TRS Standard pair #516967420

details

property	value
status	complete
benchmark	Hamming.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n031.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.24538898468 seconds
cpu usage	9.215505116
max memory	6.81406464E8

stage attributes

key	value
output-size	50871
starexec-result	NO

output

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


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


NO
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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 disproven:

(0) QTRS
(1) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 110 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) ATransformationProof [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) ATransformationProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) QReductionProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (28) YES
    (29) QDP
        (30) UsableRulesProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) QReductionProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) ATransformationProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) QReductionProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (39) YES
    (40) QDP
        (41) UsableRulesProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) QReductionProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) ATransformationProof [EQUIVALENT, 0 ms]
        (46) QDP
        (47) QReductionProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (50) YES
    (51) QDP
        (52) UsableRulesProof [EQUIVALENT, 0 ms]
        (53) QDP
        (54) QReductionProof [EQUIVALENT, 0 ms]
        (55) QDP
        (56) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (57) YES
    (58) QDP
        (59) UsableRulesProof [EQUIVALENT, 0 ms]
        (60) QDP
        (61) QReductionProof [EQUIVALENT, 0 ms]
        (62) QDP
        (63) NonTerminationLoopProof [COMPLETE, 0 ms]
        (64) NO


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

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

   app(app(app(if, true), xs), ys) -> xs
   app(app(app(if, false), xs), ys) -> ys
   app(app(lt, app(s, x)), app(s, y)) -> app(app(lt, x), y)
   app(app(lt, 0), app(s, y)) -> true
   app(app(lt, y), 0) -> false
   app(app(eq, x), x) -> true
   app(app(eq, app(s, x)), 0) -> false
   app(app(eq, 0), app(s, x)) -> false
   app(app(merge, xs), nil) -> xs
   app(app(merge, nil), ys) -> ys
   app(app(merge, app(app(cons, x), xs)), app(app(cons, y), ys)) -> app(app(app(if, app(app(lt, x), y)), app(app(cons, x), app(app(merge, xs), app(app(cons, y), ys)))), app(app(app(if, app(app(eq, x), y)), app(app(cons, x), app(app(merge, xs), ys))), app(app(cons, y), app(app(merge, app(app(cons, x), xs)), ys))))
   app(app(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))

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