SRS Standard pair #516972718

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	n117.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	16.3957138062 seconds
cpu usage	61.778383833
max memory	2.432077824E9

stage attributes

key	value
output-size	38876
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 186 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) MRRProof [EQUIVALENT, 29 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) TRUE
    (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 362 ms]
        (16) QDP
        (17) DependencyGraphProof [EQUIVALENT, 0 ms]
        (18) AND
            (19) QDP
                (20) QDPOrderProof [EQUIVALENT, 76 ms]
                (21) QDP
                (22) PisEmptyProof [EQUIVALENT, 0 ms]
                (23) YES
            (24) QDP
                (25) QDPOrderProof [EQUIVALENT, 77 ms]
                (26) QDP
                (27) PisEmptyProof [EQUIVALENT, 0 ms]
                (28) YES


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

(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))))))

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