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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

   U94(tt) -> s(length(L))
   zeros -> cons(0)
   U11(tt) -> U12(isNatIListKind)
   U12(tt) -> U13(isNatList)
   U13(tt) -> tt
   U21(tt) -> U22(isNatKind)
   U22(tt) -> U23(isNat)
   U23(tt) -> tt
   U31(tt) -> U32(isNatIListKind)
   U32(tt) -> U33(isNatList)
   U33(tt) -> tt
   U41(tt) -> U42(isNatKind)
   U42(tt) -> U43(isNatIListKind)
   U43(tt) -> U44(isNatIListKind)
   U44(tt) -> U45(isNat)
   U45(tt) -> U46(isNatIList)
   U46(tt) -> tt
   U51(tt) -> U52(isNatIListKind)
   U52(tt) -> tt
   U61(tt) -> tt
   U71(tt) -> tt
   U81(tt) -> U82(isNatKind)
   U82(tt) -> U83(isNatIListKind)
   U83(tt) -> U84(isNatIListKind)
   U84(tt) -> U85(isNat)
   U85(tt) -> U86(isNatList)
   U86(tt) -> tt
   U91(tt) -> U92(isNatIListKind)
   U92(tt) -> U93(isNat)
   U93(tt) -> U94(isNatKind)
   isNat -> tt
   isNat -> U11(isNatIListKind)
   isNat -> U21(isNatKind)
   isNatIList -> U31(isNatIListKind)
   isNatIList -> tt
   isNatIList -> U41(isNatKind)
   isNatIListKind -> tt
   isNatIListKind -> U51(isNatKind)
   isNatKind -> tt
   isNatKind -> U61(isNatIListKind)
   isNatKind -> U71(isNatKind)
   isNatList -> tt
   isNatList -> U81(isNatKind)
   length(nil) -> 0
   length(cons(N)) -> U91(isNatList)



Outermost Strategy.

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

   U94(tt) -> s(length(L))
   zeros -> cons(0)
   U11(tt) -> U12(isNatIListKind)
   U12(tt) -> U13(isNatList)
   U13(tt) -> tt
   U21(tt) -> U22(isNatKind)
   U22(tt) -> U23(isNat)
   U23(tt) -> tt
   U31(tt) -> U32(isNatIListKind)
   U32(tt) -> U33(isNatList)
   U33(tt) -> tt
   U41(tt) -> U42(isNatKind)
   U42(tt) -> U43(isNatIListKind)
   U43(tt) -> U44(isNatIListKind)
   U44(tt) -> U45(isNat)
   U45(tt) -> U46(isNatIList)
   U46(tt) -> tt
   U51(tt) -> U52(isNatIListKind)
   U52(tt) -> tt
   U61(tt) -> tt
   U71(tt) -> tt
   U81(tt) -> U82(isNatKind)
   U82(tt) -> U83(isNatIListKind)
   U83(tt) -> U84(isNatIListKind)
   U84(tt) -> U85(isNat)
   U85(tt) -> U86(isNatList)
   U86(tt) -> tt
   U91(tt) -> U92(isNatIListKind)
   U92(tt) -> U93(isNat)
   U93(tt) -> U94(isNatKind)
   isNat -> tt
   isNat -> U11(isNatIListKind)
   isNat -> U21(isNatKind)
   isNatIList -> U31(isNatIListKind)
   isNatIList -> tt
   isNatIList -> U41(isNatKind)
   isNatIListKind -> tt
   isNatIListKind -> U51(isNatKind)
   isNatKind -> tt
   isNatKind -> U61(isNatIListKind)
   isNatKind -> U71(isNatKind)
   isNatList -> tt
   isNatList -> U81(isNatKind)
   length(nil) -> 0
   length(cons(N)) -> U91(isNatList)



Outermost Strategy.

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

U94(tt) -> s(length(U94(tt))) with rule U94(tt) -> s(length(L)) at position [] and matcher [L / U94(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