SRS Standard pair #487091428

details

property	value
status	complete
benchmark	z114.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n022.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.6458 seconds
cpu usage	7.26207
user time	6.90855
system time	0.353519
max virtual memory	3.9103892E7
max residence set size	818904.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(2) QDP
(3) QDPOrderProof [EQUIVALENT, 6 ms]
(4) QDP
(5) MRRProof [EQUIVALENT, 0 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) TRUE


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

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

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

   A(c(x1)) -> B(x1)
   A(x1) -> B(b(b(x1)))
   A(x1) -> B(b(x1))
   A(x1) -> B(x1)
   B(c(b(x1))) -> A(c(x1))

The TRS R consists of the following rules:

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

   A(c(x1)) -> B(x1)
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial interpretation [POLO]:

   POL(A(x_1)) = x_1
   POL(B(x_1)) = x_1
   POL(a(x_1)) = x_1
   POL(b(x_1)) = x_1
   POL(c(x_1)) = 1 + x_1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

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


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

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   A(x1) -> B(b(b(x1)))
   A(x1) -> B(b(x1))
   A(x1) -> B(x1)
   B(c(b(x1))) -> A(c(x1))

The TRS R consists of the following rules:

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

Q is empty.

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