SRS Standard pair #487083796

details

property	value
status	complete
benchmark	size-12-alpha-3-num-286.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	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.45863 seconds
cpu usage	22.3016
user time	21.062
system time	1.23958
max virtual memory	4.045596E7
max residence set size	3674136.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) FlatCCProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RootLabelingProof [EQUIVALENT, 0 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 8 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 0 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 12 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 41 ms]
        (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPOrderProof [EQUIVALENT, 388 ms]
        (19) QDP
        (20) DependencyGraphProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) QDP
        (27) UsableRulesProof [EQUIVALENT, 2 ms]
        (28) QDP
        (29) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (30) YES


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

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

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

Q is empty.

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

(1) FlatCCProof (EQUIVALENT)
We used flat context closure [ROOTLAB]
As Q is empty the flat context closure was sound AND complete.

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

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

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

Q is empty.

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

(3) RootLabelingProof (EQUIVALENT)
We used plain root labeling [ROOTLAB] with the following heuristic:
LabelAll: All function symbols get labeled

As Q is empty the root labeling was sound AND complete.

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

(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   c_{c_1}(c_{c_1}(x1)) -> c_{b_1}(b_{a_1}(a_{c_1}(x1)))
   c_{c_1}(c_{b_1}(x1)) -> c_{b_1}(b_{a_1}(a_{b_1}(x1)))
   c_{c_1}(c_{a_1}(x1)) -> c_{b_1}(b_{a_1}(a_{a_1}(x1)))
   a_{a_1}(a_{c_1}(x1)) -> a_{c_1}(x1)
   a_{a_1}(a_{b_1}(x1)) -> a_{b_1}(x1)
   a_{a_1}(a_{a_1}(x1)) -> a_{a_1}(x1)
   b_{a_1}(a_{c_1}(x1)) -> b_{c_1}(x1)
   b_{a_1}(a_{b_1}(x1)) -> b_{b_1}(x1)
   b_{a_1}(a_{a_1}(x1)) -> b_{a_1}(x1)

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