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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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:

   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)


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

(1) CritRuleProof (COMPLETE)
The rule U94(tt) -> s(length(L)) contains free variables in its right-hand side. Hence the TRS is not-terminating.
----------------------------------------

(2)
NO