NO
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given GTRS could be disproven:

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


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

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

   U72(tt) -> s(length(L))
   U93(tt) -> cons(N)
   zeros -> cons(0)
   U11(tt) -> tt
   U21(tt) -> tt
   U31(tt) -> tt
   U41(tt) -> U42(isNatIList)
   U42(tt) -> tt
   U51(tt) -> U52(isNatList)
   U52(tt) -> tt
   U61(tt) -> U62(isNatIList)
   U62(tt) -> tt
   U71(tt) -> U72(isNat)
   U81(tt) -> nil
   U91(tt) -> U92(isNat)
   U92(tt) -> U93(isNat)
   isNat -> tt
   isNat -> U11(isNatList)
   isNat -> U21(isNat)
   isNatIList -> U31(isNatList)
   isNatIList -> tt
   isNatIList -> U41(isNat)
   isNatList -> tt
   isNatList -> U51(isNat)
   isNatList -> U61(isNat)
   length(nil) -> 0
   length(cons(N)) -> U71(isNatList)
   take(0, IL) -> U81(isNatIList)
   take(s(M), cons(N)) -> U91(isNatIList)


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

(1) CritRuleProof (COMPLETE)
The rule U72(tt) -> s(length(L)) contains free variables in its right-hand side. Hence the TRS is not-terminating.
----------------------------------------

(2)
NO