TRS Standard pair #615297723

details

property	value
status	complete
benchmark	tower_sizeChange.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n023.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	22.0507740974 seconds
cpu usage	53.460131901
max memory	2.555764736E9

stage attributes

key	value
output-size	28427
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 82 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 25 ms]
(4) QTRS
(5) AAECC Innermost [EQUIVALENT, 0 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 8 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QReductionProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) UsableRulesProof [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) QReductionProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) QDP
        (33) UsableRulesProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QReductionProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) TransformationProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) DependencyGraphProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) TransformationProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) TransformationProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) DependencyGraphProof [EQUIVALENT, 0 ms]
        (46) QDP
        (47) TransformationProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) SemLabProof [SOUND, 73 ms]
        (50) QDP
        (51) DependencyGraphProof [EQUIVALENT, 0 ms]
        (52) QDP
        (53) UsableRulesReductionPairsProof [EQUIVALENT, 7 ms]
        (54) QDP
        (55) QDPOrderProof [EQUIVALENT, 8 ms]
        (56) QDP
        (57) DependencyGraphProof [EQUIVALENT, 0 ms]
        (58) TRUE


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

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

   tower(x) -> f(a, x, s(0))
   f(a, 0, y) -> y
   f(a, s(x), y) -> f(b, y, s(x))
   f(b, y, x) -> f(a, half(x), exp(y))
   exp(0) -> s(0)
   exp(s(x)) -> double(exp(x))
   double(0) -> 0
   double(s(x)) -> s(s(double(x)))
   half(0) -> double(0)
   half(s(0)) -> half(0)
   half(s(s(x))) -> s(half(x))

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

popout

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

job log

popout

actions all output return to TRS Standard