SRS Stand 10685 pair #381723312

details

property	value
status	complete
benchmark	213437.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n114.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	16.6863939762 seconds
cpu usage	61.673880448
max memory	4.460515328E9

stage attributes

key	value
output-size	58237
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 234 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 224 ms]
(8) QDP
(9) QDPOrderProof [EQUIVALENT, 126 ms]
(10) QDP
(11) DependencyGraphProof [EQUIVALENT, 0 ms]
(12) AND
    (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 856 ms]
        (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) AND
            (18) QDP
                (19) UsableRulesProof [EQUIVALENT, 0 ms]
                (20) QDP
                (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (22) YES
            (23) QDP
                (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (25) YES
    (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 58 ms]
        (28) QDP
        (29) PisEmptyProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) QDP
        (32) QDPOrderProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) PisEmptyProof [EQUIVALENT, 0 ms]
        (35) YES
    (36) QDP
        (37) UsableRulesProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (40) YES


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

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

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

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