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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

   if(true, x, y) -> x
   if(false, x, y) -> y
   eq(0, 0) -> true
   eq(0, s(x)) -> false
   eq(s(x), s(y)) -> eq(x, y)
   plus(empty, x) -> x
   app(x, empty) -> empty
   app(x, app(empty, z)) -> app(empty, z)
   app(x, plus(y, z)) -> plus(app(x, y), app(x, z))
   app(x, app(plus(y, z), t)) -> app(plus(app(x, y), app(x, z)), t)
   app(singl(x), singl(y)) -> if(eq(x, y), singl(x), empty)

The set E consists of the following equations:

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


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

Precedence:
0 > true
0 > false
app_2 > if_3
app_2 > eq_2
app_2 > plus_2
app_2 > empty


Status:
app_2: flat status
plus_2: flat status



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(2)
YES