SRS Stand 10685 pair #381718154

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	n007.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	12.5171401501 seconds
cpu usage	46.85327341
max memory	4.573626368E9

stage attributes

key	value
output-size	10769
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 2 ms]
(4) QDP
(5) QDPOrderProof [EQUIVALENT, 183 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 28 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 720 ms]
        (13) QDP
        (14) PisEmptyProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 27 ms]
        (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 25 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].

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