|
| 1: |
|
app(app(app(if,true),xs),ys) |
→ xs |
| 2: |
|
app(app(app(if,false),xs),ys) |
→ ys |
| 3: |
|
app(app(lt,app(s,x)),app(s,y)) |
→ app(app(lt,x),y) |
| 4: |
|
app(app(lt,0),app(s,y)) |
→ true |
| 5: |
|
app(app(lt,y),0) |
→ false |
| 6: |
|
app(app(eq,x),x) |
→ true |
| 7: |
|
app(app(eq,app(s,x)),0) |
→ false |
| 8: |
|
app(app(eq,0),app(s,x)) |
→ false |
| 9: |
|
app(app(merge,xs),nil) |
→ xs |
| 10: |
|
app(app(merge,nil),ys) |
→ ys |
| 11: |
|
app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ app(app(app(if,app(app(lt,x),y)),app(app(cons,x),app(app(merge,xs),app(app(cons,y),ys)))),app(app(app(if,app(app(eq,x),y)),app(app(cons,x),app(app(merge,xs),ys))),app(app(cons,y),app(app(merge,app(app(cons,x),xs)),ys)))) |
| 12: |
|
app(app(map,f),nil) |
→ nil |
| 13: |
|
app(app(map,f),app(app(cons,x),xs)) |
→ app(app(cons,app(f,x)),app(app(map,f),xs)) |
| 14: |
|
app(app(mult,0),x) |
→ 0 |
| 15: |
|
app(app(mult,app(s,x)),y) |
→ app(app(plus,y),app(app(mult,x),y)) |
| 16: |
|
app(app(plus,0),x) |
→ 0 |
| 17: |
|
app(app(plus,app(s,x)),y) |
→ app(s,app(app(plus,x),y)) |
| 18: |
|
list1 |
→ app(app(map,app(mult,app(s,app(s,0)))),hamming) |
| 19: |
|
list2 |
→ app(app(map,app(mult,app(s,app(s,app(s,0))))),hamming) |
| 20: |
|
list3 |
→ app(app(map,app(mult,app(s,app(s,app(s,app(s,app(s,0))))))),hamming) |
| 21: |
|
hamming |
→ app(app(cons,app(s,0)),app(app(merge,list1),app(app(merge,list2),list3))) |
|
There are 62 dependency pairs:
|
| 22: |
|
APP(app(lt,app(s,x)),app(s,y)) |
→ APP(app(lt,x),y) |
| 23: |
|
APP(app(lt,app(s,x)),app(s,y)) |
→ APP(lt,x) |
| 24: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(app(if,app(app(lt,x),y)),app(app(cons,x),app(app(merge,xs),app(app(cons,y),ys)))),app(app(app(if,app(app(eq,x),y)),app(app(cons,x),app(app(merge,xs),ys))),app(app(cons,y),app(app(merge,app(app(cons,x),xs)),ys)))) |
| 25: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(if,app(app(lt,x),y)),app(app(cons,x),app(app(merge,xs),app(app(cons,y),ys)))) |
| 26: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(if,app(app(lt,x),y)) |
| 27: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(lt,x),y) |
| 28: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(lt,x) |
| 29: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(cons,x),app(app(merge,xs),app(app(cons,y),ys))) |
| 30: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(merge,xs),app(app(cons,y),ys)) |
| 31: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(app(if,app(app(eq,x),y)),app(app(cons,x),app(app(merge,xs),ys))),app(app(cons,y),app(app(merge,app(app(cons,x),xs)),ys))) |
| 32: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(if,app(app(eq,x),y)),app(app(cons,x),app(app(merge,xs),ys))) |
| 33: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(if,app(app(eq,x),y)) |
| 34: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(eq,x),y) |
| 35: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(eq,x) |
