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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Outermost Termination of the given OTRS could be disproven:

(0) OTRS
(1) OutermostNonTerminationProof [COMPLETE, 45 ms]
(2) NO


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(0)
Obligation:
Term rewrite system R:
The TRS R consists of the following rules:

   dbl(0) -> 0
   dbl(s(X)) -> s(s(dbl(X)))
   dbls(nil) -> nil
   dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y))
   sel(0, cons(X, Y)) -> X
   sel(s(X), cons(Y, Z)) -> sel(X, Z)
   indx(nil, X) -> nil
   indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z))
   from(X) -> cons(X, from(s(X)))
   dbl1(0) -> 01
   dbl1(s(X)) -> s1(s1(dbl1(X)))
   sel1(0, cons(X, Y)) -> X
   sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
   quote(0) -> 01
   quote(s(X)) -> s1(quote(X))
   quote(dbl(X)) -> dbl1(X)
   quote(sel(X, Y)) -> sel1(X, Y)



Outermost Strategy.

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(1) OutermostNonTerminationProof (COMPLETE)
Term rewrite system R:
The TRS R consists of the following rules:

   dbl(0) -> 0
   dbl(s(X)) -> s(s(dbl(X)))
   dbls(nil) -> nil
   dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y))
   sel(0, cons(X, Y)) -> X
   sel(s(X), cons(Y, Z)) -> sel(X, Z)
   indx(nil, X) -> nil
   indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z))
   from(X) -> cons(X, from(s(X)))
   dbl1(0) -> 01
   dbl1(s(X)) -> s1(s1(dbl1(X)))
   sel1(0, cons(X, Y)) -> X
   sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
   quote(0) -> 01
   quote(s(X)) -> s1(quote(X))
   quote(dbl(X)) -> dbl1(X)
   quote(sel(X, Y)) -> sel1(X, Y)



Outermost Strategy.

---------- Loop: ----------

from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X]

Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1].

Context: cons(X, [])

We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
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(2)
NO