TRS Standard pair #487073878

details

property	value
status	complete
benchmark	aprove1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.12362 seconds
cpu usage	8.73857
user time	8.42054
system time	0.318028
max virtual memory	1.8814932E7
max residence set size	548268.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 14 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 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) QDPOrderProof [EQUIVALENT, 42 ms]
        (29) QDP
        (30) UsableRulesProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) ATransformationProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) QReductionProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) TransformationProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) DependencyGraphProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) UsableRulesProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) QReductionProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) MRRProof [EQUIVALENT, 6 ms]
        (45) QDP
        (46) QDPOrderProof [EQUIVALENT, 0 ms]
        (47) QDP
        (48) DependencyGraphProof [EQUIVALENT, 0 ms]
        (49) TRUE


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

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

   ap(ap(map, f), xs) -> ap(ap(ap(if, ap(isEmpty, xs)), f), xs)
   ap(ap(ap(if, true), f), xs) -> null
   ap(ap(ap(if, null), f), xs) -> ap(ap(cons, ap(f, ap(last, xs))), ap(ap(if2, f), xs))
   ap(ap(if2, f), xs) -> ap(ap(map, f), ap(dropLast, xs))
   ap(isEmpty, null) -> true
   ap(isEmpty, ap(ap(cons, x), xs)) -> null
   ap(last, ap(ap(cons, x), null)) -> x
   ap(last, ap(ap(cons, x), ap(ap(cons, y), ys))) -> ap(last, ap(ap(cons, y), ys))
   ap(dropLast, ap(ap(cons, x), null)) -> null
   ap(dropLast, ap(ap(cons, x), ap(ap(cons, y), ys))) -> ap(ap(cons, x), ap(dropLast, ap(ap(cons, y), ys)))

Q is empty.

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

(1) Overlay + Local Confluence (EQUIVALENT)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   ap(ap(map, f), xs) -> ap(ap(ap(if, ap(isEmpty, xs)), f), xs)
   ap(ap(ap(if, true), f), xs) -> null
   ap(ap(ap(if, null), f), xs) -> ap(ap(cons, ap(f, ap(last, xs))), ap(ap(if2, f), xs))
   ap(ap(if2, f), xs) -> ap(ap(map, f), ap(dropLast, xs))
   ap(isEmpty, null) -> true
   ap(isEmpty, ap(ap(cons, x), xs)) -> null
   ap(last, ap(ap(cons, x), null)) -> x
   ap(last, ap(ap(cons, x), ap(ap(cons, y), ys))) -> ap(last, ap(ap(cons, y), ys))
   ap(dropLast, ap(ap(cons, x), null)) -> null
   ap(dropLast, ap(ap(cons, x), ap(ap(cons, y), ys))) -> ap(ap(cons, x), ap(dropLast, ap(ap(cons, y), ys)))

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