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TRS Relative pair #487081745
details
property
value
status
complete
benchmark
#3.26_rand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
2.66044 seconds
cpu usage
9.43799
user time
7.98926
system time
1.44873
max virtual memory
6897924.0
max residence set size
73012.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: strict: f(x) -> s(x) f(s(s(x))) -> s(f(f(x))) weak: rand(x) -> x rand(x) -> rand(s(x)) Proof: Arctic Interpretation Processor: dimension: 1 interpretation: [s](x0) = x0, [f](x0) = x0, [rand](x0) = 8x0 orientation: f(x) = x >= x = s(x) f(s(s(x))) = x >= x = s(f(f(x))) rand(x) = 8x >= x = x rand(x) = 8x >= 8x = rand(s(x)) problem: strict: f(x) -> s(x) f(s(s(x))) -> s(f(f(x))) weak: rand(x) -> rand(s(x)) String Reversal Processor: strict: f(x) -> s(x) s(s(f(x))) -> f(f(s(x))) weak: rand(x) -> s(rand(x)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 2] [s](x0) = [0 1 1]x0 [0 1 0] , [1 0 2] [0] [f](x0) = [0 1 1]x0 + [1] [0 1 0] [0], [2 3 0] [1] [rand](x0) = [0 0 0]x0 + [0] [0 0 0] [0] orientation: [1 0 2] [0] [1 0 2] f(x) = [0 1 1]x + [1] >= [0 1 1]x = s(x) [0 1 0] [0] [0 1 0] [1 4 4] [2] [1 4 4] [0] s(s(f(x))) = [0 3 2]x + [2] >= [0 3 2]x + [2] = f(f(s(x))) [0 2 1] [1] [0 2 1] [1] [2 3 0] [1] [2 3 0] [1] rand(x) = [0 0 0]x + [0] >= [0 0 0]x + [0] = s(rand(x)) [0 0 0] [0] [0 0 0] [0] problem: strict: f(x) -> s(x) weak: rand(x) -> s(rand(x)) String Reversal Processor: strict: f(x) -> s(x) weak: rand(x) -> rand(s(x)) Arctic Interpretation Processor: dimension: 2 interpretation: [0 -&] [s](x0) = [0 0 ]x0, [7 0] [f](x0) = [7 7]x0, [4 4] [rand](x0) = [0 0]x0 orientation: [7 0] [0 -&] f(x) = [7 7]x >= [0 0 ]x = s(x) [4 4] [4 4] rand(x) = [0 0]x >= [0 0]x = rand(s(x)) problem: strict: weak: rand(x) -> rand(s(x)) Qed
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