The rewrite relation of the following TRS is considered.
from(X) |
→ |
cons(X,n__from(s(X))) |
(1) |
2ndspos(0,Z) |
→ |
rnil |
(2) |
2ndspos(s(N),cons(X,Z)) |
→ |
2ndspos(s(N),cons2(X,activate(Z))) |
(3) |
2ndspos(s(N),cons2(X,cons(Y,Z))) |
→ |
rcons(posrecip(Y),2ndsneg(N,activate(Z))) |
(4) |
2ndsneg(0,Z) |
→ |
rnil |
(5) |
2ndsneg(s(N),cons(X,Z)) |
→ |
2ndsneg(s(N),cons2(X,activate(Z))) |
(6) |
2ndsneg(s(N),cons2(X,cons(Y,Z))) |
→ |
rcons(negrecip(Y),2ndspos(N,activate(Z))) |
(7) |
pi(X) |
→ |
2ndspos(X,from(0)) |
(8) |
plus(0,Y) |
→ |
Y |
(9) |
plus(s(X),Y) |
→ |
s(plus(X,Y)) |
(10) |
times(0,Y) |
→ |
0 |
(11) |
times(s(X),Y) |
→ |
plus(Y,times(X,Y)) |
(12) |
square(X) |
→ |
times(X,X) |
(13) |
from(X) |
→ |
n__from(X) |
(14) |
activate(n__from(X)) |
→ |
from(X) |
(15) |
activate(X) |
→ |
X |
(16) |
2ndspos#(s(N),cons(X,Z)) |
→ |
activate#(Z) |
(17) |
2ndspos#(s(N),cons(X,Z)) |
→ |
2ndspos#(s(N),cons2(X,activate(Z))) |
(18) |
2ndspos#(s(N),cons2(X,cons(Y,Z))) |
→ |
activate#(Z) |
(19) |
2ndspos#(s(N),cons2(X,cons(Y,Z))) |
→ |
2ndsneg#(N,activate(Z)) |
(20) |
2ndsneg#(s(N),cons(X,Z)) |
→ |
activate#(Z) |
(21) |
2ndsneg#(s(N),cons(X,Z)) |
→ |
2ndsneg#(s(N),cons2(X,activate(Z))) |
(22) |
2ndsneg#(s(N),cons2(X,cons(Y,Z))) |
→ |
activate#(Z) |
(23) |
2ndsneg#(s(N),cons2(X,cons(Y,Z))) |
→ |
2ndspos#(N,activate(Z)) |
(24) |
pi#(X) |
→ |
from#(0) |
(25) |
pi#(X) |
→ |
2ndspos#(X,from(0)) |
(26) |
plus#(s(X),Y) |
→ |
plus#(X,Y) |
(27) |
times#(s(X),Y) |
→ |
times#(X,Y) |
(28) |
times#(s(X),Y) |
→ |
plus#(Y,times(X,Y)) |
(29) |
square#(X) |
→ |
times#(X,X) |
(30) |
activate#(n__from(X)) |
→ |
from#(X) |
(31) |
The dependency pairs are split into 3
components.