[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**. 

```Python
1   def ILA(s, t):
2       rows = len(s)+1
3       cols = len(t)+1
4       dist = [[0 for x in range(cols)] for x in range(rows)]
5       choice = [[0 for x in range(cols)] for x in range(rows)]
6       for row in range(1, rows):
7           dist[row][0] = row
8           choice[row][0] = 'D'
9       for col in range(1, cols):
10          dist[0][col] = col
11          choice[0][col] = 'I'
12      for col in range(1, cols):
13          for row in range(1, rows):
14              if s[row-1] == t[col-1]:
15                  subs = 0
16              else:
17                  subs = 1
18              m = min(dist[row-1][col] + 1,
19                      dist[row][col-1] + 1,
20                      dist[row-1][col-1] + subs) 
21              dist[row][col] = m
22              if m == dist[row-1][col] + 1:
23                  choice[row][col] = 'D'
24              elif m == dist[row][col-1] + 1:
25                  choice[row][col] = 'I'
26              elif subs == 1:
27                  choice[row][col] = 'S'
28              else:
29                  choice[row][col] = 'N'     
30      time = dist[row][col]
31      target = int(time/2)
32      path = [None]*(time+1)
33      path[0] = s
34      path[time] = t
35      c_s = list(s)
36      c_t = list(t)
37      start = 1
38      end = time-1
39      suffix = []
40      while end >= start:
41          move = choice[len(c_s)][len(c_t)]
42          if move == 'D':
43              del c_s[-1]
44              path[start] = ''.join(c_s + suffix)
45              start += 1
46          elif move == 'I':
47              del c_t[-1]
48              path[end] = ''.join(c_t + suffix)
49              end -= 1
50          elif move == 'S':
51              suffix = [c_t[-1]] + suffix
52              del c_s[-1]
53              del c_t[-1]
54              path[start] = ''.join(c_s + suffix)
55              start += 1
56          elif move == 'N':
57              suffix = [c_t[-1]] + suffix
58              del c_s[-1]
59              del c_t[-1]
60      return path[target]
61  def solve_case(C, J):
62      return ILA(C, J)
63  def main():
64      T = int(raw_input())
65      for case_no in xrange(1,1+T):
66          C, J = raw_input().split(' ')
67          ans = solve_case(C, J)
68          print "Case #{}: {}".format(case_no, ans)
69  main()
```


**Question**: Does line `12` have control dependence over line `15` in function `ILA`? If so, provide a trace.

**Output**:


Ground truth answer: yes