/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given GTRS could be disproven:

(0) GTRS
(1) CritRuleProof [COMPLETE, 0 ms]
(2) NO


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(0)
Obligation:
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:

   tail(cons(X)) -> L
   incr(nil) -> nil
   incr(cons(X)) -> cons(s(X))
   adx(nil) -> nil
   adx(cons(X)) -> incr(cons(X))
   nats -> adx(zeros)
   zeros -> cons(0)
   head(cons(X)) -> X


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(1) CritRuleProof (COMPLETE)
The rule tail(cons(X)) -> L contains free variables in its right-hand side. Hence the TRS is not-terminating.
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(2)
NO