(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) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic path order with status [LPO].
Quasi-Precedence:
[d1, c1] > u1 > b1 > e1
[d1, c1] > u1 > a1 > e1
v1 > e1

Status:
c1: [1]
v1: [1]
a1: [1]
u1: [1]
e1: [1]
b1: [1]
d1: [1]

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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))


(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) TRUE