/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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


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

(0)
Obligation:
Term rewrite system R:
The TRS R consists of the following rules:

   U52(tt) -> N
   U64(tt) -> s(plus(N, M))
   U11(tt) -> U12(isNatKind)
   U12(tt) -> U13(isNatKind)
   U13(tt) -> U14(isNatKind)
   U14(tt) -> U15(isNat)
   U15(tt) -> U16(isNat)
   U16(tt) -> tt
   U21(tt) -> U22(isNatKind)
   U22(tt) -> U23(isNat)
   U23(tt) -> tt
   U31(tt) -> U32(isNatKind)
   U32(tt) -> tt
   U41(tt) -> tt
   U51(tt) -> U52(isNatKind)
   U61(tt) -> U62(isNatKind)
   U62(tt) -> U63(isNat)
   U63(tt) -> U64(isNatKind)
   isNat -> tt
   isNat -> U11(isNatKind)
   isNat -> U21(isNatKind)
   isNatKind -> tt
   isNatKind -> U31(isNatKind)
   isNatKind -> U41(isNatKind)
   plus(N, 0) -> U51(isNat)
   plus(N, s(M)) -> U61(isNat)



Outermost Strategy.

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

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

   U52(tt) -> N
   U64(tt) -> s(plus(N, M))
   U11(tt) -> U12(isNatKind)
   U12(tt) -> U13(isNatKind)
   U13(tt) -> U14(isNatKind)
   U14(tt) -> U15(isNat)
   U15(tt) -> U16(isNat)
   U16(tt) -> tt
   U21(tt) -> U22(isNatKind)
   U22(tt) -> U23(isNat)
   U23(tt) -> tt
   U31(tt) -> U32(isNatKind)
   U32(tt) -> tt
   U41(tt) -> tt
   U51(tt) -> U52(isNatKind)
   U61(tt) -> U62(isNatKind)
   U62(tt) -> U63(isNat)
   U63(tt) -> U64(isNatKind)
   isNat -> tt
   isNat -> U11(isNatKind)
   isNat -> U21(isNatKind)
   isNatKind -> tt
   isNatKind -> U31(isNatKind)
   isNatKind -> U41(isNatKind)
   plus(N, 0) -> U51(isNat)
   plus(N, s(M)) -> U61(isNat)



Outermost Strategy.

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

U52(tt) -> U52(tt) with rule U52(tt) -> N at position [] and matcher [N / U52(tt)]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [].

Context: []

We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
----------------------------------------

(2)
NO