NO
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given RelTRS could be disproven:

(0) RelTRS
(1) RelTRSLoopFinderProof [COMPLETE, 38 ms]
(2) NO


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(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))


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(1) RelTRSLoopFinderProof (COMPLETE)
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.
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(2)
NO