|
| 1: |
|
app(D,t) |
→ 1 |
| 2: |
|
app(D,constant) |
→ 0 |
| 3: |
|
app(D,app(app(+,x),y)) |
→ app(app(+,app(D,x)),app(D,y)) |
| 4: |
|
app(D,app(app(*,x),y)) |
→ app(app(+,app(app(*,y),app(D,x))),app(app(*,x),app(D,y))) |
| 5: |
|
app(D,app(app(-,x),y)) |
→ app(app(-,app(D,x)),app(D,y)) |
| 6: |
|
app(D,app(minus,x)) |
→ app(minus,app(D,x)) |
| 7: |
|
app(D,app(app(div,x),y)) |
→ app(app(-,app(app(div,app(D,x)),y)),app(app(div,app(app(*,x),app(D,y))),app(app(pow,y),2))) |
| 8: |
|
app(D,app(ln,x)) |
→ app(app(div,app(D,x)),x) |
| 9: |
|
app(D,app(app(pow,x),y)) |
→ app(app(+,app(app(*,app(app(*,y),app(app(pow,x),app(app(-,y),1)))),app(D,x))),app(app(*,app(app(*,app(app(pow,x),y)),app(ln,x))),app(D,y))) |
|
There are 48 dependency pairs:
|
| 10: |
|
APP(D,app(app(+,x),y)) |
→ APP(app(+,app(D,x)),app(D,y)) |
| 11: |
|
APP(D,app(app(+,x),y)) |
→ APP(+,app(D,x)) |
| 12: |
|
APP(D,app(app(+,x),y)) |
→ APP(D,x) |
| 13: |
|
APP(D,app(app(+,x),y)) |
→ APP(D,y) |
| 14: |
|
APP(D,app(app(*,x),y)) |
→ APP(app(+,app(app(*,y),app(D,x))),app(app(*,x),app(D,y))) |
| 15: |
|
APP(D,app(app(*,x),y)) |
→ APP(+,app(app(*,y),app(D,x))) |
| 16: |
|
APP(D,app(app(*,x),y)) |
→ APP(app(*,y),app(D,x)) |
| 17: |
|
APP(D,app(app(*,x),y)) |
→ APP(*,y) |
| 18: |
|
APP(D,app(app(*,x),y)) |
→ APP(D,x) |
| 19: |
|
APP(D,app(app(*,x),y)) |
→ APP(app(*,x),app(D,y)) |
| 20: |
|
APP(D,app(app(*,x),y)) |
→ APP(D,y) |
| 21: |
|
APP(D,app(app(-,x),y)) |
→ APP(app(-,app(D,x)),app(D,y)) |
| 22: |
|
APP(D,app(app(-,x),y)) |
→ APP(-,app(D,x)) |
| 23: |
|
APP(D,app(app(-,x),y)) |
→ APP(D,x) |
| 24: |
|
APP(D,app(app(-,x),y)) |
→ APP(D,y) |
| 25: |
|
APP(D,app(minus,x)) |
→ APP(minus,app(D,x)) |
| 26: |
|
APP(D,app(minus,x)) |
→ APP(D,x) |
| 27: |
|
APP(D,app(app(div,x),y)) |
→ APP(app(-,app(app(div,app(D,x)),y)),app(app(div,app(app(*,x),app(D,y))),app(app(pow,y),2))) |
| 28: |
|
APP(D,app(app(div,x),y)) |
→ APP(-,app(app(div,app(D,x)),y)) |
| 29: |
|
APP(D,app(app(div,x),y)) |
→ APP(app(div,app(D,x)),y) |
| 30: |
|
APP(D,app(app(div,x),y)) |
→ APP(div,app(D,x)) |
| 31: |
|
APP(D,app(app(div,x),y)) |
→ APP(D,x) |
| 32: |
|
APP(D,app(app(div,x),y)) |
→ APP(app(div,app(app(*,x),app(D,y))),app(app(pow,y),2)) |
| 33: |
|
APP(D,app(app(div,x),y)) |
→ APP(div,app(app(*,x),app(D,y))) |
| 34: |
|
APP(D,app(app(div,x),y)) |
→ APP(app(*,x),app(D,y)) |
| 35: |
|
APP(D,app(app(div,x),y)) |
→ APP(*,x) |
| 36: |
|
APP(D,app(app(div,x),y)) |
→ APP(D,y) |
| 37: |
|
APP(D,app(app(div,x),y)) |
→ APP(app(pow,y),2) |
| 38: |
|
APP(D,app(app(div,x),y)) |
→ APP(pow,y) |
| 39: |
|
APP(D,app(ln,x)) |
→ APP(app(div,app(D,x)),x) |
| 40: |
|
APP(D,app(ln,x)) |
→ APP(div,app(D,x)) |
| 41: |
|
APP(D,app(ln,x)) |
→ APP(D,x) |
| 42: |
|
APP(D,app(app(pow,x),y)) |
→ APP(app(+,app(app(*,app(app(*,y),app(app(pow,x),app(app(-,y),1)))),app(D,x))),app(app(*,app(app(*,app(app(pow,x),y)),app(ln,x))),app(D,y))) |
| 43: |
|
APP(D,app(app(pow,x),y)) |
→ APP(+,app(app(*,app(app(*,y),app(app(pow,x),app(app(-,y),1)))),app(D,x))) |
| 44: |
|
APP(D,app(app(pow,x),y)) |
→ APP(app(*,app(app(*,y),app(app(pow,x),app(app(-,y),1)))),app(D,x)) |
| 45: |
|
APP(D,app(app(pow,x),y)) |
→ APP(*,app(app(*,y),app(app(pow,x),app(app(-,y),1)))) |
| 46: |
|
APP(D,app(app(pow,x),y)) |
→ APP(app(*,y),app(app(pow,x),app(app(-,y),1))) |
| 47: |
|
APP(D,app(app(pow,x),y)) |
→ APP(*,y) |
| 48: |
|
APP(D,app(app(pow,x),y)) |
→ APP(app(pow,x),app(app(-,y),1)) |
| 49: |
|
APP(D,app(app(pow,x),y)) |
→ APP(app(-,y),1) |
| 50: |
|
APP(D,app(app(pow,x),y)) |
→ APP(-,y) |
| 51: |
|
APP(D,app(app(pow,x),y)) |
→ APP(D,x) |
| 52: |
|
APP(D,app(app(pow,x),y)) |
→ APP(app(*,app(app(*,app(app(pow,x),y)),app(ln,x))),app(D,y)) |
| 53: |
|
APP(D,app(app(pow,x),y)) |
→ APP(*,app(app(*,app(app(pow,x),y)),app(ln,x))) |
| 54: |
|
APP(D,app(app(pow,x),y)) |
→ APP(app(*,app(app(pow,x),y)),app(ln,x)) |
| 55: |
|
APP(D,app(app(pow,x),y)) |
→ APP(*,app(app(pow,x),y)) |
| 56: |
|
APP(D,app(app(pow,x),y)) |
→ APP(ln,x) |
| 57: |
|
APP(D,app(app(pow,x),y)) |
→ APP(D,y) |
|
The approximated dependency graph contains one SCC:
{12,13,18,20,23,24,26,31,36,41,51,57}.