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


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NO
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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:

   U11(tt) -> s(length(L))
   U31(tt) -> cons(N)
   and(tt) -> X
   zeros -> cons(0)
   U21(tt) -> nil
   isNat -> tt
   isNat -> isNatList
   isNat -> isNat
   isNatIList -> isNatList
   isNatIList -> tt
   isNatIList -> and(isNat)
   isNatList -> tt
   isNatList -> and(isNat)
   length(nil) -> 0
   length(cons(N)) -> U11(and(isNatList))
   take(0, IL) -> U21(isNatIList)
   take(s(M), cons(N)) -> U31(and(isNatIList))



Outermost Strategy.

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

   U11(tt) -> s(length(L))
   U31(tt) -> cons(N)
   and(tt) -> X
   zeros -> cons(0)
   U21(tt) -> nil
   isNat -> tt
   isNat -> isNatList
   isNat -> isNat
   isNatIList -> isNatList
   isNatIList -> tt
   isNatIList -> and(isNat)
   isNatList -> tt
   isNatList -> and(isNat)
   length(nil) -> 0
   length(cons(N)) -> U11(and(isNatList))
   take(0, IL) -> U21(isNatIList)
   take(s(M), cons(N)) -> U31(and(isNatIList))



Outermost Strategy.

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

U11(tt) -> s(length(U11(tt))) with rule U11(tt) -> s(length(L)) at position [] and matcher [L / U11(tt)]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].

Context: s(length([]))

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