SRS Standard pair #487083604

details

property	value
status	complete
benchmark	size-12-alpha-3-num-561.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	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.23042 seconds
cpu usage	13.6804
user time	13.0138
system time	0.666609
max virtual memory	2.0612132E7
max residence set size	1970312.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 49 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 1 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) QDPOrderProof [EQUIVALENT, 19 ms]
        (23) QDP
        (24) PisEmptyProof [EQUIVALENT, 0 ms]
        (25) YES


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

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

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

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

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

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