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TRS Relative pair #487081706
details
property
value
status
complete
benchmark
#3.7_rand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
2.95368 seconds
cpu usage
10.6125
user time
8.35696
system time
2.25557
max virtual memory
6911720.0
max residence set size
68240.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: strict: half(0()) -> 0() half(s(s(x))) -> s(half(x)) log(s(0())) -> 0() log(s(s(x))) -> s(log(s(half(x)))) weak: rand(x) -> x rand(x) -> rand(s(x)) Proof: Arctic Interpretation Processor: dimension: 1 interpretation: [rand](x0) = 2x0, [half](x0) = x0, [log](x0) = x0, [0] = 1, [s](x0) = x0 orientation: half(0()) = 1 >= 1 = 0() half(s(s(x))) = x >= x = s(half(x)) log(s(0())) = 1 >= 1 = 0() log(s(s(x))) = x >= x = s(log(s(half(x)))) rand(x) = 2x >= x = x rand(x) = 2x >= 2x = rand(s(x)) problem: strict: half(0()) -> 0() half(s(s(x))) -> s(half(x)) log(s(0())) -> 0() log(s(s(x))) -> s(log(s(half(x)))) weak: rand(x) -> rand(s(x)) Arctic Interpretation Processor: dimension: 1 interpretation: [rand](x0) = 8x0, [half](x0) = x0, [log](x0) = 4x0, [0] = 4, [s](x0) = x0 orientation: half(0()) = 4 >= 4 = 0() half(s(s(x))) = x >= x = s(half(x)) log(s(0())) = 8 >= 4 = 0() log(s(s(x))) = 4x >= 4x = s(log(s(half(x)))) rand(x) = 8x >= 8x = rand(s(x)) problem: strict: half(0()) -> 0() half(s(s(x))) -> s(half(x)) log(s(s(x))) -> s(log(s(half(x)))) weak: rand(x) -> rand(s(x)) Matrix Interpretation Processor: dim=2 interpretation: [2 0] [0] [rand](x0) = [0 0]x0 + [1], [half](x0) = x0, [2 1] [0] [log](x0) = [0 1]x0 + [1], [0] [0] = [0], [0] [s](x0) = x0 + [1] orientation: [0] [0] half(0()) = [0] >= [0] = 0() [0] [0] half(s(s(x))) = x + [2] >= x + [1] = s(half(x)) [2 1] [2] [2 1] [1] log(s(s(x))) = [0 1]x + [3] >= [0 1]x + [3] = s(log(s(half(x))))
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