Platform claims not to support CPU time, falling back to wall time.
Cannot find out cpu time on external processes, falling back to wall time!
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.
----------------------------------------
(4)
YES