The rewrite relation of the following TRS is considered.
nats | → | cons(0,n__incr(nats)) | (1) |
pairs | → | cons(0,n__incr(odds)) | (2) |
odds | → | incr(pairs) | (3) |
incr(cons(X,XS)) | → | cons(s(X),n__incr(activate(XS))) | (4) |
head(cons(X,XS)) | → | X | (5) |
tail(cons(X,XS)) | → | activate(XS) | (6) |
incr(X) | → | n__incr(X) | (7) |
activate(n__incr(X)) | → | incr(X) | (8) |
activate(X) | → | X | (9) |
tail(cons(X,XS)) | → | activate(XS) | (6) |
head(cons(X,XS)) | → | X | (5) |
nats# | → | nats# | (10) |
pairs# | → | odds# | (11) |
odds# | → | incr#(pairs) | (12) |
odds# | → | pairs# | (13) |
incr#(cons(X,XS)) | → | activate#(XS) | (14) |
activate#(n__incr(X)) | → | incr#(X) | (15) |
pairs# | → | odds# | (11) |
odds# | → | incr#(pairs) | (12) |
odds# | → | pairs# | (13) |
incr#(cons(X,XS)) | → | activate#(XS) | (14) |
activate#(n__incr(X)) | → | incr#(X) | (15) |
nats | → | cons(0,n__incr(nats)) | (1) |
pairs | → | cons(0,n__incr(odds)) | (2) |
odds | → | incr(pairs) | (3) |
incr(cons(X,XS)) | → | cons(s(X),n__incr(activate(XS))) | (4) |
incr(X) | → | n__incr(X) | (7) |
activate(n__incr(X)) | → | incr(X) | (8) |
activate(X) | → | X | (9) |
t0 | = | nats# |
→P | nats# | |
= | t1 |