NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given RelTRS could be disproven:

(0) RelTRS
(1) RelTRSLoopFinderProof [COMPLETE, 27 ms]
(2) NO


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(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)


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