|
| 1: |
|
app(app(minus,0),y) |
→ 0 |
| 2: |
|
app(app(minus,app(s,x)),0) |
→ app(s,x) |
| 3: |
|
app(app(minus,app(s,x)),app(s,y)) |
→ app(app(minus,x),y) |
| 4: |
|
app(app(le,0),y) |
→ true |
| 5: |
|
app(app(le,app(s,x)),0) |
→ false |
| 6: |
|
app(app(le,app(s,x)),app(s,y)) |
→ app(app(le,x),y) |
| 7: |
|
app(app(app(if,true),x),y) |
→ x |
| 8: |
|
app(app(app(if,false),x),y) |
→ y |
| 9: |
|
app(perfectp,0) |
→ false |
| 10: |
|
app(perfectp,app(s,x)) |
→ app(app(app(app(f,x),app(s,0)),app(s,x)),app(s,x)) |
| 11: |
|
app(app(app(app(f,0),y),0),u) |
→ true |
| 12: |
|
app(app(app(app(f,0),y),app(s,z)),u) |
→ false |
| 13: |
|
app(app(app(app(f,app(s,x)),0),z),u) |
→ app(app(app(app(f,x),u),app(app(minus,z),app(s,x))),u) |
| 14: |
|
app(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ app(app(app(if,app(app(le,x),y)),app(app(app(app(f,app(s,x)),app(app(minus,y),x)),z),u)),app(app(app(app(f,x),u),z),u)) |
|
There are 29 dependency pairs:
|
| 15: |
|
APP(app(minus,app(s,x)),app(s,y)) |
→ APP(app(minus,x),y) |
| 16: |
|
APP(app(minus,app(s,x)),app(s,y)) |
→ APP(minus,x) |
| 17: |
|
APP(app(le,app(s,x)),app(s,y)) |
→ APP(app(le,x),y) |
| 18: |
|
APP(app(le,app(s,x)),app(s,y)) |
→ APP(le,x) |
| 19: |
|
APP(perfectp,app(s,x)) |
→ APP(app(app(app(f,x),app(s,0)),app(s,x)),app(s,x)) |
| 20: |
|
APP(perfectp,app(s,x)) |
→ APP(app(app(f,x),app(s,0)),app(s,x)) |
| 21: |
|
APP(perfectp,app(s,x)) |
→ APP(app(f,x),app(s,0)) |
| 22: |
|
APP(perfectp,app(s,x)) |
→ APP(f,x) |
| 23: |
|
APP(perfectp,app(s,x)) |
→ APP(s,0) |
| 24: |
|
APP(app(app(app(f,app(s,x)),0),z),u) |
→ APP(app(app(app(f,x),u),app(app(minus,z),app(s,x))),u) |
| 25: |
|
APP(app(app(app(f,app(s,x)),0),z),u) |
→ APP(app(app(f,x),u),app(app(minus,z),app(s,x))) |
| 26: |
|
APP(app(app(app(f,app(s,x)),0),z),u) |
→ APP(app(f,x),u) |
| 27: |
|
APP(app(app(app(f,app(s,x)),0),z),u) |
→ APP(f,x) |
| 28: |
|
APP(app(app(app(f,app(s,x)),0),z),u) |
→ APP(app(minus,z),app(s,x)) |
| 29: |
|
APP(app(app(app(f,app(s,x)),0),z),u) |
→ APP(minus,z) |
| 30: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(app(if,app(app(le,x),y)),app(app(app(app(f,app(s,x)),app(app(minus,y),x)),z),u)),app(app(app(app(f,x),u),z),u)) |
| 31: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(if,app(app(le,x),y)),app(app(app(app(f,app(s,x)),app(app(minus,y),x)),z),u)) |
| 32: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(if,app(app(le,x),y)) |
| 33: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(le,x),y) |
| 34: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(le,x) |
| 35: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(app(app(f,app(s,x)),app(app(minus,y),x)),z),u) |
| 36: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(app(f,app(s,x)),app(app(minus,y),x)),z) |
| 37: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(f,app(s,x)),app(app(minus,y),x)) |
| 38: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(minus,y),x) |
| 39: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(minus,y) |
| 40: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(app(app(f,x),u),z),u) |
| 41: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(app(f,x),u),z) |
| 42: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(app(f,x),u) |
| 43: |
|
APP(app(app(app(f,app(s,x)),app(s,y)),z),u) |
→ APP(f,x) |
|
The approximated dependency graph contains one SCC:
{15,17,19-21,24-26,28,30,31,33,35,36,38,40-42}.