|
| 1: |
|
from(X) |
→ cons(X,n__from(n__s(X))) |
| 2: |
|
2ndspos(0,Z) |
→ rnil |
| 3: |
|
2ndspos(s(N),cons(X,n__cons(Y,Z))) |
→ rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z))) |
| 4: |
|
2ndsneg(0,Z) |
→ rnil |
| 5: |
|
2ndsneg(s(N),cons(X,n__cons(Y,Z))) |
→ rcons(negrecip(activate(Y)),2ndspos(N,activate(Z))) |
| 6: |
|
pi(X) |
→ 2ndspos(X,from(0)) |
| 7: |
|
plus(0,Y) |
→ Y |
| 8: |
|
plus(s(X),Y) |
→ s(plus(X,Y)) |
| 9: |
|
times(0,Y) |
→ 0 |
| 10: |
|
times(s(X),Y) |
→ plus(Y,times(X,Y)) |
| 11: |
|
square(X) |
→ times(X,X) |
| 12: |
|
from(X) |
→ n__from(X) |
| 13: |
|
s(X) |
→ n__s(X) |
| 14: |
|
cons(X1,X2) |
→ n__cons(X1,X2) |
| 15: |
|
activate(n__from(X)) |
→ from(activate(X)) |
| 16: |
|
activate(n__s(X)) |
→ s(activate(X)) |
| 17: |
|
activate(n__cons(X1,X2)) |
→ cons(activate(X1),X2) |
| 18: |
|
activate(X) |
→ X |
|
There are 20 dependency pairs:
|
| 19: |
|
FROM(X) |
→ CONS(X,n__from(n__s(X))) |
| 20: |
|
2ndspos#(s(N),cons(X,n__cons(Y,Z))) |
→ ACTIVATE(Y) |
| 21: |
|
2ndspos#(s(N),cons(X,n__cons(Y,Z))) |
→ 2ndsneg#(N,activate(Z)) |
| 22: |
|
2ndspos#(s(N),cons(X,n__cons(Y,Z))) |
→ ACTIVATE(Z) |
| 23: |
|
2ndsneg#(s(N),cons(X,n__cons(Y,Z))) |
→ ACTIVATE(Y) |
| 24: |
|
2ndsneg#(s(N),cons(X,n__cons(Y,Z))) |
→ 2ndspos#(N,activate(Z)) |
| 25: |
|
2ndsneg#(s(N),cons(X,n__cons(Y,Z))) |
→ ACTIVATE(Z) |
| 26: |
|
PI(X) |
→ 2ndspos#(X,from(0)) |
| 27: |
|
PI(X) |
→ FROM(0) |
| 28: |
|
PLUS(s(X),Y) |
→ S(plus(X,Y)) |
| 29: |
|
PLUS(s(X),Y) |
→ PLUS(X,Y) |
| 30: |
|
TIMES(s(X),Y) |
→ PLUS(Y,times(X,Y)) |
| 31: |
|
TIMES(s(X),Y) |
→ TIMES(X,Y) |
| 32: |
|
SQUARE(X) |
→ TIMES(X,X) |
| 33: |
|
ACTIVATE(n__from(X)) |
→ FROM(activate(X)) |
| 34: |
|
ACTIVATE(n__from(X)) |
→ ACTIVATE(X) |
| 35: |
|
ACTIVATE(n__s(X)) |
→ S(activate(X)) |
| 36: |
|
ACTIVATE(n__s(X)) |
→ ACTIVATE(X) |
| 37: |
|
ACTIVATE(n__cons(X1,X2)) |
→ CONS(activate(X1),X2) |
| 38: |
|
ACTIVATE(n__cons(X1,X2)) |
→ ACTIVATE(X1) |
|
The approximated dependency graph contains 4 SCCs:
{34,36,38},
{21,24},
{29}
and {31}.