| 36: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(cons,x),app(app(merge,xs),ys)) |
| 37: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(merge,xs),ys) |
| 38: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(merge,xs) |
| 39: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(cons,y),app(app(merge,app(app(cons,x),xs)),ys)) |
| 40: |
|
APP(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) |
→ APP(app(merge,app(app(cons,x),xs)),ys) |
| 41: |
|
APP(app(map,f),app(app(cons,x),xs)) |
→ APP(app(cons,app(f,x)),app(app(map,f),xs)) |
| 42: |
|
APP(app(map,f),app(app(cons,x),xs)) |
→ APP(cons,app(f,x)) |
| 43: |
|
APP(app(map,f),app(app(cons,x),xs)) |
→ APP(f,x) |
| 44: |
|
APP(app(map,f),app(app(cons,x),xs)) |
→ APP(app(map,f),xs) |
| 45: |
|
APP(app(mult,app(s,x)),y) |
→ APP(app(plus,y),app(app(mult,x),y)) |
| 46: |
|
APP(app(mult,app(s,x)),y) |
→ APP(plus,y) |
| 47: |
|
APP(app(mult,app(s,x)),y) |
→ APP(app(mult,x),y) |
| 48: |
|
APP(app(mult,app(s,x)),y) |
→ APP(mult,x) |
| 49: |
|
APP(app(plus,app(s,x)),y) |
→ APP(s,app(app(plus,x),y)) |
| 50: |
|
APP(app(plus,app(s,x)),y) |
→ APP(app(plus,x),y) |
| 51: |
|
APP(app(plus,app(s,x)),y) |
→ APP(plus,x) |
| 52: |
|
LIST1 |
→ APP(app(map,app(mult,app(s,app(s,0)))),hamming) |
| 53: |
|
LIST1 |
→ APP(map,app(mult,app(s,app(s,0)))) |
| 54: |
|
LIST1 |
→ APP(mult,app(s,app(s,0))) |
| 55: |
|
LIST1 |
→ APP(s,app(s,0)) |
| 56: |
|
LIST1 |
→ APP(s,0) |
| 57: |
|
LIST1 |
→ HAMMING |
| 58: |
|
LIST2 |
→ APP(app(map,app(mult,app(s,app(s,app(s,0))))),hamming) |
| 59: |
|
LIST2 |
→ APP(map,app(mult,app(s,app(s,app(s,0))))) |
| 60: |
|
LIST2 |
→ APP(mult,app(s,app(s,app(s,0)))) |
| 61: |
|
LIST2 |
→ APP(s,app(s,app(s,0))) |
| 62: |
|
LIST2 |
→ APP(s,app(s,0)) |
| 63: |
|
LIST2 |
→ APP(s,0) |
| 64: |
|
LIST2 |
→ HAMMING |
| 65: |
|
LIST3 |
→ APP(app(map,app(mult,app(s,app(s,app(s,app(s,app(s,0))))))),hamming) |
| 66: |
|
LIST3 |
→ APP(map,app(mult,app(s,app(s,app(s,app(s,app(s,0))))))) |
| 67: |
|
LIST3 |
→ APP(mult,app(s,app(s,app(s,app(s,app(s,0)))))) |
| 68: |
|
LIST3 |
→ APP(s,app(s,app(s,app(s,app(s,0))))) |
| 69: |
|
LIST3 |
→ APP(s,app(s,app(s,app(s,0)))) |
| 70: |
|
LIST3 |
→ APP(s,app(s,app(s,0))) |
| 71: |
|
LIST3 |
→ APP(s,app(s,0)) |
| 72: |
|
LIST3 |
→ APP(s,0) |
| 73: |
|
LIST3 |
→ HAMMING |
| 74: |
|
HAMMING |
→ APP(app(cons,app(s,0)),app(app(merge,list1),app(app(merge,list2),list3))) |
| 75: |
|
HAMMING |
→ APP(cons,app(s,0)) |
| 76: |
|
HAMMING |
→ APP(s,0) |
| 77: |
|
HAMMING |
→ APP(app(merge,list1),app(app(merge,list2),list3)) |
| 78: |
|
HAMMING |
→ APP(merge,list1) |
| 79: |
|
HAMMING |
→ LIST1 |
| 80: |
|
HAMMING |
→ APP(app(merge,list2),list3) |
| 81: |
|
HAMMING |
→ APP(merge,list2) |
| 82: |
|
HAMMING |
→ LIST2 |
| 83: |
|
HAMMING |
→ LIST3 |
|
The approximated dependency graph contains 2 SCCs:
{22,24,25,27,29-32,34,36,37,39-41,43-45,47,50}
and {57,64,73,79,82,83}.