/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given RelTRS could be disproven:

(0) RelTRS
(1) RelTRSLoopFinderProof [COMPLETE, 30.5 s]
(2) NO


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

   a(c(c(x1))) -> c(c(a(x1)))
   a(b(b(x1))) -> b(b(a(x1)))
   a(a(c(x1))) -> b(b(a(x1)))
   b(c(a(x1))) -> a(c(c(x1)))

The relative TRS consists of the following S rules:

   a(c(a(x1))) -> a(c(b(x1)))
   b(a(a(x1))) -> a(a(a(x1)))


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(1) RelTRSLoopFinderProof (COMPLETE)
The following loop was found:

---------- Loop: ----------

b(b(a(a(c(a(c(a(x1)))))))) -> b(b(a(a(c(b(c(a(x1)))))))) with rule a(c(a(x1'))) -> a(c(b(x1'))) at position [0,0,0] and matcher [x1' / c(a(x1))]

b(b(a(a(c(b(c(a(x1)))))))) -> b(b(a(a(c(a(c(c(x1)))))))) with rule b(c(a(x1'))) -> a(c(c(x1'))) at position [0,0,0,0,0] and matcher [x1' / x1]

b(b(a(a(c(a(c(c(x1)))))))) -> b(b(a(a(c(c(c(a(x1)))))))) with rule a(c(c(x1'))) -> c(c(a(x1'))) at position [0,0,0,0,0] and matcher [x1' / x1]

b(b(a(a(c(c(c(a(x1)))))))) -> b(a(a(a(c(c(c(a(x1)))))))) with rule b(a(a(x1'))) -> a(a(a(x1'))) at position [0] and matcher [x1' / c(c(c(a(x1))))]

b(a(a(a(c(c(c(a(x1)))))))) -> b(a(a(c(c(a(c(a(x1)))))))) with rule a(c(c(x1'))) -> c(c(a(x1'))) at position [0,0,0] and matcher [x1' / c(a(x1))]

b(a(a(c(c(a(c(a(x1)))))))) -> a(a(a(c(c(a(c(a(x1)))))))) with rule b(a(a(x1'))) -> a(a(a(x1'))) at position [] and matcher [x1' / c(c(a(c(a(x1)))))]

a(a(a(c(c(a(c(a(x1)))))))) -> a(b(b(a(c(a(c(a(x1)))))))) with rule a(a(c(x1'))) -> b(b(a(x1'))) at position [0] and matcher [x1' / c(a(c(a(x1))))]

a(b(b(a(c(a(c(a(x1)))))))) -> b(b(a(a(c(a(c(a(x1)))))))) with rule a(b(b(x1'))) -> b(b(a(x1'))) at position [] and matcher [x1' / a(c(a(c(a(x1)))))]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [].

Context: []

Therefore, the relative TRS problem does not terminate.
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(2)
NO