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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RisEmptyProof [EQUIVALENT, 4 ms]
(4) YES


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

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   -(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -(-(x, y), -(x, y))

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Knuth-Bendix order [KBO] with precedence:neg_1 > -_2

and weight map:

   neg_1=1
   -_2=0

The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   -(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -(-(x, y), -(x, y))




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

(2)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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

(3) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
----------------------------------------

(4)
YES