TRS Stand 20472 pair #381709955

details

property	value
status	complete
benchmark	kabasci06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n052.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.06763005257 seconds
cpu usage	5.281881725
max memory	3.62508288E8

stage attributes

key	value
output-size	15447
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 22 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) ATransformationProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) MNOCProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) ATransformationProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) MRRProof [EQUIVALENT, 8 ms]
        (20) QDP
        (21) DependencyGraphProof [EQUIVALENT, 0 ms]
        (22) TRUE
    (23) QDP
        (24) QDPApplicativeOrderProof [EQUIVALENT, 44 ms]
        (25) QDP
        (26) PisEmptyProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (32) YES


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

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

   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(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, app(p, app(s, x))), app(p, app(s, y)))
   app(p, app(s, x)) -> x
   app(app(div, 0), app(s, y)) -> 0
   app(app(div, app(s, x)), app(s, y)) -> app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
   app(id, x) -> x
   app(id, x) -> app(s, app(s, app(s, x)))
   app(id, app(p, x)) -> app(id, app(s, app(id, x)))

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(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(minus, app(s, x)), app(s, y)) -> APP(app(minus, app(p, app(s, x))), app(p, app(s, y)))
   APP(app(minus, app(s, x)), app(s, y)) -> APP(minus, app(p, app(s, x)))
   APP(app(minus, app(s, x)), app(s, y)) -> APP(p, app(s, x))
   APP(app(minus, app(s, x)), app(s, y)) -> APP(p, app(s, y))
   APP(app(div, app(s, x)), app(s, y)) -> APP(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y)))
   APP(app(div, app(s, x)), app(s, y)) -> APP(app(div, app(app(minus, x), app(id, y))), app(s, y))
   APP(app(div, app(s, x)), app(s, y)) -> APP(div, app(app(minus, x), app(id, y)))
   APP(app(div, app(s, x)), app(s, y)) -> APP(app(minus, x), app(id, y))
   APP(app(div, app(s, x)), app(s, y)) -> APP(minus, x)
   APP(app(div, app(s, x)), app(s, y)) -> APP(id, y)
   APP(id, x) -> APP(s, app(s, app(s, x)))
   APP(id, x) -> APP(s, app(s, x))
   APP(id, x) -> APP(s, x)
   APP(id, app(p, x)) -> APP(id, app(s, app(id, x)))
   APP(id, app(p, x)) -> APP(s, app(id, x))
   APP(id, app(p, x)) -> APP(id, x)

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