Termination w.r.t. Q proof of TRS/SK902.58.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:

f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(x)

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(x)

Q is empty.

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

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

[g₁, h_3] > a > b > f₂
i₁ > f₂

Status:

b: multiset
i₁: [1]
a: multiset
h₃: [2,1,3]
f₂: [2,1]
g₁: [1]