TRS Innermost pair #487092893

details

property	value
status	complete
benchmark	queue.raml.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.88538 seconds
cpu usage	14.2134
user time	13.7526
system time	0.460774
max virtual memory	1.87702E7
max residence set size	714728.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 8 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QReductionProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QReductionProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) MRRProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) DependencyGraphProof [EQUIVALENT, 0 ms]
        (20) TRUE
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) MRRProof [EQUIVALENT, 13 ms]
        (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 17 ms]
        (29) QDP
        (30) DependencyGraphProof [EQUIVALENT, 0 ms]
        (31) TRUE
    (32) QDP
        (33) UsableRulesProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QReductionProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) QDPOrderProof [EQUIVALENT, 77 ms]
        (38) QDP
        (39) DependencyGraphProof [EQUIVALENT, 0 ms]
        (40) TRUE


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

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

   breadth(@breadth@1, @breadth@2) -> breadth#1(dequeue(@breadth@1, @breadth@2))
   breadth#1(tuple#2(@queue', @elem)) -> breadth#2(@elem, @queue')
   breadth#2(::(@z, @_@9), @queue') -> breadth#3(breadth#4(@z), @queue')
   breadth#2(nil, @queue') -> nil
   breadth#3(tuple#2(@x, @ys), @queue') -> ::(@x, breadth#5(enqueues(@ys, @queue')))
   breadth#4(tuple#4(@children@3, @children@4, @children@5, @children@6)) -> children(@children@3, @children@4, @children@5, @children@6)
   breadth#5(tuple#2(@breadth@7, @breadth@8)) -> breadth(@breadth@7, @breadth@8)
   children(@a, @b, @l1, @l2) -> tuple#2(tuple#2(@a, @b), children#1(@l1, @b, @l2))
   children#1(::(@x, @xs), @b, @l2) -> children#3(@l2, @b, @x, @xs)
   children#1(nil, @b, @l2) -> children#2(@l2, @b)
   children#2(::(@y, @ys), @b) -> ::(tuple#4(@y, @b, nil, @ys), nil)
   children#2(nil, @b) -> nil
   children#3(::(@y, @ys), @b, @x, @xs) -> ::(tuple#4(@x, @b, nil, @xs), ::(tuple#4(@x, @y, @xs, @ys), nil))
   children#3(nil, @b, @x, @xs) -> nil
   copyover(@copyover@1, @copyover@2) -> copyover#1(tuple#2(@copyover@1, @copyover@2))
   copyover#1(tuple#2(@inq, @outq)) -> copyover#2(@inq, @outq)
   copyover#2(::(@x, @xs), @outq) -> copyover(@xs, ::(@x, @outq))
   copyover#2(nil, @outq) -> tuple#2(nil, @outq)
   dequeue(@dequeue@1, @dequeue@2) -> dequeue#1(tuple#2(@dequeue@1, @dequeue@2))
   dequeue#1(tuple#2(@inq, @outq)) -> dequeue#2(@outq, @inq)
   dequeue#2(::(@y, @ys), @inq) -> tuple#2(tuple#2(@inq, @ys), ::(@y, nil))
   dequeue#2(nil, @inq) -> dequeue#3(@inq)
   dequeue#3(::(@x, @xs)) -> dequeue#4(copyover(::(@x, @xs), nil))
   dequeue#3(nil) -> tuple#2(tuple#2(nil, nil), nil)
   dequeue#4(tuple#2(@dequeue@3, @dequeue@4)) -> dequeue(@dequeue@3, @dequeue@4)
   empty(@x) -> tuple#2(nil, nil)
   enqueue(@x, @queue) -> enqueue#1(@queue, @x)
   enqueue#1(tuple#2(@inq, @outq), @x) -> tuple#2(::(@x, @inq), @outq)
   enqueues(@l, @queue) -> enqueues#1(@l, @queue)
   enqueues#1(::(@x, @xs), @queue) -> enqueues(@xs, enqueue(@x, @queue))
   enqueues#1(nil, @queue) -> @queue
   startBreadth(@xs) -> startBreadth#1(@xs)
   startBreadth#1(::(@x, @xs)) -> startBreadth#2(enqueue(tuple#4(@x, @x, @xs, @xs), empty(#unit)))
   startBreadth#1(nil) -> nil
   startBreadth#2(tuple#2(@breadth@1, @breadth@2)) -> breadth(@breadth@1, @breadth@2)

The set Q consists of the following terms:

   breadth(x0, x1)
   breadth#1(tuple#2(x0, x1))
   breadth#2(::(x0, x1), x2)
   breadth#2(nil, x0)
   breadth#3(tuple#2(x0, x1), x2)

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