SRS Standard pair #516976102

details

property	value
status	complete
benchmark	dup05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	Trafo_06

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	4.94316601753 seconds
cpu usage	16.347363741
max memory	1.334276096E9

stage attributes

key	value
output-size	14103
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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, 44 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 1 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 87 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) AND
            (14) QDP
                (15) QDPOrderProof [EQUIVALENT, 5 ms]
                (16) QDP
                (17) PisEmptyProof [EQUIVALENT, 0 ms]
                (18) YES
            (19) QDP
                (20) QDPOrderProof [EQUIVALENT, 7 ms]
                (21) QDP
                (22) PisEmptyProof [EQUIVALENT, 0 ms]
                (23) YES
    (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 60 ms]
        (26) QDP
        (27) PisEmptyProof [EQUIVALENT, 0 ms]
        (28) YES


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

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

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

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

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

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