TRS Standard pair #516964865

details

property	value
status	complete
benchmark	13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n086.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	14.0037088394 seconds
cpu usage	31.518347438
max memory	1.46642944E9

stage attributes

key	value
output-size	20681
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) DependencyPairsProof [EQUIVALENT, 10 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPApplicativeOrderProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) ATransformationProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) UsableRulesProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES


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

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

   app(app(*, x), app(app(+, y), z)) -> app(app(+, app(app(*, x), y)), app(app(*, x), z))
   app(app(*, app(app(+, y), z)), x) -> app(app(+, app(app(*, x), y)), app(app(*, x), z))
   app(app(*, app(app(*, x), y)), z) -> app(app(*, x), app(app(*, y), z))
   app(app(+, app(app(+, x), y)), z) -> app(app(+, x), app(app(+, y), z))
   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))
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
   app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   APP(app(*, x), app(app(+, y), z)) -> APP(app(+, app(app(*, x), y)), app(app(*, x), z))
   APP(app(*, x), app(app(+, y), z)) -> APP(+, app(app(*, x), y))
   APP(app(*, x), app(app(+, y), z)) -> APP(app(*, x), y)
   APP(app(*, x), app(app(+, y), z)) -> APP(app(*, x), z)
   APP(app(*, app(app(+, y), z)), x) -> APP(app(+, app(app(*, x), y)), app(app(*, x), z))
   APP(app(*, app(app(+, y), z)), x) -> APP(+, app(app(*, x), y))
   APP(app(*, app(app(+, y), z)), x) -> APP(app(*, x), y)
   APP(app(*, app(app(+, y), z)), x) -> APP(*, x)
   APP(app(*, app(app(+, y), z)), x) -> APP(app(*, x), z)
   APP(app(*, app(app(*, x), y)), z) -> APP(app(*, x), app(app(*, y), z))
   APP(app(*, app(app(*, x), y)), z) -> APP(app(*, y), z)
   APP(app(*, app(app(*, x), y)), z) -> APP(*, y)
   APP(app(+, app(app(+, x), y)), z) -> APP(app(+, x), app(app(+, y), z))
   APP(app(+, app(app(+, x), y)), z) -> APP(app(+, y), z)
   APP(app(+, app(app(+, x), y)), z) -> APP(+, y)
   APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs))
   APP(app(map, f), app(app(cons, x), xs)) -> APP(cons, app(f, x))
   APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x)
   APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs)
   APP(app(filter, f), app(app(cons, x), xs)) -> APP(app(app(app(filter2, app(f, x)), f), x), xs)
   APP(app(filter, f), app(app(cons, x), xs)) -> APP(app(app(filter2, app(f, x)), f), x)
   APP(app(filter, f), app(app(cons, x), xs)) -> APP(app(filter2, app(f, x)), f)
   APP(app(filter, f), app(app(cons, x), xs)) -> APP(filter2, app(f, x))
   APP(app(filter, f), app(app(cons, x), xs)) -> APP(f, x)
   APP(app(app(app(filter2, true), f), x), xs) -> APP(app(cons, x), app(app(filter, f), xs))
   APP(app(app(app(filter2, true), f), x), xs) -> APP(cons, x)

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