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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given GTRS could be disproven:

(0) GTRS
(1) CritRuleProof [COMPLETE, 0 ms]
(2) NO


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(0)
Obligation:
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:

   U71(tt) -> s(length(L))
   U91(tt) -> cons(N)
   and(tt) -> X
   zeros -> cons(0)
   U11(tt) -> U12(isNatList)
   U12(tt) -> tt
   U21(tt) -> U22(isNat)
   U22(tt) -> tt
   U31(tt) -> U32(isNatList)
   U32(tt) -> tt
   U41(tt) -> U42(isNat)
   U42(tt) -> U43(isNatIList)
   U43(tt) -> tt
   U51(tt) -> U52(isNat)
   U52(tt) -> U53(isNatList)
   U53(tt) -> tt
   U61(tt) -> U62(isNat)
   U62(tt) -> U63(isNatIList)
   U63(tt) -> tt
   U81(tt) -> nil
   isNat -> tt
   isNat -> U11(isNatIListKind)
   isNat -> U21(isNatKind)
   isNatIList -> U31(isNatIListKind)
   isNatIList -> tt
   isNatIList -> U41(and(isNatKind))
   isNatIListKind -> tt
   isNatIListKind -> and(isNatKind)
   isNatKind -> tt
   isNatKind -> isNatIListKind
   isNatKind -> isNatKind
   isNatList -> tt
   isNatList -> U51(and(isNatKind))
   isNatList -> U61(and(isNatKind))
   length(nil) -> 0
   length(cons(N)) -> U71(and(and(isNatList)))
   take(0, IL) -> U81(and(isNatIList))
   take(s(M), cons(N)) -> U91(and(and(isNatIList)))


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(1) CritRuleProof (COMPLETE)
The rule U71(tt) -> s(length(L)) contains free variables in its right-hand side. Hence the TRS is not-terminating.
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(2)
NO