The rewrite relation of the following TRS is considered.
2ndspos(s(N),cons(X)) | → | 2ndspos(s(N),cons2(Z)) | (1) |
2ndspos(s(N),cons2(cons(Y))) | → | rcons(posrecip(Y),2ndsneg(N,Z)) | (2) |
2ndsneg(s(N),cons(X)) | → | 2ndsneg(s(N),cons2(Z)) | (3) |
2ndsneg(s(N),cons2(cons(Y))) | → | rcons(negrecip(Y),2ndspos(N,Z)) | (4) |
from(X) | → | cons(X) | (5) |
2ndspos(0,Z) | → | rnil | (6) |
2ndsneg(0,Z) | → | rnil | (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) |
t0 | = | 2ndspos(s(N),cons(X)) |
→ | 2ndspos(s(N),cons2(2ndspos(s(N),cons(X)))) | |
= | t1 |