SRS Standard pair #487089376

details

property	value
status	complete
benchmark	aprove5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.15274 seconds
cpu usage	28.9193
user time	27.6394
system time	1.27984
max virtual memory	1.04604868E8
max residence set size	3696508.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 20 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 1 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) MNOCProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QReductionProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QDP
        (23) UsableRulesProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) MNOCProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) MRRProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) PisEmptyProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) QDP
        (32) UsableRulesProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) QDPOrderProof [EQUIVALENT, 22 ms]
        (35) QDP
        (36) DependencyGraphProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QDPOrderProof [EQUIVALENT, 12 ms]
        (39) QDP
        (40) QDPOrderProof [EQUIVALENT, 340 ms]
        (41) QDP
        (42) QDPOrderProof [EQUIVALENT, 200 ms]
        (43) QDP
        (44) DependencyGraphProof [EQUIVALENT, 0 ms]
        (45) TRUE


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

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

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

Q is empty.

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

(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:

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

Q is empty.

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

(3) QTRSRRRProof (EQUIVALENT)

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