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TRS Relative pair #487081673
details
property
value
status
complete
benchmark
#3.54_rand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
2.80279 seconds
cpu usage
9.18645
user time
7.25729
system time
1.92916
max virtual memory
5623164.0
max residence set size
68424.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: strict: f(g(x)) -> g(f(f(x))) f(h(x)) -> h(g(x)) f'(s(x),y,y) -> f'(y,x,s(x)) weak: rand(x) -> x rand(x) -> rand(s(x)) Proof: Matrix Interpretation Processor: dim=2 interpretation: [2 0] [1 0] [1 0] [f'](x0, x1, x2) = [0 2]x0 + [0 0]x1 + [0 2]x2, [1 0] [f](x0) = [2 0]x0, [1 0] [s](x0) = [0 0]x0, [3 0] [2] [rand](x0) = [0 2]x0 + [0], [g](x0) = x0, [1 1] [h](x0) = [2 2]x0 orientation: [1 0] [1 0] f(g(x)) = [2 0]x >= [2 0]x = g(f(f(x))) [1 1] [1 1] f(h(x)) = [2 2]x >= [2 2]x = h(g(x)) [2 0] [2 0] [2 0] [2 0] f'(s(x),y,y) = [0 0]x + [0 2]y >= [0 0]x + [0 2]y = f'(y,x,s(x)) [3 0] [2] rand(x) = [0 2]x + [0] >= x = x [3 0] [2] [3 0] [2] rand(x) = [0 2]x + [0] >= [0 0]x + [0] = rand(s(x)) problem: strict: f(g(x)) -> g(f(f(x))) f(h(x)) -> h(g(x)) f'(s(x),y,y) -> f'(y,x,s(x)) weak: rand(x) -> rand(s(x)) Matrix Interpretation Processor: dim=2 interpretation: [2 1] [1 2] [1 0] [1] [f'](x0, x1, x2) = [3 1]x0 + [1 0]x1 + [2 1]x2 + [0], [1 0] [0] [f](x0) = [0 0]x0 + [2], [1 0] [0] [s](x0) = [0 2]x0 + [2], [1 0] [1] [rand](x0) = [0 0]x0 + [0], [1 0] [g](x0) = [0 0]x0, [1 3] [2] [h](x0) = [0 0]x0 + [0] orientation: [1 0] [0] [1 0] f(g(x)) = [0 0]x + [2] >= [0 0]x = g(f(f(x))) [1 3] [2] [1 0] [2] f(h(x)) = [0 0]x + [2] >= [0 0]x + [0] = h(g(x)) [2 2] [2 2] [3] [2 2] [2 1] [1] f'(s(x),y,y) = [3 2]x + [3 1]y + [2] >= [3 2]x + [3 1]y + [2] = f'(y,x,s(x)) [1 0] [1] [1 0] [1] rand(x) = [0 0]x + [0] >= [0 0]x + [0] = rand(s(x)) problem: strict: f(g(x)) -> g(f(f(x))) f(h(x)) -> h(g(x)) weak: rand(x) -> rand(s(x)) String Reversal Processor: strict: g(f(x)) -> f(f(g(x))) h(f(x)) -> g(h(x)) weak: rand(x) -> s(rand(x)) Matrix Interpretation Processor: dim=2
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