Platform claims not to support CPU time, falling back to wall time.
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proof of /home/fs5/ayamada/tpdb/relative/Relative_05/rt1-2.trs
# AProVE Commit ID: 2b684c7cda508b1711f707cb42f127e64fe1df88 ffrohn 20140415 dirty


Termination of the given RelTRS could be proven:

(0) RelTRS
(1) RelTRSRRRProof [EQUIVALENT, 378 ms]
(2) RelTRS
(3) RIsEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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(0)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   f(x) -> x
   g(x) -> x

The relative TRS consists of the following S rules:

   f(x) -> g(x)
   g(x) -> f(x)


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(1) RelTRSRRRProof (EQUIVALENT)
We used the following monotonic ordering for rule removal:
Polynomial interpretation [POLO]:

   POL(f(x_1)) = 1 + x_1
   POL(g(x_1)) = 1 + x_1
With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
Rules from R:

   f(x) -> x
   g(x) -> x
Rules from S:
none




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(2)
Obligation:
Relative term rewrite system:
R is empty.
The relative TRS consists of the following S rules:

   f(x) -> g(x)
   g(x) -> f(x)


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