TRS Standard pair #487073313

details

property	value
status	complete
benchmark	016.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	AotoYamada_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.83357 seconds
cpu usage	4.38822
user time	4.21446
system time	0.173765
max virtual memory	1.8408912E7
max residence set size	261208.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 3 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES


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

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

   app(app(neq, 0), 0) -> false
   app(app(neq, 0), app(s, y)) -> true
   app(app(neq, app(s, x)), 0) -> true
   app(app(neq, app(s, x)), app(s, y)) -> app(app(neq, x), y)
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, y), ys)) -> app(app(app(filtersub, app(f, y)), f), app(app(cons, y), ys))
   app(app(app(filtersub, true), f), app(app(cons, y), ys)) -> app(app(cons, y), app(app(filter, f), ys))
   app(app(app(filtersub, false), f), app(app(cons, y), ys)) -> app(app(filter, f), ys)
   nonzero -> app(filter, app(neq, 0))

Q is empty.

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

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

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

   app(app(neq, 0), 0) -> false
   app(app(neq, 0), app(s, y)) -> true
   app(app(neq, app(s, x)), 0) -> true
   app(app(neq, app(s, x)), app(s, y)) -> app(app(neq, x), y)
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, y), ys)) -> app(app(app(filtersub, app(f, y)), f), app(app(cons, y), ys))
   app(app(app(filtersub, true), f), app(app(cons, y), ys)) -> app(app(cons, y), app(app(filter, f), ys))
   app(app(app(filtersub, false), f), app(app(cons, y), ys)) -> app(app(filter, f), ys)
   nonzero -> app(filter, app(neq, 0))

The set Q consists of the following terms:

   app(app(neq, 0), 0)
   app(app(neq, 0), app(s, x0))
   app(app(neq, app(s, x0)), 0)
   app(app(neq, app(s, x0)), app(s, x1))
   app(app(filter, x0), nil)
   app(app(filter, x0), app(app(cons, x1), x2))
   app(app(app(filtersub, true), x0), app(app(cons, x1), x2))
   app(app(app(filtersub, false), x0), app(app(cons, x1), x2))
   nonzero


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

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

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   APP(app(neq, app(s, x)), app(s, y)) -> APP(app(neq, x), y)
   APP(app(neq, app(s, x)), app(s, y)) -> APP(neq, x)

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard