SRS Standard pair #487091092

details

property	value
status	complete
benchmark	multum2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	12.8918 seconds
cpu usage	47.4506
user time	45.6601
system time	1.79053
max virtual memory	6.292098E7
max residence set size	4225356.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 9 ms]
(4) QDP
(5) QDPOrderProof [EQUIVALENT, 242 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 219 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 747 ms]
        (13) QDP
        (14) PisEmptyProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 112 ms]
        (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 99 ms]
        (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES


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

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

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

Q is empty.

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

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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

The TRS R consists of the following rules:

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

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

(5) 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(b(x1)))
The remaining pairs can at least be oriented weakly.
Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:

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