TRS Inner 89993 pair #381733435

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	n092.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.83302807808 seconds
cpu usage	13.677885163
max memory	5.79252224E8

stage attributes

key	value
output-size	56927
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 26 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, 12 ms]
        (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 16 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, 88 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:

popout

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

job log

popout

actions all output return to TRS Inner 89993