Termination w.r.t. Q of the following Term Rewriting System could be proven:

Q restricted rewrite system:
The TRS R consists of the following rules:

a(a(x1)) → b(c(x1))
b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
d(d(d(x1))) → a(c(x1))

Q is empty.


QTRS
  ↳ DirectTerminationProof

Q restricted rewrite system:
The TRS R consists of the following rules:

a(a(x1)) → b(c(x1))
b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
d(d(d(x1))) → a(c(x1))

Q is empty.

We use [27] with the following order to prove termination.

Knuth-Bendix order [24] with precedence:
trivial

and weight map:

c_1=1696
b_1=1408
d_1=1088
a_1=1560
dummyConstant=1