TRS Standard pair #487072778

details

property	value
status	complete
benchmark	reverse.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n186.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.54031 seconds
cpu usage	6.87546
user time	6.60635
system time	0.269118
max virtual memory	1.8546532E7
max residence set size	404404.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 22 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) TransformationProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) DependencyGraphProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) UsableRulesProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QReductionProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) QDPOrderProof [EQUIVALENT, 6 ms]
        (42) QDP
        (43) DependencyGraphProof [EQUIVALENT, 0 ms]
        (44) TRUE


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

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

   isEmpty(nil) -> true
   isEmpty(cons(x, xs)) -> false
   last(cons(x, nil)) -> x
   last(cons(x, cons(y, ys))) -> last(cons(y, ys))
   dropLast(nil) -> nil
   dropLast(cons(x, nil)) -> nil
   dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys)))
   append(nil, ys) -> ys
   append(cons(x, xs), ys) -> cons(x, append(xs, ys))
   reverse(xs) -> rev(xs, nil)
   rev(xs, ys) -> if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys)
   if(true, xs, ys, zs) -> zs
   if(false, xs, ys, zs) -> rev(xs, 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:

   isEmpty(nil) -> true
   isEmpty(cons(x, xs)) -> false
   last(cons(x, nil)) -> x
   last(cons(x, cons(y, ys))) -> last(cons(y, ys))
   dropLast(nil) -> nil
   dropLast(cons(x, nil)) -> nil
   dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys)))
   append(nil, ys) -> ys
   append(cons(x, xs), ys) -> cons(x, append(xs, ys))
   reverse(xs) -> rev(xs, nil)
   rev(xs, ys) -> if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys)
   if(true, xs, ys, zs) -> zs

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