SRS Standard pair #487089358

details

property	value
status	complete
benchmark	aprove4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n023.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.05847 seconds
cpu usage	27.9272
user time	26.5489
system time	1.37826
max virtual memory	8.3709868E7
max residence set size	3794420.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 56 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 24 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) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES
    (17) QDP
        (18) UsableRulesProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) MRRProof [EQUIVALENT, 12 ms]
        (21) QDP
        (22) DependencyGraphProof [EQUIVALENT, 0 ms]
        (23) AND
            (24) QDP
                (25) UsableRulesProof [EQUIVALENT, 0 ms]
                (26) QDP
                (27) MRRProof [EQUIVALENT, 5 ms]
                (28) QDP
                (29) MNOCProof [EQUIVALENT, 0 ms]
                (30) QDP
                (31) QDPOrderProof [EQUIVALENT, 15 ms]
                (32) QDP
                (33) PisEmptyProof [EQUIVALENT, 0 ms]
                (34) YES
            (35) QDP
                (36) MRRProof [EQUIVALENT, 22 ms]
                (37) QDP
                (38) QDPOrderProof [EQUIVALENT, 0 ms]
                (39) QDP
                (40) PisEmptyProof [EQUIVALENT, 0 ms]
                (41) YES
    (42) QDP
        (43) UsableRulesProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) QDPOrderProof [EQUIVALENT, 43 ms]
        (46) QDP
        (47) PisEmptyProof [EQUIVALENT, 0 ms]
        (48) YES


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

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

   log(s(x1)) -> s(log(half(s(x1))))
   half(0(x1)) -> 0(s(s(half(x1))))
   half(s(0(x1))) -> 0(x1)
   half(s(s(x1))) -> s(half(p(s(s(x1)))))
   half(half(s(s(s(s(x1)))))) -> s(s(half(half(x1))))
   p(s(s(s(x1)))) -> s(p(s(s(x1))))
   s(s(p(s(x1)))) -> s(s(x1))
   0(x1) -> x1

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0(x_1)) = 1 + x_1
   POL(half(x_1)) = x_1
   POL(log(x_1)) = x_1
   POL(p(x_1)) = x_1
   POL(s(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   0(x1) -> x1




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

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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