The rewrite relation of the following TRS is considered.
from(X) | → | cons(X,from(s(X))) | (1) |
sel(0,cons(X,XS)) | → | X | (2) |
sel(s(N),cons(X,XS)) | → | sel(N,XS) | (3) |
minus(X,0) | → | 0 | (4) |
minus(s(X),s(Y)) | → | minus(X,Y) | (5) |
quot(0,s(Y)) | → | 0 | (6) |
quot(s(X),s(Y)) | → | s(quot(minus(X,Y),s(Y))) | (7) |
zWquot(XS,nil) | → | nil | (8) |
zWquot(nil,XS) | → | nil | (9) |
zWquot(cons(X,XS),cons(Y,YS)) | → | cons(quot(X,Y),zWquot(XS,YS)) | (10) |
from(x0) |
sel(0,cons(x0,x1)) |
sel(s(x0),cons(x1,x2)) |
minus(x0,0) |
minus(s(x0),s(x1)) |
quot(0,s(x0)) |
quot(s(x0),s(x1)) |
zWquot(x0,nil) |
zWquot(nil,x0) |
zWquot(cons(x0,x1),cons(x2,x3)) |
from#(X) | → | from#(s(X)) | (11) |
sel#(s(N),cons(X,XS)) | → | sel#(N,XS) | (12) |
minus#(s(X),s(Y)) | → | minus#(X,Y) | (13) |
quot#(s(X),s(Y)) | → | quot#(minus(X,Y),s(Y)) | (14) |
quot#(s(X),s(Y)) | → | minus#(X,Y) | (15) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | quot#(X,Y) | (16) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | zWquot#(XS,YS) | (17) |
sel#(s(N),cons(X,XS)) | → | sel#(N,XS) | (12) |
minus#(s(X),s(Y)) | → | minus#(X,Y) | (13) |
quot#(s(X),s(Y)) | → | quot#(minus(X,Y),s(Y)) | (14) |
quot#(s(X),s(Y)) | → | minus#(X,Y) | (15) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | quot#(X,Y) | (16) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | zWquot#(XS,YS) | (17) |
from(X) | → | cons(X,from(s(X))) | (1) |
sel(0,cons(X,XS)) | → | X | (2) |
sel(s(N),cons(X,XS)) | → | sel(N,XS) | (3) |
minus(X,0) | → | 0 | (4) |
minus(s(X),s(Y)) | → | minus(X,Y) | (5) |
quot(0,s(Y)) | → | 0 | (6) |
quot(s(X),s(Y)) | → | s(quot(minus(X,Y),s(Y))) | (7) |
zWquot(XS,nil) | → | nil | (8) |
zWquot(nil,XS) | → | nil | (9) |
zWquot(cons(X,XS),cons(Y,YS)) | → | cons(quot(X,Y),zWquot(XS,YS)) | (10) |
We restrict the innermost strategy to the following left hand sides.
There are no lhss.
from#(s(z0)) | → | from#(s(s(z0))) | (18) |
from#(s(s(z0))) | → | from#(s(s(s(z0)))) | (19) |
t0 | = | from#(s(s(z0))) |
→P | from#(s(s(s(z0)))) | |
= | t1 |