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