TRS Standard pair #615303715

details

property	value
status	complete
benchmark	thiemann34.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n025.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	4.7345161438 seconds
cpu usage	14.277886625
max memory	1.104769024E9

stage attributes

key	value
output-size	26461
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished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) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 26 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) TransformationProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) UsableRulesProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) QReductionProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) NonInfProof [EQUIVALENT, 57 ms]
        (33) AND
            (34) QDP
                (35) DependencyGraphProof [EQUIVALENT, 0 ms]
                (36) TRUE
            (37) QDP
                (38) DependencyGraphProof [EQUIVALENT, 0 ms]
                (39) TRUE


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

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

   gt(s(x), 0) -> true
   gt(0, y) -> false
   gt(s(x), s(y)) -> gt(x, y)
   divides(x, y) -> div(x, y, y)
   div(0, 0, z) -> true
   div(0, s(x), z) -> false
   div(s(x), 0, s(z)) -> div(s(x), s(z), s(z))
   div(s(x), s(y), z) -> div(x, y, z)
   prime(x) -> test(x, s(s(0)))
   test(x, y) -> if1(gt(x, y), x, y)
   if1(true, x, y) -> if2(divides(x, y), x, y)
   if1(false, x, y) -> true
   if2(true, x, y) -> false
   if2(false, x, y) -> test(x, s(y))

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:

   gt(s(x), 0) -> true
   gt(0, y) -> false
   gt(s(x), s(y)) -> gt(x, y)
   divides(x, y) -> div(x, y, y)
   div(0, 0, z) -> true
   div(0, s(x), z) -> false
   div(s(x), 0, s(z)) -> div(s(x), s(z), s(z))
   div(s(x), s(y), z) -> div(x, y, z)
   prime(x) -> test(x, s(s(0)))
   test(x, y) -> if1(gt(x, y), x, y)

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