SRS Standard pair #487087012

details

property	value
status	complete
benchmark	212037.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	23.7406 seconds
cpu usage	90.6277
user time	88.0563
system time	2.57141
max virtual memory	3.750546E7
max residence set size	4954484.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 225 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPOrderProof [EQUIVALENT, 274 ms]
        (14) QDP
        (15) DependencyGraphProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 174 ms]
        (18) QDP
        (19) DependencyGraphProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 106 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 83 ms]
        (24) QDP
        (25) DependencyGraphProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 73 ms]
        (28) QDP
        (29) QDPOrderProof [EQUIVALENT, 54 ms]
        (30) QDP
        (31) DependencyGraphProof [EQUIVALENT, 0 ms]
        (32) AND
            (33) QDP
                (34) QDPOrderProof [EQUIVALENT, 3321 ms]
                (35) QDP
                (36) DependencyGraphProof [EQUIVALENT, 0 ms]
                (37) QDP
                (38) UsableRulesProof [EQUIVALENT, 0 ms]
                (39) QDP
                (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (41) YES
            (42) QDP
                (43) QDPOrderProof [EQUIVALENT, 42 ms]
                (44) QDP
                (45) PisEmptyProof [EQUIVALENT, 0 ms]
                (46) YES


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

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

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

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