/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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:

   sel(s(X), cons(Y)) -> sel(X, Z)
   sel1(s(X), cons(Y)) -> sel1(X, Z)
   first1(s(X), cons(Y)) -> cons1(quote, first1(X, Z))
   quote -> sel1(X, Z)
   quote1 -> first1(X, Z)
   sel(0, cons(X)) -> X
   first(0, Z) -> nil
   first(s(X), cons(Y)) -> cons(Y)
   from(X) -> cons(X)
   sel1(0, cons(X)) -> quote
   first1(0, Z) -> nil1
   quote -> 01
   quote1 -> cons1(quote, quote1)
   quote1 -> nil1
   quote -> s1(quote)
   unquote(01) -> 0
   unquote(s1(X)) -> s(unquote(X))
   unquote1(nil1) -> nil
   unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
   fcons(X, Z) -> cons(X)


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