SRS Standard pair #516974446

details

property	value
status	complete
benchmark	size-12-alpha-3-num-1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n098.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.38130688667 seconds
cpu usage	18.404051271
max memory	1.311117312E9

stage attributes

key	value
output-size	26007
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) FlatCCProof [EQUIVALENT, 0 ms]
(4) QTRS
(5) RootLabelingProof [EQUIVALENT, 0 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 47 ms]
(8) QTRS
(9) DependencyPairsProof [EQUIVALENT, 13 ms]
(10) QDP
(11) DependencyGraphProof [EQUIVALENT, 1 ms]
(12) QDP
(13) QDPOrderProof [EQUIVALENT, 42 ms]
(14) QDP
(15) DependencyGraphProof [EQUIVALENT, 0 ms]
(16) AND
    (17) QDP
        (18) UsableRulesProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QDP
        (23) UsableRulesProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (26) YES


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

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

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

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

Q is empty.

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

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

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

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

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

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