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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

   1 -> s(0)
   2 -> s(1)
   3 -> s(2)
   4 -> s(3)
   5 -> s(4)
   6 -> s(5)
   7 -> s(6)
   8 -> s(7)
   9 -> s(8)
   max'(0, x) -> x
   max'(s(x), s(y)) -> s(max'(x, y))
   app(empty, X) -> X
   max(singl(x)) -> x
   max(app(singl(x), Y)) -> max2(x, Y)
   max2(x, empty) -> x
   max2(x, singl(y)) -> max'(x, y)
   max2(x, app(singl(y), Z)) -> max2(max'(x, y), Z)

The set E consists of the following equations:

   max'(x, y) == max'(y, x)
   app(x, y) == app(y, x)
   app(app(x, y), z) == app(x, app(y, z))


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

Precedence:
9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1 > s_1
9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1 > 0
app_2 > max2_2 > max'_2 > s_1


Status:
app_2: flat status
max2_2: [2,1]
max'_2: multiset status



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(2)
YES