TRS Standard pair #516967195

details

property	value
status	complete
benchmark	#3.53.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n119.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.39626097679 seconds
cpu usage	6.431125146
max memory	5.21879552E8

stage attributes

key	value
output-size	33531
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) AAECC Innermost [EQUIVALENT, 0 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) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) UsableRulesProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QReductionProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QReductionProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) QDP
        (38) UsableRulesProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) QReductionProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) MRRProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) PisEmptyProof [EQUIVALENT, 0 ms]
        (45) YES
    (46) QDP
        (47) UsableRulesProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) QReductionProof [EQUIVALENT, 0 ms]
        (50) QDP
        (51) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (52) YES
    (53) QDP
        (54) UsableRulesProof [EQUIVALENT, 0 ms]
        (55) QDP
        (56) QReductionProof [EQUIVALENT, 0 ms]
        (57) QDP
        (58) QDPOrderProof [EQUIVALENT, 0 ms]
        (59) QDP
        (60) PisEmptyProof [EQUIVALENT, 0 ms]
        (61) YES


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

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

   minus(x, 0) -> x
   minus(s(x), s(y)) -> minus(x, y)
   quot(0, s(y)) -> 0
   quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
   app(nil, y) -> y
   app(add(n, x), y) -> add(n, app(x, y))
   reverse(nil) -> nil
   reverse(add(n, x)) -> app(reverse(x), add(n, nil))
   shuffle(nil) -> nil
   shuffle(add(n, x)) -> add(n, shuffle(reverse(x)))
   concat(leaf, y) -> y
   concat(cons(u, v), y) -> cons(u, concat(v, y))
   less_leaves(x, leaf) -> false
   less_leaves(leaf, cons(w, z)) -> true
   less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z))

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard