SRS Standard pair #516975688

details

property	value
status	complete
benchmark	secr4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n119.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	15.0230960846 seconds
cpu usage	56.142013391
max memory	3.410505728E9

stage attributes

key	value
output-size	12484
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 18 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPOrderProof [EQUIVALENT, 300 ms]
        (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 100 ms]
        (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 100 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 231 ms]
        (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) TRUE
    (18) QDP
        (19) UsableRulesProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES


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

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

Q is empty.

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(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
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(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   A(a(x1)) -> B(b(b(x1)))
   A(a(x1)) -> B(b(x1))
   A(a(x1)) -> B(x1)
   A(x1) -> C(d(x1))
   B(b(x1)) -> C(c(c(x1)))
   B(b(x1)) -> C(c(x1))
   B(b(x1)) -> C(x1)
   E(d(x1)) -> A(b(c(d(e(x1)))))
   E(d(x1)) -> B(c(d(e(x1))))
   E(d(x1)) -> C(d(e(x1)))
   E(d(x1)) -> E(x1)
   E(c(x1)) -> B(a(a(e(x1))))
   E(c(x1)) -> A(a(e(x1)))
   E(c(x1)) -> A(e(x1))
   E(c(x1)) -> E(x1)
   C(d(d(x1))) -> A(x1)

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(3) DependencyGraphProof (EQUIVALENT)

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