SRS Relative pair #487521181

details

property	value
status	complete
benchmark	random-160.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.09559297562 seconds
cpu usage	4.891048257
max memory	3.94969088E8

stage attributes

key	value
output-size	2866
starexec-result	YES

output

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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 19 ms]
(4) RelTRS
(5) RIsEmptyProof [EQUIVALENT, 4 ms]
(6) YES


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

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

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

The relative TRS consists of the following S rules:

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


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

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

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

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

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


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

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

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

The relative TRS consists of the following S rules:

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


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

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

and weight map:

   b_1=1
   a_1=1
   c_1=1

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

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

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