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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

   s(p(x)) -> x
   p(s(x)) -> x
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))
   plus(p(x), y) -> p(plus(x, y))
   plus(i(x), x) -> 0
   plus(x, plus(i(x), y)) -> y
   i(0) -> 0
   i(s(x)) -> p(i(x))
   i(p(x)) -> s(i(x))
   i(i(x)) -> x
   i(plus(x, y)) -> plus(i(y), i(x))
   times(0, y) -> 0
   times(s(x), y) -> plus(times(x, y), y)
   times(p(x), y) -> plus(times(x, y), i(y))

The set E consists of the following equations:

   plus(x, y) == plus(y, x)
   times(x, y) == times(y, x)
   plus(plus(x, y), z) == plus(x, plus(y, z))
   times(times(x, y), z) == times(x, times(y, z))


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

Precedence:
times_2 > i_1 > plus_2 > s_1
times_2 > i_1 > plus_2 > p_1
times_2 > i_1 > 0


Status:
plus_2: flat status
times_2: flat status



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(2)
YES