YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
(2) YES


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

   dx(X) -> 1
   dx(0) -> 0
   dx(1) -> 0
   dx(a) -> 0
   dx(+(f, g)) -> +(dx(f), dx(g))
   dx(*(f, g)) -> +(*(dx(f), g), *(dx(g), f))
   dx(-(f, g)) -> -(dx(f), dx(g))
   dx(neg(f)) -> neg(dx(f))
   dx(/(f, g)) -> -(/(dx(f), g), /(*(dx(g), f), exp(g, 2)))
   dx(ln(f)) -> /(dx(f), f)
   dx(exp(f, g)) -> +(*(dx(f), *(exp(f, -(g, 1)), g)), *(dx(g), *(exp(f, g), ln(f))))

The set E consists of the following equations:

   *(x, y) == *(y, x)
   +(x, y) == +(y, x)
   *(*(x, y), z) == *(x, *(y, z))
   +(+(x, y), z) == +(x, +(y, z))


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(1) EDirectTerminationProof (EQUIVALENT)
We use [DA_FALKE] with the following order to prove termination.

Precedence:
dx_1 > 1
dx_1 > 0
dx_1 > +_2
dx_1 > *_2
dx_1 > -_2
dx_1 > neg_1
dx_1 > /_2
dx_1 > exp_2
dx_1 > 2
dx_1 > ln_1


Status:
*_2: flat status
+_2: flat status



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(2)
YES