The rewrite relation of the following TRS is considered.
from(X) | → | cons(X,from(s(X))) | (1) |
2ndspos(0,Z) | → | rnil | (2) |
2ndspos(s(N),cons(X,cons(Y,Z))) | → | rcons(posrecip(Y),2ndsneg(N,Z)) | (3) |
2ndsneg(0,Z) | → | rnil | (4) |
2ndsneg(s(N),cons(X,cons(Y,Z))) | → | rcons(negrecip(Y),2ndspos(N,Z)) | (5) |
pi(X) | → | 2ndspos(X,from(0)) | (6) |
plus(0,Y) | → | Y | (7) |
plus(s(X),Y) | → | s(plus(X,Y)) | (8) |
times(0,Y) | → | 0 | (9) |
times(s(X),Y) | → | plus(Y,times(X,Y)) | (10) |
square(X) | → | times(X,X) | (11) |
from(x0) |
2ndspos(0,x0) |
2ndspos(s(x0),cons(x1,cons(x2,x3))) |
2ndsneg(0,x0) |
2ndsneg(s(x0),cons(x1,cons(x2,x3))) |
pi(x0) |
plus(0,x0) |
plus(s(x0),x1) |
times(0,x0) |
times(s(x0),x1) |
square(x0) |
from#(X) | → | from#(s(X)) | (12) |
2ndspos#(s(N),cons(X,cons(Y,Z))) | → | 2ndsneg#(N,Z) | (13) |
2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | 2ndspos#(N,Z) | (14) |
pi#(X) | → | 2ndspos#(X,from(0)) | (15) |
pi#(X) | → | from#(0) | (16) |
plus#(s(X),Y) | → | plus#(X,Y) | (17) |
times#(s(X),Y) | → | plus#(Y,times(X,Y)) | (18) |
times#(s(X),Y) | → | times#(X,Y) | (19) |
square#(X) | → | times#(X,X) | (20) |
2ndspos#(s(N),cons(X,cons(Y,Z))) | → | 2ndsneg#(N,Z) | (13) |
2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | 2ndspos#(N,Z) | (14) |
pi#(X) | → | 2ndspos#(X,from(0)) | (15) |
pi#(X) | → | from#(0) | (16) |
plus#(s(X),Y) | → | plus#(X,Y) | (17) |
times#(s(X),Y) | → | plus#(Y,times(X,Y)) | (18) |
times#(s(X),Y) | → | times#(X,Y) | (19) |
square#(X) | → | times#(X,X) | (20) |
from(X) | → | cons(X,from(s(X))) | (1) |
2ndspos(0,Z) | → | rnil | (2) |
2ndspos(s(N),cons(X,cons(Y,Z))) | → | rcons(posrecip(Y),2ndsneg(N,Z)) | (3) |
2ndsneg(0,Z) | → | rnil | (4) |
2ndsneg(s(N),cons(X,cons(Y,Z))) | → | rcons(negrecip(Y),2ndspos(N,Z)) | (5) |
pi(X) | → | 2ndspos(X,from(0)) | (6) |
plus(0,Y) | → | Y | (7) |
plus(s(X),Y) | → | s(plus(X,Y)) | (8) |
times(0,Y) | → | 0 | (9) |
times(s(X),Y) | → | plus(Y,times(X,Y)) | (10) |
square(X) | → | times(X,X) | (11) |
We restrict the innermost strategy to the following left hand sides.
There are no lhss.
from#(s(z0)) | → | from#(s(s(z0))) | (21) |
from#(s(s(z0))) | → | from#(s(s(s(z0)))) | (22) |
t0 | = | from#(s(s(z0))) |
→P | from#(s(s(s(z0)))) | |
= | t1 |