SRS Standard pair #516968254

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	n116.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	8.64650797844 seconds
cpu usage	30.214925704
max memory	1.467871232E9

stage attributes

key	value
output-size	21592
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) QTRSRRRProof [EQUIVALENT, 52 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 26 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) QDPOrderProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) DependencyGraphProof [EQUIVALENT, 0 ms]
        (23) AND
            (24) QDP
                (25) UsableRulesProof [EQUIVALENT, 0 ms]
                (26) QDP
                (27) MRRProof [EQUIVALENT, 8 ms]
                (28) QDP
                (29) MNOCProof [EQUIVALENT, 0 ms]
                (30) QDP
                (31) QDPOrderProof [EQUIVALENT, 32 ms]
                (32) QDP
                (33) PisEmptyProof [EQUIVALENT, 0 ms]
                (34) YES
            (35) QDP
                (36) QDPOrderProof [EQUIVALENT, 10 ms]
                (37) QDP
                (38) MRRProof [EQUIVALENT, 20 ms]
                (39) QDP
                (40) QDPOrderProof [EQUIVALENT, 45 ms]
                (41) QDP
                (42) PisEmptyProof [EQUIVALENT, 0 ms]
                (43) YES
    (44) QDP
        (45) UsableRulesProof [EQUIVALENT, 0 ms]
        (46) QDP
        (47) QDPOrderProof [EQUIVALENT, 103 ms]
        (48) QDP
        (49) PisEmptyProof [EQUIVALENT, 0 ms]
        (50) 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

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