SRS Stand 10685 pair #381719600

details

property	value
status	complete
benchmark	z121.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n052.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.88735294342 seconds
cpu usage	8.548306601
max memory	1.508773888E9

stage attributes

key	value
output-size	5841
starexec-result	YES

output

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


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 2 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 23 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 2 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 2 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES


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

   f(f(x1)) -> b(b(b(x1)))
   a(f(x1)) -> f(a(a(x1)))
   b(b(x1)) -> c(c(a(c(x1))))
   d(b(x1)) -> d(a(b(x1)))
   c(c(x1)) -> d(d(d(x1)))
   b(d(x1)) -> d(b(x1))
   c(d(d(x1))) -> f(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:

   f(f(x1)) -> b(b(b(x1)))
   f(a(x1)) -> a(a(f(x1)))
   b(b(x1)) -> c(a(c(c(x1))))
   b(d(x1)) -> b(a(d(x1)))
   c(c(x1)) -> d(d(d(x1)))
   d(b(x1)) -> b(d(x1))
   d(d(c(x1))) -> f(x1)

Q is empty.

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

   POL(a(x_1)) = x_1
   POL(b(x_1)) = 53 + x_1
   POL(c(x_1)) = 35 + x_1
   POL(d(x_1)) = 23 + x_1
   POL(f(x_1)) = 80 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   f(f(x1)) -> b(b(b(x1)))
   b(b(x1)) -> c(a(c(c(x1))))
   c(c(x1)) -> d(d(d(x1)))
   d(d(c(x1))) -> f(x1)




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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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