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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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


----------------------------------------

(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)
   union(empty, x) -> x
   inter(empty, x) -> empty
   inter(union(y, z), x) -> union(inter(x, y), inter(x, z))
   inter(singl(x), singl(y)) -> if(eq(x, y), singl(x), empty)

The set E consists of the following equations:

   eq(x, y) == eq(y, x)
   inter(x, y) == inter(y, x)
   union(x, y) == union(y, x)
   inter(inter(x, y), z) == inter(x, inter(y, z))
   union(union(x, y), z) == union(x, union(y, z))


----------------------------------------

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

Precedence:
s_1 > false
inter_2 > if_3
inter_2 > eq_2 > true
inter_2 > union_2
singl_1 > empty


Status:
inter_2: flat status
union_2: flat status
eq_2: flat status



----------------------------------------

(2)
YES