SRS Standard pair #487511381

details

property	value
status	complete
benchmark	beans6.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n123.star.cs.uiowa.edu
space	Zantema_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.68324995041 seconds
cpu usage	23.239292304
max memory	3.450671104E9

stage attributes

key	value
output-size	5449
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 16 ms]
(2) QDP
(3) QDPOrderProof [EQUIVALENT, 27 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 47 ms]
(8) QDP
(9) PisEmptyProof [EQUIVALENT, 0 ms]
(10) YES


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

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   B(a(a(x1))) -> A(b(c(x1)))
   B(a(a(x1))) -> B(c(x1))
   B(a(a(x1))) -> C(x1)
   C(a(x1)) -> A(c(x1))
   C(a(x1)) -> C(x1)
   C(b(x1)) -> B(a(x1))
   C(b(x1)) -> A(x1)
   A(a(b(x1))) -> B(a(x1))
   A(a(b(x1))) -> A(x1)
   A(d(x1)) -> A(x1)
   B(d(x1)) -> A(b(x1))
   B(d(x1)) -> B(x1)
   A(a(x1)) -> A(b(a(x1)))
   A(a(x1)) -> B(a(x1))

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(3) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   B(a(a(x1))) -> A(b(c(x1)))
   B(a(a(x1))) -> B(c(x1))
   B(a(a(x1))) -> C(x1)
   C(a(x1)) -> A(c(x1))
   C(a(x1)) -> C(x1)
   C(b(x1)) -> A(x1)
   A(a(b(x1))) -> A(x1)
   A(d(x1)) -> A(x1)
   B(d(x1)) -> A(b(x1))
   B(d(x1)) -> B(x1)
The remaining pairs can at least be oriented weakly.

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