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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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:

   U41(tt) -> N
   U51(tt) -> s(plus(N, M))
   U71(tt) -> plus(x(N, M), N)
   and(tt) -> X
   U11(tt) -> U12(isNat)
   U12(tt) -> U13(isNat)
   U13(tt) -> tt
   U21(tt) -> U22(isNat)
   U22(tt) -> tt
   U31(tt) -> U32(isNat)
   U32(tt) -> U33(isNat)
   U33(tt) -> tt
   U61(tt) -> 0
   isNat -> tt
   isNat -> U11(and(isNatKind))
   isNat -> U21(isNatKind)
   isNat -> U31(and(isNatKind))
   isNatKind -> tt
   isNatKind -> and(isNatKind)
   isNatKind -> isNatKind
   plus(N, 0) -> U41(and(isNat))
   plus(N, s(M)) -> U51(and(and(isNat)))
   x(N, 0) -> U61(and(isNat))
   x(N, s(M)) -> U71(and(and(isNat)))


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(1) CritRuleProof (COMPLETE)
The rule U41(tt) -> N contains free variables in its right-hand side. Hence the TRS is not-terminating.
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(2)
NO