TRS Stand 20472 pair #381711452

details

property	value
status	complete
benchmark	#3.57.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	Applicative_first_order_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.47654700279 seconds
cpu usage	6.569239902
max memory	4.91061248E8

stage attributes

key	value
output-size	41079
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 21 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) ATransformationProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) ATransformationProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) MNOCProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) ATransformationProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) UsableRulesReductionPairsProof [EQUIVALENT, 4 ms]
        (27) QDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) UsableRulesReductionPairsProof [EQUIVALENT, 16 ms]
        (34) QDP
        (35) MRRProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) MRRProof [EQUIVALENT, 13 ms]
        (38) QDP
        (39) DependencyGraphProof [EQUIVALENT, 0 ms]
        (40) TRUE
    (41) QDP
        (42) UsableRulesProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) MNOCProof [EQUIVALENT, 0 ms]
        (45) QDP
        (46) ATransformationProof [EQUIVALENT, 0 ms]
        (47) QDP
        (48) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (49) YES
    (50) QDP
        (51) QDPOrderProof [EQUIVALENT, 12 ms]
        (52) QDP
        (53) PisEmptyProof [EQUIVALENT, 0 ms]
        (54) YES
    (55) QDP
        (56) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (57) YES


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

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

   app'(app'(minus, x), 0) -> x
   app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y)
   app'(app'(minus, app'(app'(minus, x), y)), z) -> app'(app'(minus, x), app'(app'(plus, y), z))
   app'(app'(quot, 0), app'(s, y)) -> 0
   app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y)))
   app'(app'(plus, 0), y) -> y
   app'(app'(plus, app'(s, x)), y) -> app'(s, app'(app'(plus, x), y))
   app'(app'(app, nil), k) -> k
   app'(app'(app, l), nil) -> l
   app'(app'(app, app'(app'(cons, x), l)), k) -> app'(app'(cons, x), app'(app'(app, l), k))
   app'(sum, app'(app'(cons, x), nil)) -> app'(app'(cons, x), nil)
   app'(sum, app'(app'(cons, x), app'(app'(cons, y), l))) -> app'(sum, app'(app'(cons, app'(app'(plus, x), y)), l))
   app'(sum, app'(app'(app, l), app'(app'(cons, x), app'(app'(cons, y), k)))) -> app'(sum, app'(app'(app, l), app'(sum, app'(app'(cons, x), app'(app'(cons, y), k)))))
   app'(app'(map, f), nil) -> nil
   app'(app'(map, f), app'(app'(cons, x), xs)) -> app'(app'(cons, app'(f, x)), app'(app'(map, f), xs))
   app'(app'(filter, f), nil) -> nil
   app'(app'(filter, f), app'(app'(cons, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs)
   app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(cons, x), app'(app'(filter, f), xs))
   app'(app'(app'(app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs)

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