TRS Standard pair #615303218

details

property	value
status	complete
benchmark	#3.55.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	2.78960394859 seconds
cpu usage	7.840935281
max memory	4.63003648E8

stage attributes

key	value
output-size	80545
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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

(0) QTRS
(1) Overlay + Local Confluence [EQUIVALENT, 55 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 80 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 2 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) ATransformationProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QReductionProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) ATransformationProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QReductionProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) ATransformationProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) QReductionProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) QDP
        (35) UsableRulesProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) ATransformationProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QReductionProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (42) YES
    (43) QDP
        (44) UsableRulesProof [EQUIVALENT, 0 ms]
        (45) QDP
        (46) ATransformationProof [EQUIVALENT, 0 ms]
        (47) QDP
        (48) QReductionProof [EQUIVALENT, 0 ms]
        (49) QDP
        (50) QDPOrderProof [EQUIVALENT, 46 ms]
        (51) QDP
        (52) PisEmptyProof [EQUIVALENT, 0 ms]
        (53) YES
    (54) QDP
        (55) UsableRulesProof [EQUIVALENT, 0 ms]
        (56) QDP
        (57) ATransformationProof [EQUIVALENT, 0 ms]
        (58) QDP
        (59) QReductionProof [EQUIVALENT, 0 ms]
        (60) QDP
        (61) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (62) YES
    (63) QDP
        (64) UsableRulesProof [EQUIVALENT, 0 ms]
        (65) QDP
        (66) ATransformationProof [EQUIVALENT, 0 ms]
        (67) QDP
        (68) QReductionProof [EQUIVALENT, 0 ms]
        (69) QDP
        (70) QDPOrderProof [EQUIVALENT, 0 ms]
        (71) QDP
        (72) PisEmptyProof [EQUIVALENT, 0 ms]
        (73) YES
    (74) QDP
        (75) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (76) YES


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

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

   app'(app'(minus, x), 0) -> x

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