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


--------------------------------------------------------------------------------


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given RelTRS could be disproven:

(0) RelTRS
(1) RelTRS Reverse [EQUIVALENT, 0 ms]
(2) RelTRS
(3) RelTRSLoopFinderProof [COMPLETE, 0 ms]
(4) NO


----------------------------------------

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

   b(a(x)) -> a(b(x))

The relative TRS consists of the following S rules:

   a(x) -> a(a(x))
   b(x) -> b(b(x))


----------------------------------------

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

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

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

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


----------------------------------------

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

   a(b(x)) -> b(a(x))

The relative TRS consists of the following S rules:

   a(x) -> a(a(x))
   b(x) -> b(b(x))


----------------------------------------

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

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

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

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

Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].

Context: b([])

Therefore, the relative TRS problem does not terminate.
----------------------------------------

(4)
NO