YES
proof of SK90_4.05.trs
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 jera 20211004 unpublished


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

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 64 ms]
(2) QTRS
(3) RisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

   *(x, +(y, z)) -> +(*(x, y), *(x, z))
   *(+(x, y), z) -> +(*(x, z), *(y, z))
   *(x, 1) -> x
   *(1, y) -> y

Q is empty.

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(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Quasi precedence:
*_2 > +_2
1 > +_2


Status:
*_2: multiset status
+_2: multiset status
1: multiset status

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

   *(x, +(y, z)) -> +(*(x, y), *(x, z))
   *(+(x, y), z) -> +(*(x, z), *(y, z))
   *(x, 1) -> x
   *(1, y) -> y




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

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(3) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(4)
YES