TRS Standard pair #516966330

details

property	value
status	timeout (wallclock)
benchmark	parting02_doublelist.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
space	AProVE_08

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	301.139460087 seconds
cpu usage	17.431944366
max memory	1.23836416E9

stage attributes

unavailable

output

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


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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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 7 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) TransformationProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) TransformationProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) TransformationProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) UsableRulesProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) QReductionProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) Induction-Processor [SOUND, 3 ms]
        (44) AND
            (45) QDP
                (46) PisEmptyProof [EQUIVALENT, 0 ms]
                (47) YES
            (48) QTRS
                (49) QTRSRRRProof [EQUIVALENT, 72 ms]
                (50) QTRS
                (51) QTRSRRRProof [EQUIVALENT, 0 ms]
                (52) QTRS
                (53) RisEmptyProof [EQUIVALENT, 0 ms]
                (54) YES


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

   double(0) -> 0
   double(s(x)) -> s(s(double(x)))
   del(x, nil) -> nil
   del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs)
   if(true, x, y, xs) -> xs
   if(false, x, y, xs) -> cons(y, del(x, xs))
   eq(0, 0) -> true
   eq(0, s(y)) -> false
   eq(s(x), 0) -> false
   eq(s(x), s(y)) -> eq(x, y)
   first(nil) -> 0
   first(cons(x, xs)) -> x
   doublelist(nil) -> nil
   doublelist(cons(x, xs)) -> cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs))))

Q is empty.

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(1) Overlay + Local Confluence (EQUIVALENT)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
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