TRS Standard pair #516967485

details

property	value
status	complete
benchmark	aprove09.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.31072306633 seconds
cpu usage	16.011716295
max memory	1.199439872E9

stage attributes

key	value
output-size	52423
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) AAECC Innermost [EQUIVALENT, 27 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 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) NonInfProof [EQUIVALENT, 53 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) TRUE
    (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QReductionProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) QDP
        (38) UsableRulesProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) QReductionProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) TransformationProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) UsableRulesProof [EQUIVALENT, 0 ms]
        (45) QDP
        (46) QReductionProof [EQUIVALENT, 0 ms]
        (47) QDP
        (48) TransformationProof [EQUIVALENT, 0 ms]
        (49) QDP
        (50) TransformationProof [EQUIVALENT, 0 ms]
        (51) QDP
        (52) DependencyGraphProof [EQUIVALENT, 0 ms]
        (53) QDP
        (54) TransformationProof [EQUIVALENT, 0 ms]
        (55) QDP
        (56) TransformationProof [EQUIVALENT, 0 ms]
        (57) QDP
        (58) TransformationProof [EQUIVALENT, 0 ms]
        (59) QDP
        (60) TransformationProof [EQUIVALENT, 0 ms]
        (61) QDP
        (62) DependencyGraphProof [EQUIVALENT, 0 ms]
        (63) QDP
        (64) TransformationProof [EQUIVALENT, 0 ms]
        (65) QDP
        (66) DependencyGraphProof [EQUIVALENT, 0 ms]
        (67) QDP
        (68) TransformationProof [EQUIVALENT, 0 ms]
        (69) QDP
        (70) QDPOrderProof [EQUIVALENT, 30 ms]
        (71) QDP
        (72) DependencyGraphProof [EQUIVALENT, 0 ms]
        (73) TRUE


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

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

   div(x, y) -> div2(x, y, 0)
   div2(x, y, i) -> if1(le(y, 0), le(y, x), x, y, plus(i, 0), inc(i))
   if1(true, b, x, y, i, j) -> divZeroError
   if1(false, b, x, y, i, j) -> if2(b, x, y, i, j)

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