/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 208 ms]
(2) NO


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

   from(X) -> cons(X, n__from(s(X)))
   length(n__nil) -> 0
   length(n__cons(X, Y)) -> s(length1(activate(Y)))
   length1(X) -> length(activate(X))
   from(X) -> n__from(X)
   nil -> n__nil
   cons(X1, X2) -> n__cons(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__nil) -> nil
   activate(n__cons(X1, X2)) -> cons(X1, X2)
   activate(X) -> X



Outermost Strategy.

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

   from(X) -> cons(X, n__from(s(X)))
   length(n__nil) -> 0
   length(n__cons(X, Y)) -> s(length1(activate(Y)))
   length1(X) -> length(activate(X))
   from(X) -> n__from(X)
   nil -> n__nil
   cons(X1, X2) -> n__cons(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__nil) -> nil
   activate(n__cons(X1, X2)) -> cons(X1, X2)
   activate(X) -> X



Outermost Strategy.

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

length1(activate(n__from(X'))) -> length(activate(activate(n__from(X')))) with rule length1(X) -> length(activate(X)) at position [] and matcher [X / activate(n__from(X'))]

length(activate(activate(n__from(X')))) -> length(activate(n__from(X'))) with rule activate(X) -> X at position [0] and matcher [X / activate(n__from(X'))]

length(activate(n__from(X'))) -> length(from(X')) with rule activate(n__from(X'')) -> from(X'') at position [0] and matcher [X'' / X']

length(from(X')) -> length(cons(X', n__from(s(X')))) with rule from(X) -> cons(X, n__from(s(X))) at position [0] and matcher [X / X']

length(cons(X', n__from(s(X')))) -> length(n__cons(X', n__from(s(X')))) with rule cons(X1, X2) -> n__cons(X1, X2) at position [0] and matcher [X1 / X', X2 / n__from(s(X'))]

length(n__cons(X', n__from(s(X')))) -> s(length1(activate(n__from(s(X'))))) with rule length(n__cons(X, Y)) -> s(length1(activate(Y))) at position [] and matcher [X / X', Y / n__from(s(X'))]

Now an instance of the first term with Matcher [X' / s(X')] occurs in the last term at position [0].

Context: s([])

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