|
| 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(pred,app(s,x)) |
→ x |
| 5: |
|
app(app(minus,x),0) |
→ x |
| 6: |
|
app(app(minus,x),app(s,y)) |
→ app(pred,app(app(minus,x),y)) |
| 7: |
|
app(app(gcd,0),y) |
→ y |
| 8: |
|
app(app(gcd,app(s,x)),0) |
→ app(s,x) |
| 9: |
|
app(app(gcd,app(s,x)),app(s,y)) |
→ app(app(app(if_gcd,app(app(le,y),x)),app(s,x)),app(s,y)) |
| 10: |
|
app(app(app(if_gcd,true),app(s,x)),app(s,y)) |
→ app(app(gcd,app(app(minus,x),y)),app(s,y)) |
| 11: |
|
app(app(app(if_gcd,false),app(s,x)),app(s,y)) |
→ app(app(gcd,app(app(minus,y),x)),app(s,x)) |
|
There are 17 dependency pairs:
|
| 12: |
|
APP(app(le,app(s,x)),app(s,y)) |
→ APP(app(le,x),y) |
| 13: |
|
APP(app(le,app(s,x)),app(s,y)) |
→ APP(le,x) |
| 14: |
|
APP(app(minus,x),app(s,y)) |
→ APP(pred,app(app(minus,x),y)) |
| 15: |
|
APP(app(minus,x),app(s,y)) |
→ APP(app(minus,x),y) |
| 16: |
|
APP(app(gcd,app(s,x)),app(s,y)) |
→ APP(app(app(if_gcd,app(app(le,y),x)),app(s,x)),app(s,y)) |
| 17: |
|
APP(app(gcd,app(s,x)),app(s,y)) |
→ APP(app(if_gcd,app(app(le,y),x)),app(s,x)) |
| 18: |
|
APP(app(gcd,app(s,x)),app(s,y)) |
→ APP(if_gcd,app(app(le,y),x)) |
| 19: |
|
APP(app(gcd,app(s,x)),app(s,y)) |
→ APP(app(le,y),x) |
| 20: |
|
APP(app(gcd,app(s,x)),app(s,y)) |
→ APP(le,y) |
| 21: |
|
APP(app(app(if_gcd,true),app(s,x)),app(s,y)) |
→ APP(app(gcd,app(app(minus,x),y)),app(s,y)) |
| 22: |
|
APP(app(app(if_gcd,true),app(s,x)),app(s,y)) |
→ APP(gcd,app(app(minus,x),y)) |
| 23: |
|
APP(app(app(if_gcd,true),app(s,x)),app(s,y)) |
→ APP(app(minus,x),y) |
| 24: |
|
APP(app(app(if_gcd,true),app(s,x)),app(s,y)) |
→ APP(minus,x) |
| 25: |
|
APP(app(app(if_gcd,false),app(s,x)),app(s,y)) |
→ APP(app(gcd,app(app(minus,y),x)),app(s,x)) |
| 26: |
|
APP(app(app(if_gcd,false),app(s,x)),app(s,y)) |
→ APP(gcd,app(app(minus,y),x)) |
| 27: |
|
APP(app(app(if_gcd,false),app(s,x)),app(s,y)) |
→ APP(app(minus,y),x) |
| 28: |
|
APP(app(app(if_gcd,false),app(s,x)),app(s,y)) |
→ APP(minus,y) |
|
The approximated dependency graph contains 2 SCCs:
{15}
and {12,16,17,19,21,23,25,27}.