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/Mixed_relative_TRS/assoc.trs
# AProVE Commit ID: 2b684c7cda508b1711f707cb42f127e64fe1df88 ffrohn 20140415 dirty
Termination of the given RelTRS could be disproven:
(0) RelTRS
(1) RelTRSLoopFinderProof [COMPLETE, 236 ms]
(2) NO
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(0)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:
f(a, x) -> f(x, f(b, x))
The relative TRS consists of the following S rules:
f(f(x, y), z) -> f(x, f(y, z))
f(x, f(y, z)) -> f(f(x, y), z)
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(1) RelTRSLoopFinderProof (COMPLETE)
The following loop was found:
---------- Loop: ----------
f(a, f(x', f(y', a))) -> f(a, f(f(x', y'), a)) with rule f(x'', f(y'', z)) -> f(f(x'', y''), z) at position [1] and matcher [x'' / x', y'' / y', z / a]
f(a, f(f(x', y'), a)) -> f(f(f(x', y'), a), f(b, f(f(x', y'), a))) with rule f(a, x) -> f(x, f(b, x)) at position [] and matcher [x / f(f(x', y'), a)]
f(f(f(x', y'), a), f(b, f(f(x', y'), a))) -> f(f(x', y'), f(a, f(b, f(f(x', y'), a)))) with rule f(f(x, y), z) -> f(x, f(y, z)) at position [] and matcher [x / f(x', y'), y / a, z / f(b, f(f(x', y'), a))]
Now an instance of the first term with Matcher [x' / b, y' / f(x', y')] occurs in the last term at position [1].
Context: f(f(x', y'), [])
Therefore, the relative TRS problem does not terminate.
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(2)
NO