SRS Standard pair #516971932

details

property	value
status	complete
benchmark	68535.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	64.4247381687 seconds
cpu usage	243.144492563
max memory	1.0830557184E10

stage attributes

key	value
output-size	97883
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) QTRSRRRProof [EQUIVALENT, 171 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 455 ms]
(4) QDP
(5) QDPOrderProof [EQUIVALENT, 1384 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 54 ms]
        (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 55 ms]
        (13) QDP
        (14) PisEmptyProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 3402 ms]
        (18) QDP
        (19) PisEmptyProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) QDPOrderProof [EQUIVALENT, 59 ms]
        (23) QDP
        (24) QDPOrderProof [EQUIVALENT, 40 ms]
        (25) QDP
        (26) QDPOrderProof [EQUIVALENT, 4382 ms]
        (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 4468 ms]
        (29) QDP
        (30) PisEmptyProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) QDP
        (33) QDPOrderProof [EQUIVALENT, 72 ms]
        (34) QDP
        (35) QDPOrderProof [EQUIVALENT, 53 ms]
        (36) QDP
        (37) QDPOrderProof [EQUIVALENT, 59 ms]
        (38) QDP
        (39) DependencyGraphProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) QDPOrderProof [EQUIVALENT, 63 ms]
        (42) QDP
        (43) QDPOrderProof [EQUIVALENT, 41 ms]
        (44) QDP
        (45) PisEmptyProof [EQUIVALENT, 0 ms]
        (46) YES


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

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

   0(0(1(1(x1)))) -> 2(2(1(3(x1))))
   1(4(0(4(x1)))) -> 1(2(3(1(x1))))
   3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1)))))
   1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1))))))
   2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1)))))))
   5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1)))))))
   0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1))))))))
   4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1))))))))
   4(3(0(2(5(3(1(2(3(x1))))))))) -> 4(1(1(0(0(0(5(3(x1))))))))
   4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1))))))))))
   4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1))))))))))
   3(0(4(4(4(5(3(1(2(5(0(4(x1)))))))))))) -> 5(3(3(0(3(5(1(0(0(1(0(x1)))))))))))
   4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1))))))))))))
   5(4(2(3(0(4(3(2(2(2(4(1(x1)))))))))))) -> 5(1(0(2(4(4(4(5(1(4(1(x1)))))))))))
   3(0(0(2(1(1(3(1(5(0(5(1(0(5(x1)))))))))))))) -> 5(1(0(1(2(2(1(3(3(1(0(2(5(x1)))))))))))))
   0(4(2(4(1(1(5(3(0(2(2(0(5(1(5(x1))))))))))))))) -> 1(1(0(0(3(5(5(1(1(2(5(3(5(5(x1))))))))))))))
   0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1)))))))))))))))
   2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1))))))))))))))))
   0(0(0(2(0(3(0(5(1(0(5(0(5(1(0(4(3(x1))))))))))))))))) -> 0(0(1(4(5(0(0(2(0(0(1(1(3(2(5(3(x1))))))))))))))))
   1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1)))))))))))))))))
   2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1)))))))))))))))))
   1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1))))))))))))))))))
   2(4(2(1(5(5(0(1(0(4(2(2(2(3(4(1(0(4(x1)))))))))))))))))) -> 2(1(3(2(1(2(2(5(1(1(3(5(4(4(5(5(5(x1)))))))))))))))))
   5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1))))))))))))))))))
   0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))))))))))))

Q is empty.

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(1) QTRSRRRProof (EQUIVALENT)

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