SRS Stand 10685 pair #381717881

details

property	value
status	complete
benchmark	z113.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n099.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.84489107132 seconds
cpu usage	12.164671957
max memory	1.880629248E9

stage attributes

key	value
output-size	6995
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 5 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 4 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 5 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 6 ms]
        (13) QDP
        (14) DependencyGraphProof [EQUIVALENT, 0 ms]
        (15) TRUE
    (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES


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

   1(1(x1)) -> 4(3(x1))
   1(2(x1)) -> 2(1(x1))
   2(2(x1)) -> 1(1(1(x1)))
   3(3(x1)) -> 5(6(x1))
   3(4(x1)) -> 1(1(x1))
   4(4(x1)) -> 3(x1)
   5(5(x1)) -> 6(2(x1))
   5(6(x1)) -> 1(2(x1))
   6(6(x1)) -> 2(1(x1))

Q is empty.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   1(1(x1)) -> 3(4(x1))
   2(1(x1)) -> 1(2(x1))
   2(2(x1)) -> 1(1(1(x1)))
   3(3(x1)) -> 6(5(x1))
   4(3(x1)) -> 1(1(x1))
   4(4(x1)) -> 3(x1)
   5(5(x1)) -> 2(6(x1))
   6(5(x1)) -> 2(1(x1))
   6(6(x1)) -> 1(2(x1))

Q is empty.

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(3) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(1(x_1)) = 85 + x_1
   POL(2(x_1)) = 128 + x_1
   POL(3(x_1)) = 113 + x_1
   POL(4(x_1)) = 57 + x_1
   POL(5(x_1)) = 118 + x_1
   POL(6(x_1)) = 107 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   2(2(x1)) -> 1(1(1(x1)))
   3(3(x1)) -> 6(5(x1))
   4(4(x1)) -> 3(x1)
   5(5(x1)) -> 2(6(x1))
   6(5(x1)) -> 2(1(x1))
   6(6(x1)) -> 1(2(x1))

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