TRS Innermost pair #487092909

details

property	value
status	complete
benchmark	#4.34.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Applicative_AG01_innermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.05645 seconds
cpu usage	5.09156
user time	4.88005
system time	0.211512
max virtual memory	1.8477524E7
max residence set size	293264.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 4 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) ATransformationProof [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) ATransformationProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QReductionProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 15 ms]
        (22) QDP
        (23) PisEmptyProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES


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

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

   app(f, 0) -> true
   app(f, 1) -> false
   app(f, app(s, x)) -> app(f, x)
   app(app(app(if, true), x), y) -> x
   app(app(app(if, false), x), y) -> y
   app(app(g, app(s, x)), app(s, y)) -> app(app(app(if, app(f, x)), app(s, x)), app(s, y))
   app(app(g, x), app(c, y)) -> app(app(g, x), app(app(g, app(s, app(c, y))), y))
   app(app(map, fun), nil) -> nil
   app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
   app(app(filter, fun), nil) -> nil
   app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
   app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
   app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)

The set Q consists of the following terms:

   app(f, 0)
   app(f, 1)
   app(f, app(s, x0))
   app(app(app(if, true), x0), x1)
   app(app(app(if, false), x0), x1)
   app(app(g, app(s, x0)), app(s, x1))
   app(app(g, x0), app(c, x1))
   app(app(map, x0), nil)
   app(app(map, x0), app(app(cons, x1), x2))
   app(app(filter, x0), nil)
   app(app(filter, x0), app(app(cons, x1), x2))
   app(app(app(app(filter2, true), x0), x1), x2)
   app(app(app(app(filter2, false), x0), x1), x2)


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

(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(f, app(s, x)) -> APP(f, x)
   APP(app(g, app(s, x)), app(s, y)) -> APP(app(app(if, app(f, x)), app(s, x)), app(s, y))
   APP(app(g, app(s, x)), app(s, y)) -> APP(app(if, app(f, x)), app(s, x))
   APP(app(g, app(s, x)), app(s, y)) -> APP(if, app(f, x))
   APP(app(g, app(s, x)), app(s, y)) -> APP(f, x)
   APP(app(g, x), app(c, y)) -> APP(app(g, x), app(app(g, app(s, app(c, y))), y))
   APP(app(g, x), app(c, y)) -> APP(app(g, app(s, app(c, y))), y)
   APP(app(g, x), app(c, y)) -> APP(g, app(s, app(c, y)))
   APP(app(g, x), app(c, y)) -> APP(s, app(c, y))
   APP(app(map, fun), app(app(cons, x), xs)) -> APP(app(cons, app(fun, x)), app(app(map, fun), xs))
   APP(app(map, fun), app(app(cons, x), xs)) -> APP(cons, app(fun, x))
   APP(app(map, fun), app(app(cons, x), xs)) -> APP(fun, x)
   APP(app(map, fun), app(app(cons, x), xs)) -> APP(app(map, fun), xs)
   APP(app(filter, fun), app(app(cons, x), xs)) -> APP(app(app(app(filter2, app(fun, x)), fun), x), xs)

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