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:

D(t) → 1
D(constant) → 0
D(+(x, y)) → +(D(x), D(y))
D(*(x, y)) → +(*(y, D(x)), *(x, D(y)))
D(-(x, y)) → -(D(x), D(y))

Q is empty.


QTRS
  ↳ DirectTerminationProof

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

D(t) → 1
D(constant) → 0
D(+(x, y)) → +(D(x), D(y))
D(*(x, y)) → +(*(y, D(x)), *(x, D(y)))
D(-(x, y)) → -(D(x), D(y))

Q is empty.

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

Recursive path order with status [2].
Quasi-Precedence:
[D1, 1, *2] > 0 > +2
[D1, 1, *2] > -2 > +2
t > +2
constant > +2

Status:
+2: multiset
t: multiset
1: multiset
D1: [1]
-2: [2,1]
0: multiset
constant: multiset
*2: [1,2]