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


--------------------------------------------------------------------------------


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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


----------------------------------------

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

   sel(s(N), cons(X)) -> sel(N, XS)
   from(X) -> cons(X)
   sel(0, cons(X)) -> X
   minus(X, 0) -> 0
   minus(s(X), s(Y)) -> minus(X, Y)
   quot(0, s(Y)) -> 0
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
   zWquot(XS, nil) -> nil
   zWquot(nil, XS) -> nil
   zWquot(cons(X), cons(Y)) -> cons(quot(X, Y))



Outermost Strategy.

----------------------------------------

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

   sel(s(N), cons(X)) -> sel(N, XS)
   from(X) -> cons(X)
   sel(0, cons(X)) -> X
   minus(X, 0) -> 0
   minus(s(X), s(Y)) -> minus(X, Y)
   quot(0, s(Y)) -> 0
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
   zWquot(XS, nil) -> nil
   zWquot(nil, XS) -> nil
   zWquot(cons(X), cons(Y)) -> cons(quot(X, Y))



Outermost Strategy.

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

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

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

Context: sel(N, [])

We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
----------------------------------------

(2)
NO