TRS Innermost pair #516979501

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	n085.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.42606401443 seconds
cpu usage	16.858767873
max memory	8.96585728E8

stage attributes

key	value
output-size	56920
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 4 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, 11 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, 16 ms]
        (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 32 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, 92 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 Innermost