/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given RelTRS could be disproven:

(0) RelTRS
(1) RelTRSLoopFinderProof [COMPLETE, 66 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