SRS Standard pair #487088194

details

property	value
status	complete
benchmark	212892.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.90507 seconds
cpu usage	28.1153
user time	26.9907
system time	1.12456
max virtual memory	4.0323852E7
max residence set size	3194120.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 201 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) MRRProof [EQUIVALENT, 13 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) TRUE
    (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 227 ms]
        (16) QDP
        (17) DependencyGraphProof [EQUIVALENT, 0 ms]
        (18) AND
            (19) QDP
                (20) QDPOrderProof [EQUIVALENT, 95 ms]
                (21) QDP
                (22) PisEmptyProof [EQUIVALENT, 0 ms]
                (23) YES
            (24) QDP
                (25) QDPOrderProof [EQUIVALENT, 0 ms]
                (26) QDP
                (27) PisEmptyProof [EQUIVALENT, 0 ms]
                (28) YES


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

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

Q is empty.

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