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:

rev(nil) → nil
rev(.(x, y)) → ++(rev(y), .(x, nil))
car(.(x, y)) → x
cdr(.(x, y)) → y
null(nil) → true
null(.(x, y)) → false
++(nil, y) → y
++(.(x, y), z) → .(x, ++(y, z))

Q is empty.


↳ QTRS
  ↳ DirectTerminationProof

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

rev(nil) → nil
rev(.(x, y)) → ++(rev(y), .(x, nil))
car(.(x, y)) → x
cdr(.(x, y)) → y
null(nil) → true
null(.(x, y)) → false
++(nil, y) → y
++(.(x, y), z) → .(x, ++(y, z))

Q is empty.

We use [23] with the following order to prove termination.

Recursive path order with status [2].
Precedence:
rev1 > ++2 > .2 > nil
car1 > nil
cdr1 > nil
null1 > true > nil
null1 > false > nil

Status:
cdr1: multiset
car1: multiset
true: multiset
++2: [1,2]
rev1: [1]
false: multiset
null1: multiset
nil: multiset
.2: multiset