The rewrite relation of the following TRS is considered.
nats | → | cons(0,n__incr(n__nats)) | (1) |
pairs | → | cons(0,n__incr(n__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) |
nats | → | n__nats | (8) |
odds | → | n__odds | (9) |
activate(n__incr(X)) | → | incr(activate(X)) | (10) |
activate(n__nats) | → | nats | (11) |
activate(n__odds) | → | odds | (12) |
activate(X) | → | X | (13) |
tail(cons(X,XS)) | → | activate(XS) | (6) |
head(cons(X,XS)) | → | X | (5) |
odds# | → | incr#(pairs) | (14) |
odds# | → | pairs# | (15) |
incr#(cons(X,XS)) | → | activate#(XS) | (16) |
activate#(n__incr(X)) | → | incr#(activate(X)) | (17) |
activate#(n__incr(X)) | → | activate#(X) | (18) |
activate#(n__nats) | → | nats# | (19) |
activate#(n__odds) | → | odds# | (20) |
odds# | → | pairs# | (15) |
activate#(n__nats) | → | nats# | (19) |
odds# | → | incr#(cons(0,n__incr(n__odds))) | (21) |
activate#(n__incr(n__incr(x0))) | → | incr#(incr(activate(x0))) | (22) |
activate#(n__incr(n__nats)) | → | incr#(nats) | (23) |
activate#(n__incr(n__odds)) | → | incr#(odds) | (24) |
activate#(n__incr(x0)) | → | incr#(x0) | (25) |
activate#(n__incr(n__nats)) | → | incr#(cons(0,n__incr(n__nats))) | (26) |
activate#(n__incr(n__nats)) | → | incr#(n__nats) | (27) |
activate#(n__incr(n__nats)) | → | incr#(n__nats) | (27) |
t0 | = | activate#(n__incr(n__nats)) |
→P | incr#(cons(0,n__incr(n__nats))) | |
→P | activate#(n__incr(n__nats)) | |
= | t2 |