Termination w.r.t. Q of the given QTRS could be proven:

(0) Obligation:

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

d(x) → e(u(x))
d(u(x)) → c(x)
c(u(x)) → b(x)
v(e(x)) → x
b(u(x)) → a(e(x))

Q is empty.

(1) DirectTerminationProof (EQUIVALENT transformation)

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

Knuth-Bendix order [KBO] with precedence:

d₁ > c₁ > b₁ > a₁ > u₁ > v₁ > e₁

and weight map:

d_1=3
e_1=2
u_1=1
c_1=4
b_1=5
v_1=1
a_1=4

The variable weight is 1

(2) TRUE