TRS Standard pair #615297639

details

property	value
status	complete
benchmark	identity.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n155.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	2.31141114235 seconds
cpu usage	6.201073509
max memory	3.34077952E8

stage attributes

key	value
output-size	13205
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 82 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 21 ms]
(4) QTRS
(5) AAECC Innermost [EQUIVALENT, 0 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 0 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QReductionProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) UsableRulesProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QReductionProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QReductionProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) QDPOrderProof [EQUIVALENT, 62 ms]
        (31) QDP
        (32) PisEmptyProof [EQUIVALENT, 0 ms]
        (33) YES


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

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

   g(x, 0) -> 0
   g(d, s(x)) -> s(s(g(d, x)))
   g(h, s(0)) -> 0
   g(h, s(s(x))) -> s(g(h, x))
   double(x) -> g(d, x)
   half(x) -> g(h, x)
   f(s(x), y) -> f(half(s(x)), double(y))
   f(s(0), y) -> y
   id(x) -> f(x, s(0))

Q is empty.

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

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

   POL(0) = 0
   POL(d) = 0
   POL(double(x_1)) = x_1
   POL(f(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(g(x_1, x_2)) = x_1 + x_2
   POL(h) = 0
   POL(half(x_1)) = x_1
   POL(id(x_1)) = 2 + 2*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:

   id(x) -> f(x, s(0))




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

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

   g(x, 0) -> 0
   g(d, s(x)) -> s(s(g(d, x)))
   g(h, s(0)) -> 0

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