SRS Standard pair #487083214

details

property	value
status	complete
benchmark	x04.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_07_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.62419 seconds
cpu usage	26.6069
user time	25.1048
system time	1.50209
max virtual memory	4.191084E7
max residence set size	3928480.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 44 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 2 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 4 ms]
        (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 86 ms]
        (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 52 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPOrderProof [EQUIVALENT, 111 ms]
        (17) QDP
        (18) DependencyGraphProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QDPOrderProof [EQUIVALENT, 73 ms]
        (21) QDP
        (22) PisEmptyProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 3 ms]
        (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 8 ms]
        (28) QDP
        (29) PisEmptyProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) QDP
        (32) QDPOrderProof [EQUIVALENT, 75 ms]
        (33) QDP
        (34) PisEmptyProof [EQUIVALENT, 0 ms]
        (35) YES


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

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

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

Q is empty.

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

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

   POL(a(x_1)) = x_1
   POL(b(x_1)) = x_1
   POL(c(x_1)) = 1 + x_1
   POL(d(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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




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

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

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

Q is empty.

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

(3) DependencyPairsProof (EQUIVALENT)

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