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