/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 ms]
(2) NO


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

   app(nil, YS) -> YS
   app(cons(X, XS), YS) -> cons(X, n__app(activate(XS), YS))
   from(X) -> cons(X, n__from(s(X)))
   zWadr(nil, YS) -> nil
   zWadr(XS, nil) -> nil
   zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, n__nil)), n__zWadr(activate(XS), activate(YS)))
   prefix(L) -> cons(nil, n__zWadr(L, prefix(L)))
   app(X1, X2) -> n__app(X1, X2)
   from(X) -> n__from(X)
   nil -> n__nil
   zWadr(X1, X2) -> n__zWadr(X1, X2)
   activate(n__app(X1, X2)) -> app(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__nil) -> nil
   activate(n__zWadr(X1, X2)) -> zWadr(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:

   app(nil, YS) -> YS
   app(cons(X, XS), YS) -> cons(X, n__app(activate(XS), YS))
   from(X) -> cons(X, n__from(s(X)))
   zWadr(nil, YS) -> nil
   zWadr(XS, nil) -> nil
   zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, n__nil)), n__zWadr(activate(XS), activate(YS)))
   prefix(L) -> cons(nil, n__zWadr(L, prefix(L)))
   app(X1, X2) -> n__app(X1, X2)
   from(X) -> n__from(X)
   nil -> n__nil
   zWadr(X1, X2) -> n__zWadr(X1, X2)
   activate(n__app(X1, X2)) -> app(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__nil) -> nil
   activate(n__zWadr(X1, X2)) -> zWadr(X1, X2)
   activate(X) -> X



Outermost Strategy.

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

prefix(L) -> cons(nil, n__zWadr(L, prefix(L))) with rule prefix(L') -> cons(nil, n__zWadr(L', prefix(L'))) at position [] and matcher [L' / L]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [1,1].

Context: cons(nil, n__zWadr(L, []))

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