TRS Standard pair #487066813

details

property	value
status	complete
benchmark	qsort.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n190.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.3362 seconds
cpu usage	32.8938
user time	31.2513
system time	1.64252
max virtual memory	1.9819036E7
max residence set size	3074164.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 27 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [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) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) QDP
        (36) UsableRulesProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QReductionProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) TransformationProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) TransformationProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) Induction-Processor [SOUND, 3 ms]
        (45) AND
            (46) QDP
                (47) UsableRulesProof [EQUIVALENT, 0 ms]
                (48) QDP
                (49) QReductionProof [EQUIVALENT, 0 ms]
                (50) QDP
                (51) Induction-Processor [SOUND, 3 ms]
                (52) AND
                    (53) QDP
                        (54) PisEmptyProof [EQUIVALENT, 0 ms]
                        (55) YES
                    (56) QTRS
                        (57) QTRSRRRProof [EQUIVALENT, 40 ms]
                        (58) QTRS
                        (59) QTRSRRRProof [EQUIVALENT, 0 ms]
                        (60) QTRS
                        (61) RisEmptyProof [EQUIVALENT, 0 ms]
                        (62) YES
            (63) QTRS
                (64) QTRSRRRProof [EQUIVALENT, 92 ms]
                (65) QTRS
                (66) QTRSRRRProof [EQUIVALENT, 0 ms]
                (67) QTRS
                (68) RisEmptyProof [EQUIVALENT, 0 ms]
                (69) YES


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

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

   qsort(nil) -> nil
   qsort(cons(x, xs)) -> append(qsort(filterlow(x, cons(x, xs))), cons(x, qsort(filterhigh(x, cons(x, xs)))))
   filterlow(n, nil) -> nil
   filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
   if1(true, n, x, xs) -> filterlow(n, xs)
   if1(false, n, x, xs) -> cons(x, filterlow(n, xs))
   filterhigh(n, nil) -> nil
   filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
   if2(true, n, x, xs) -> filterhigh(n, xs)
   if2(false, n, x, xs) -> cons(x, filterhigh(n, xs))
   ge(x, 0) -> true
   ge(0, s(x)) -> false
   ge(s(x), s(y)) -> ge(x, y)
   append(nil, ys) -> ys

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