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

Q is empty.


QTRS
  ↳ DirectTerminationProof

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

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

Q is empty.

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

Knuth-Bendix order [24] with precedence:
b1 > c1

and weight map:

c_1=38
b_1=92
d_1=12
a_1=140
dummyConstant=1