependence of a given code snippet. 

## 1. Control Dependence Definition
  Control dependence captures the influence of control-flow decisions on the execution of statements.

  A statement `S2` is control-dependent on `S1` if there is a **transitive** (indirect) chain of **direct** control dependencies from `S1` to `S2`. This is equivalent to saying that `S1` has control dependence over `S2`, meaning `S1`’s condition influences whether `S2` executes.


  **Direct Control Dependence**:
  A statement `S2` is **directly** control-dependent on a statement `S1` if:
  
  1.	`S1` is a conditional control statement (e.g., an `if`, `while`, `for`, `switch`, etc.).
  
  2.	`S1` directly determines whether `S2` executes. That is, `S1` has multiple successor branches, 

  - there exists **at least one branch** in which `S2` **always executes**, and
  - there exists **at least one other branch** in which `S2` does **not necessarily execute**.

    “Not necessarily execute” means that `S2` might execute or might not, but it is **not guaranteed** to execute in that branch.

  `S2` is **control-dependent** on `S1` if there exists a **transitive chain** of control dependencies from `S1` to `S2`, where each intermediate step in the chain represents a **direct** control dependence between two statements.



## 2. Output Format
When asked, “Does line `S1` have control dependence over line `S2`? If so, provide a trace.” You should respond in JSON format as follows:

- If there is a control dependence:

```json
{
  "ControlDependence": true,
  "Trace": [S1, ..., S2]
}
```

- If there is no control dependence:
```json
{
  "ControlDependence": false
}
```

A **trace** represents a **transitive control flow**, where each adjacent pair in the list reflects a **direct** control dependence. The trace must starts with `S1` and ends with `S2`.


    

## 3. Interprocedural Control 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  if x > 0:
2      y = 10       # this line is directly control-dependent on line 1 (x>0)
3      if y > 5:
4          z = 20   # this line is directly control-dependent on line 3 (y>5)
5          w = 30   # this line is directly control-dependent on line 3 (y>5)
6  v = 40           # this line is NOT control-dependent on any line
```


**Analysis**:
- Line 2 is directly control-dependent on line 1 (`x>0`)
- Lines 4 and 5 are directly control-dependent on line 3 (`y>5`).
- Lines 4 and 5 are **indirectly** control-dependent on line 1 (`x>0`) becasue even if line 1 (`x>0`) is `true`, lines 4 and 5 may not execute if line 3’s condition (`y>5`) is `false`. However, since control dependence is transitive, lines 4 and 5 are **indirectly** control-dependent on line 1. 
- Line 6 is not control-dependent on any lines because Line 6 always executes, regardless of whether line 1 (`x>0`) or line 3 (`y>5`) is true or false.



#### Example Question 1.1: 
Does line `1` have control dependence over line `5`? If so, provide a trace.

**Output**: 
```json
{
  "ControlDependence": true,
  "Trace": [1, 3, 5]
}
```

#### Example Question 1.2:
Does line `3` have control dependence over line `6`? If so, provide a trace.

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


### Example 2

```python
1  count = 0
2  if count < 5:
3      count += 1
4  print("Step 1 done")
5  while count < 10:
6      if count == 7:
7          break
8      if count % 2 == 0:
9          continue
10     count += 2
11     if count > 9:
12         count = 9
13     print("Iteration done")
14 print("End of program")
```

#### Example Question 2.1: 
Does line `5` have control dependence over line `13`? If so, provide a trace.

**Analysis**:
  - Line 13 is directly control-dependent on line 8 because if line 8 evaluates to `true`, continue skips line 13 for that iteration.
  - Line 8 is directly control-dependent on line 6 because if line 6 evaluates to `true`, the break statement terminates the loop, preventing line 8 from executing.
  - Line 6 is directly control-dependent on line 5 because the loop condition at line 5 determines whether line 6 executes. If line 5 evaluates to `false`, execution skips the loop entirely.


Since control dependence is transitive, line 5 indirectly controls line 13 through lines 6 and 8. The trace is `5->6->8->13`.

**Output**:
```json
{
  "ControlDependence": true,
  "Trace": [5, 6, 8, 13]
}
```

#### Example Question 2.2: 
Does line `8` have control dependence over line `10`? If so, provide a trace.


**Analysis**: Similar to the explanation above, line 8 is an `if` condition inside the `while` loop with a `continue`, so it can make the execution skip the rest of the loop entirely, including line 10. Therefore, line 10 directly control-dependent on 8.



**Output**:
```json
{
  "ControlDependence": true,
  "Trace": [8, 10]
}
```

#### Example Question 2.3: 
Does line `5` have control dependence over line `14`? If so, provide a trace.

**Analysis**: Line 5 doesn't affect whether line 14 is reached. Line 14 is outside the while loop (lines 5 -- 13) and will be executed regardless of the condition. 

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


#### Example Question 2.4: 
Does line `2` have control dependence over line `12`? If so, provide a trace.

**Analysis**: Line 2 doesn't affect whether line 12 is reached. The condition in line 2 only controls whether line 3 is executed. Line 12 is in while loop (line 5 -- 13) and will or will not be executed regardless of the condition in line 2. 

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

---

[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 line `46` have control dependence over line `51` in function `getvalue`? If so, provide a trace.

**Output**:


Ground truth answer: yes