SRS Standard pair #487091050

details

property	value
status	complete
benchmark	secr9.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	12.9575 seconds
cpu usage	34.7623
user time	32.9554
system time	1.80688
max virtual memory	8.3684596E7
max residence set size	3978288.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 36 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPOrderProof [EQUIVALENT, 101 ms]
        (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 57 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPOrderProof [EQUIVALENT, 78 ms]
        (17) QDP
        (18) PisEmptyProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 2 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 47 ms]
        (24) QDP
        (25) PisEmptyProof [EQUIVALENT, 0 ms]
        (26) YES
    (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 39 ms]
        (29) QDP
        (30) DependencyGraphProof [EQUIVALENT, 0 ms]
        (31) AND
            (32) QDP
                (33) QDPOrderProof [EQUIVALENT, 0 ms]
                (34) QDP
                (35) PisEmptyProof [EQUIVALENT, 0 ms]
                (36) YES
            (37) QDP
                (38) UsableRulesProof [EQUIVALENT, 0 ms]
                (39) QDP
                (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (41) YES


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

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

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

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