TRS Standard pair #516966135

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	n055.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.44613003731 seconds
cpu usage	9.320541752
max memory	5.7315328E8

stage attributes

key	value
output-size	25466
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 8 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, 36 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

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