(0) Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:
f(act, y) → f(el(nact), y)
f(x, nact) → f(x, act)
act → el(nact)
l(el(x)) → el(l(x))
el(r(x)) → r(el(x))
The relative TRS consists of the following S rules:
nact → l(nact)
nact → r(nact)
(1) RelTRSLoopFinderProof (COMPLETE transformation)
The following loop was found:
---------- Loop: ----------
el(nact) → el(r(nact)) with rule nact → r(nact) at position [0] and matcher [ ]
el(r(nact)) → r(el(nact)) with rule el(r(x)) → r(el(x)) at position [] and matcher [x / nact]
Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].
Context: r([])
Therefore, the relative TRS problem does not terminate.
(2) NO