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


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given RelTRS could be proven:

(0) RelTRS
(1) RelTRS Reverse [EQUIVALENT, 0 ms]
(2) RelTRS
(3) RelTRSRRRProof [EQUIVALENT, 5 ms]
(4) RelTRS
(5) RIsEmptyProof [EQUIVALENT, 0 ms]
(6) YES


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

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

The relative TRS consists of the following S rules:

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


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(1) RelTRS Reverse (EQUIVALENT)
We have reversed the following relative TRS [REVERSE]:
The set of rules R is 
   c(a(a(x1))) -> c(b(a(x1)))
   c(b(c(x1))) -> a(c(b(x1)))

The set of rules S is 
   b(b(c(x1))) -> b(b(b(x1)))
   c(b(c(x1))) -> b(c(b(x1)))
   b(b(a(x1))) -> c(a(c(x1)))
   a(c(a(x1))) -> c(b(b(x1)))

We have obtained the following relative TRS:
The set of rules R is 
   a(a(c(x1))) -> a(b(c(x1)))
   c(b(c(x1))) -> b(c(a(x1)))

The set of rules S is 
   c(b(b(x1))) -> b(b(b(x1)))
   c(b(c(x1))) -> b(c(b(x1)))
   a(b(b(x1))) -> c(a(c(x1)))
   a(c(a(x1))) -> b(b(c(x1)))


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

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

The relative TRS consists of the following S rules:

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


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(3) RelTRSRRRProof (EQUIVALENT)
We used the following monotonic ordering for rule removal:
Knuth-Bendix order [KBO] with precedence:a_1 > c_1 > b_1

and weight map:

   a_1=1
   c_1=1
   b_1=1

The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
Rules from R:

   a(a(c(x1))) -> a(b(c(x1)))
   c(b(c(x1))) -> b(c(a(x1)))
Rules from S:

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




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(4)
Obligation:
Relative term rewrite system:
R is empty.
S is empty.

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(5) RIsEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(6)
YES