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TRS Relative pair #487081818
details
property
value
status
complete
benchmark
rt-rw4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
Mixed_relative_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.31967 seconds
cpu usage
17.8417
user time
16.5494
system time
1.2923
max virtual memory
1.88092E7
max residence set size
3179768.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 136 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 24 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 16 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 21 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 136 ms] (10) RelTRS (11) RelTRSRRRProof [EQUIVALENT, 8 ms] (12) RelTRS (13) RelTRSRRRProof [EQUIVALENT, 5 ms] (14) RelTRS (15) RelTRSRRRProof [EQUIVALENT, 12 ms] (16) RelTRS (17) RIsEmptyProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: RAo(R) -> R RAn(R) -> R WAo(W) -> W WAn(W) -> W The relative TRS consists of the following S rules: Rw -> RIn(Rw) Ww -> WIn(Ww) top(ok(sys_r(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_r(read(RAo(r), x), write(W, Ww)))) top(ok(sys_w(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_w(read(RAo(r), x), write(W, Ww)))) top(ok(sys_r(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_r(read(RAn(r), x), write(W, Ww)))) top(ok(sys_w(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_w(read(RAn(r), x), write(W, Ww)))) top(ok(sys_r(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_r(read(R, Rw), write(WAn(W), y)))) top(ok(sys_w(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_w(read(R, Rw), write(WAn(W), y)))) top(ok(sys_r(read(R, Rw), write(W, WIo(y))))) -> top(check(sys_r(read(R, Rw), write(WAo(W), y)))) top(ok(sys_w(read(R, Rw), write(W, WIo(y))))) -> top(check(sys_w(read(R, Rw), write(WAo(W), y)))) top(ok(sys_r(read(r, RIo(x)), write(W, y)))) -> top(check(sys_w(read(RAo(r), x), write(W, y)))) top(ok(sys_r(read(r, RIn(x)), write(W, y)))) -> top(check(sys_w(read(RAn(r), x), write(W, y)))) top(ok(sys_w(read(R, x), write(W, WIo(y))))) -> top(check(sys_r(read(R, x), write(WAo(W), y)))) top(ok(sys_w(read(R, x), write(W, WIn(y))))) -> top(check(sys_r(read(R, x), write(WAn(W), y)))) check(RIo(x)) -> ok(RIo(x)) check(RAo(x)) -> RAo(check(x)) check(RAn(x)) -> RAn(check(x)) check(WAo(x)) -> WAo(check(x)) check(WAn(x)) -> WAn(check(x)) check(RIo(x)) -> RIo(check(x)) check(RIn(x)) -> RIn(check(x)) check(WIo(x)) -> WIo(check(x)) check(WIn(x)) -> WIn(check(x)) check(sys_r(x, y)) -> sys_r(check(x), y) check(sys_r(x, y)) -> sys_r(x, check(y)) check(sys_w(x, y)) -> sys_w(check(x), y) check(sys_w(x, y)) -> sys_w(x, check(y)) RAo(ok(x)) -> ok(RAo(x)) RAn(ok(x)) -> ok(RAn(x)) WAo(ok(x)) -> ok(WAo(x)) WAn(ok(x)) -> ok(WAn(x)) RIn(ok(x)) -> ok(RIn(x)) WIo(ok(x)) -> ok(WIo(x)) WIn(ok(x)) -> ok(WIn(x)) sys_r(ok(x), y) -> ok(sys_r(x, y)) sys_r(x, ok(y)) -> ok(sys_r(x, y)) sys_w(ok(x), y) -> ok(sys_w(x, y)) sys_w(x, ok(y)) -> ok(sys_w(x, y)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(R) = 0 POL(RAn(x_1)) = x_1 POL(RAo(x_1)) = x_1 POL(RIn(x_1)) = x_1 POL(RIo(x_1)) = x_1 POL(Rw) = 0 POL(W) = 0 POL(WAn(x_1)) = x_1 POL(WAo(x_1)) = x_1 POL(WIn(x_1)) = x_1 POL(WIo(x_1)) = 1 + x_1 POL(Ww) = 0
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