SRS Standard pair #487086808

details

property	value
status	complete
benchmark	214169.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.51574 seconds
cpu usage	30.1247
user time	29.035
system time	1.08968
max virtual memory	2.1024664E7
max residence set size	3533720.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 185 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) MRRProof [EQUIVALENT, 19 ms]
        (11) QDP
        (12) PisEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 185 ms]
        (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 114 ms]
        (18) QDP
        (19) PisEmptyProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 1 ms]
        (23) YES
    (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 83 ms]
        (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 101 ms]
        (28) QDP
        (29) PisEmptyProof [EQUIVALENT, 0 ms]
        (30) YES


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

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

   0(0(1(x1))) -> 0(0(2(1(3(x1)))))
   0(0(1(x1))) -> 0(0(2(2(3(1(x1))))))
   0(4(1(x1))) -> 0(4(2(2(1(x1)))))
   0(4(1(x1))) -> 0(2(3(1(4(2(x1))))))
   1(0(1(x1))) -> 0(2(1(1(x1))))
   1(0(1(x1))) -> 0(2(1(1(2(x1)))))
   1(0(1(x1))) -> 1(0(3(2(1(x1)))))
   1(4(0(x1))) -> 1(0(3(2(4(2(x1))))))
   1(4(1(x1))) -> 4(2(1(1(x1))))
   1(4(1(x1))) -> 4(2(1(1(2(1(x1))))))
   4(0(1(x1))) -> 4(0(2(1(x1))))
   5(0(1(x1))) -> 5(0(2(1(x1))))
   5(0(1(x1))) -> 0(2(1(5(3(x1)))))
   5(0(1(x1))) -> 0(3(2(1(5(5(x1))))))
   5(0(1(x1))) -> 3(0(2(3(5(1(x1))))))
   5(0(5(x1))) -> 0(3(2(5(3(5(x1))))))
   5(4(1(x1))) -> 2(4(2(5(1(3(x1))))))
   5(4(1(x1))) -> 4(5(2(1(3(3(x1))))))
   0(0(4(5(x1)))) -> 0(5(0(2(4(2(x1))))))
   0(1(2(0(x1)))) -> 2(0(2(1(0(x1)))))
   0(2(0(1(x1)))) -> 0(0(2(1(3(x1)))))
   0(3(4(0(x1)))) -> 3(2(4(0(0(3(x1))))))
   0(4(0(4(x1)))) -> 0(0(3(2(4(4(x1))))))
   1(0(1(4(x1)))) -> 2(3(1(1(4(0(x1))))))
   1(0(3(1(x1)))) -> 4(2(3(1(1(0(x1))))))
   1(2(0(4(x1)))) -> 1(4(2(0(3(2(x1))))))
   1(3(0(4(x1)))) -> 4(0(3(2(1(3(x1))))))
   1(4(1(5(x1)))) -> 2(1(2(5(1(4(x1))))))
   4(0(5(1(x1)))) -> 0(2(4(2(1(5(x1))))))
   4(1(0(0(x1)))) -> 3(2(1(4(0(0(x1))))))
   4(1(0(4(x1)))) -> 4(4(0(2(1(x1)))))
   5(0(0(1(x1)))) -> 0(3(2(5(1(0(x1))))))
   5(0(3(1(x1)))) -> 0(5(3(2(1(x1)))))
   5(0(3(1(x1)))) -> 0(3(5(2(2(1(x1))))))
   5(0(5(1(x1)))) -> 5(2(5(3(1(0(x1))))))
   5(2(4(1(x1)))) -> 2(1(4(2(5(x1)))))
   5(4(1(5(x1)))) -> 4(5(5(2(1(x1)))))
   5(4(1(5(x1)))) -> 2(1(5(4(2(5(x1))))))
   5(4(3(1(x1)))) -> 5(4(2(1(3(x1)))))
   5(4(3(1(x1)))) -> 3(5(2(4(2(1(x1))))))
   5(4(3(1(x1)))) -> 5(2(4(3(2(1(x1))))))
   5(5(0(4(x1)))) -> 5(0(2(5(4(2(x1))))))
   0(0(3(3(1(x1))))) -> 0(3(0(1(2(3(x1))))))
   0(2(4(3(1(x1))))) -> 0(2(3(1(4(2(x1))))))
   0(5(4(1(1(x1))))) -> 4(0(2(5(1(1(x1))))))
   1(2(4(3(1(x1))))) -> 1(2(3(3(1(4(x1))))))
   4(0(0(3(1(x1))))) -> 4(0(3(2(1(0(x1))))))
   4(0(0(3(1(x1))))) -> 4(3(2(0(0(1(x1))))))
   5(1(0(0(5(x1))))) -> 5(0(0(2(1(5(x1))))))
   5(4(2(0(1(x1))))) -> 2(5(4(0(2(1(x1))))))

Q is empty.

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