SRS Standard pair #487086166

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	n144.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	56.2497 seconds
cpu usage	217.786
user time	210.321
system time	7.46512
max virtual memory	6.298198E7
max residence set size	1.2239556E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 131 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 535 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 921 ms]
(8) QDP
(9) QDPOrderProof [EQUIVALENT, 426 ms]
(10) QDP
(11) QDPOrderProof [EQUIVALENT, 352 ms]
(12) QDP
(13) QDPOrderProof [EQUIVALENT, 494 ms]
(14) QDP
(15) QDPOrderProof [EQUIVALENT, 569 ms]
(16) QDP
(17) DependencyGraphProof [EQUIVALENT, 0 ms]
(18) AND
    (19) QDP
        (20) QDPOrderProof [EQUIVALENT, 51 ms]
        (21) QDP
        (22) PisEmptyProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 50 ms]
        (26) QDP
        (27) PisEmptyProof [EQUIVALENT, 0 ms]
        (28) YES
    (29) QDP
        (30) QDPOrderProof [EQUIVALENT, 54 ms]
        (31) QDP
        (32) QDPOrderProof [EQUIVALENT, 33 ms]
        (33) QDP
        (34) QDPOrderProof [EQUIVALENT, 42 ms]
        (35) QDP
        (36) QDPOrderProof [EQUIVALENT, 41 ms]
        (37) QDP
        (38) PisEmptyProof [EQUIVALENT, 0 ms]
        (39) YES
    (40) QDP
        (41) QDPOrderProof [EQUIVALENT, 45 ms]
        (42) QDP
        (43) DependencyGraphProof [EQUIVALENT, 0 ms]
        (44) AND
            (45) QDP
                (46) QDPOrderProof [EQUIVALENT, 52 ms]
                (47) QDP
                (48) QDPOrderProof [EQUIVALENT, 40 ms]
                (49) QDP
                (50) PisEmptyProof [EQUIVALENT, 0 ms]
                (51) YES
            (52) QDP
                (53) QDPOrderProof [EQUIVALENT, 40 ms]
                (54) QDP
                (55) PisEmptyProof [EQUIVALENT, 0 ms]
                (56) 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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