SRS Standard pair #487086940

details

property	value
status	complete
benchmark	212026.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	27.6004 seconds
cpu usage	105.664
user time	102.791
system time	2.87295
max virtual memory	4.1978928E7
max residence set size	5576824.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 203 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) QDP
(5) QDPOrderProof [EQUIVALENT, 321 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 1 ms]
(8) QDP
(9) QDPOrderProof [EQUIVALENT, 196 ms]
(10) QDP
(11) DependencyGraphProof [EQUIVALENT, 0 ms]
(12) QDP
(13) QDPOrderProof [EQUIVALENT, 101 ms]
(14) QDP
(15) DependencyGraphProof [EQUIVALENT, 0 ms]
(16) AND
    (17) QDP
        (18) QDPOrderProof [EQUIVALENT, 66 ms]
        (19) QDP
        (20) QDPOrderProof [EQUIVALENT, 3441 ms]
        (21) QDP
        (22) PisEmptyProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 50 ms]
        (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 70 ms]
        (28) QDP
        (29) QDPOrderProof [EQUIVALENT, 71 ms]
        (30) QDP
        (31) PisEmptyProof [EQUIVALENT, 0 ms]
        (32) YES


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

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

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

Q is empty.

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