YES Termination proof of rt1-1.trs

Termination of the given RelTRS could be proven:

0 RelTRS
↳1 RelTRStoRelADPProof (⇔, 0 ms)
↳2 RelADPP
↳3 RelADPDepGraphProof (⇔, 0 ms)
↳4 TRUE

(0) Obligation:

Relative term rewrite system:
The relative TRS consists of the following R rules:

f(x) → x

The relative TRS consists of the following S rules:

a → g(a)

(1) RelTRStoRelADPProof (EQUIVALENT transformation)

We upgrade the RelTRS problem to an equivalent Relative ADP Problem [IJCAR24].

(2) Obligation:

Relative ADP Problem with
absolute ADPs:

f(x) → x

and relative ADPs:

a → g(A)

(3) RelADPDepGraphProof (EQUIVALENT transformation)

We use the relative dependency graph processor [IJCAR24].
The approximation of the Relative Dependency Graph contains:
0 SCCs with nodes from P_abs,
0 Lassos,
Result: This relative DT problem is equivalent to 0 subproblems.

(4) TRUE