Termination w.r.t. Q proof of TRS/SK902.29.trs

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:

prime(0) → false
prime(s(0)) → false
prime(s(s(x))) → prime1(s(s(x)), s(x))
prime1(x, 0) → false
prime1(x, s(0)) → true
prime1(x, s(s(y))) → and(not(divp(s(s(y)), x)), prime1(x, s(y)))
divp(x, y) → =(rem(x, y), 0)

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

prime(0) → false
prime(s(0)) → false
prime(s(s(x))) → prime1(s(s(x)), s(x))
prime1(x, 0) → false
prime1(x, s(0)) → true
prime1(x, s(s(y))) → and(not(divp(s(s(y)), x)), prime1(x, s(y)))
divp(x, y) → =(rem(x, y), 0)

Q is empty.

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

Lexicographic path order with status [19].
Quasi-Precedence:

[prime₁, s_1] > [false, prime1₂, true] > not₁ > and₂
[prime₁, s_1] > [false, prime1₂, true] > divp₂ > 0 > and₂
[prime₁, s_1] > [false, prime1₂, true] > divp₂ > =₂ > and₂
[prime₁, s_1] > [false, prime1₂, true] > divp₂ > rem₂ > and₂

Status:

true: multiset
rem₂: [1,2]
prime₁: [1]
and₂: [2,1]
false: multiset
divp₂: [2,1]
0: multiset
s₁: [1]
=₂: [1,2]
prime1₂: [2,1]
not₁: [1]