YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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:

   +(0, x) -> x
   +(s(x), s(y)) -> s(s(+(x, y)))
   *(0, x) -> 0
   *(s(x), s(y)) -> s(+(+(x, y), *(x, y)))
   U(empty, b) -> b
   sum(empty) -> 0
   sum(singl(x)) -> x
   sum(U(x, y)) -> +(sum(x), sum(y))
   prod(empty) -> s(0)
   prod(singl(x)) -> x
   prod(U(x, y)) -> *(prod(x), prod(y))

The set E consists of the following equations:

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


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

Precedence:
U_2 > +_2 > s_1
U_2 > sum_1
empty > 0
prod_1 > *_2 > +_2 > s_1


Status:
*_2: flat status
+_2: flat status
U_2: flat status



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(2)
YES