SRS Standard pair #487090882

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	n143.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	15.0539 seconds
cpu usage	56.0683
user time	54.4236
system time	1.64476
max virtual memory	3.9913228E7
max residence set size	4177404.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPOrderProof [EQUIVALENT, 238 ms]
        (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 211 ms]
        (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 58 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 258 ms]
        (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) TRUE
    (18) QDP
        (19) UsableRulesProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 2 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.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(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)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 6 less nodes.
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(4)
Complex Obligation (AND)

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