TRS Standard pair #487073983

details

property	value
status	complete
benchmark	aprove2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.62274 seconds
cpu usage	9.08093
user time	8.71931
system time	0.361624
max virtual memory	1.8549788E7
max residence set size	457212.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 12 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) TransformationProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) TransformationProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) TransformationProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) DependencyGraphProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) TransformationProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) TransformationProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) TransformationProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) TransformationProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) TransformationProof [EQUIVALENT, 0 ms]
        (45) QDP
        (46) TransformationProof [EQUIVALENT, 0 ms]
        (47) QDP
        (48) DependencyGraphProof [EQUIVALENT, 0 ms]
        (49) AND
            (50) QDP
                (51) TransformationProof [EQUIVALENT, 0 ms]
                (52) QDP
                (53) TransformationProof [EQUIVALENT, 0 ms]
                (54) QDP
                (55) QDPOrderProof [EQUIVALENT, 19 ms]
                (56) QDP
                (57) PisEmptyProof [EQUIVALENT, 0 ms]
                (58) YES
            (59) QDP
                (60) UsableRulesProof [EQUIVALENT, 0 ms]
                (61) QDP
                (62) QReductionProof [EQUIVALENT, 0 ms]
                (63) QDP
                (64) TransformationProof [EQUIVALENT, 0 ms]
                (65) QDP
                (66) UsableRulesProof [EQUIVALENT, 0 ms]
                (67) QDP
                (68) QReductionProof [EQUIVALENT, 0 ms]
                (69) QDP
                (70) TransformationProof [EQUIVALENT, 0 ms]
                (71) QDP
                (72) TransformationProof [EQUIVALENT, 0 ms]
                (73) QDP
                (74) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (75) YES


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

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

   ge(x, 0) -> true
   ge(0, s(x)) -> false
   ge(s(x), s(y)) -> ge(x, y)
   minus(x, 0) -> x
   minus(s(x), s(y)) -> minus(x, y)
   div(x, y) -> ify(ge(y, s(0)), x, y)
   ify(false, x, y) -> divByZeroError
   ify(true, x, y) -> if(ge(x, y), x, y)

popout

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

job log

popout

actions all output return to TRS Standard