|
| 1: |
|
a__from(X) |
→ cons(mark(X),from(s(X))) |
| 2: |
|
a__sel(0,cons(X,XS)) |
→ mark(X) |
| 3: |
|
a__sel(s(N),cons(X,XS)) |
→ a__sel(mark(N),mark(XS)) |
| 4: |
|
a__minus(X,0) |
→ 0 |
| 5: |
|
a__minus(s(X),s(Y)) |
→ a__minus(mark(X),mark(Y)) |
| 6: |
|
a__quot(0,s(Y)) |
→ 0 |
| 7: |
|
a__quot(s(X),s(Y)) |
→ s(a__quot(a__minus(mark(X),mark(Y)),s(mark(Y)))) |
| 8: |
|
a__zWquot(XS,nil) |
→ nil |
| 9: |
|
a__zWquot(nil,XS) |
→ nil |
| 10: |
|
a__zWquot(cons(X,XS),cons(Y,YS)) |
→ cons(a__quot(mark(X),mark(Y)),zWquot(XS,YS)) |
| 11: |
|
mark(from(X)) |
→ a__from(mark(X)) |
| 12: |
|
mark(sel(X1,X2)) |
→ a__sel(mark(X1),mark(X2)) |
| 13: |
|
mark(minus(X1,X2)) |
→ a__minus(mark(X1),mark(X2)) |
| 14: |
|
mark(quot(X1,X2)) |
→ a__quot(mark(X1),mark(X2)) |
| 15: |
|
mark(zWquot(X1,X2)) |
→ a__zWquot(mark(X1),mark(X2)) |
| 16: |
|
mark(cons(X1,X2)) |
→ cons(mark(X1),X2) |
| 17: |
|
mark(s(X)) |
→ s(mark(X)) |
| 18: |
|
mark(0) |
→ 0 |
| 19: |
|
mark(nil) |
→ nil |
| 20: |
|
a__from(X) |
→ from(X) |
| 21: |
|
a__sel(X1,X2) |
→ sel(X1,X2) |
| 22: |
|
a__minus(X1,X2) |
→ minus(X1,X2) |
| 23: |
|
a__quot(X1,X2) |
→ quot(X1,X2) |
| 24: |
|
a__zWquot(X1,X2) |
→ zWquot(X1,X2) |
|
There are 31 dependency pairs:
|
| 25: |
|
A__FROM(X) |
→ MARK(X) |
| 26: |
|
A__SEL(0,cons(X,XS)) |
→ MARK(X) |
| 27: |
|
A__SEL(s(N),cons(X,XS)) |
→ A__SEL(mark(N),mark(XS)) |
| 28: |
|
A__SEL(s(N),cons(X,XS)) |
→ MARK(N) |
| 29: |
|
A__SEL(s(N),cons(X,XS)) |
→ MARK(XS) |
| 30: |
|
A__MINUS(s(X),s(Y)) |
→ A__MINUS(mark(X),mark(Y)) |
| 31: |
|
A__MINUS(s(X),s(Y)) |
→ MARK(X) |
| 32: |
|
A__MINUS(s(X),s(Y)) |
→ MARK(Y) |
| 33: |
|
A__QUOT(s(X),s(Y)) |
→ A__QUOT(a__minus(mark(X),mark(Y)),s(mark(Y))) |
| 34: |
|
A__QUOT(s(X),s(Y)) |
→ A__MINUS(mark(X),mark(Y)) |
| 35: |
|
A__QUOT(s(X),s(Y)) |
→ MARK(X) |
| 36: |
|
A__QUOT(s(X),s(Y)) |
→ MARK(Y) |
| 37: |
|
A__ZWQUOT(cons(X,XS),cons(Y,YS)) |
→ A__QUOT(mark(X),mark(Y)) |
| 38: |
|
A__ZWQUOT(cons(X,XS),cons(Y,YS)) |
→ MARK(X) |
| 39: |
|
A__ZWQUOT(cons(X,XS),cons(Y,YS)) |
→ MARK(Y) |
| 40: |
|
MARK(from(X)) |
→ A__FROM(mark(X)) |
| 41: |
|
MARK(from(X)) |
→ MARK(X) |
| 42: |
|
MARK(sel(X1,X2)) |
→ A__SEL(mark(X1),mark(X2)) |
| 43: |
|
MARK(sel(X1,X2)) |
→ MARK(X1) |
| 44: |
|
MARK(sel(X1,X2)) |
→ MARK(X2) |
| 45: |
|
MARK(minus(X1,X2)) |
→ A__MINUS(mark(X1),mark(X2)) |
| 46: |
|
MARK(minus(X1,X2)) |
→ MARK(X1) |
| 47: |
|
MARK(minus(X1,X2)) |
→ MARK(X2) |
| 48: |
|
MARK(quot(X1,X2)) |
→ A__QUOT(mark(X1),mark(X2)) |
| 49: |
|
MARK(quot(X1,X2)) |
→ MARK(X1) |
| 50: |
|
MARK(quot(X1,X2)) |
→ MARK(X2) |
| 51: |
|
MARK(zWquot(X1,X2)) |
→ A__ZWQUOT(mark(X1),mark(X2)) |
| 52: |
|
MARK(zWquot(X1,X2)) |
→ MARK(X1) |
| 53: |
|
MARK(zWquot(X1,X2)) |
→ MARK(X2) |
| 54: |
|
MARK(cons(X1,X2)) |
→ MARK(X1) |
| 55: |
|
MARK(s(X)) |
→ MARK(X) |
|
Consider the SCC {25-55}.