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