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TRS Relative pair #487081925
details
property
value
status
complete
benchmark
rt1-3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
Relative_05
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
1.24228 seconds
cpu usage
3.80147
user time
3.01306
system time
0.788408
max virtual memory
6326628.0
max residence set size
63412.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: strict: t(f(x),g(y),f(z)) -> t(z,g(x),g(y)) t(g(x),g(y),f(z)) -> t(f(y),f(z),x) weak: f(g(x)) -> g(f(x)) g(f(x)) -> f(g(x)) f(f(x)) -> g(g(x)) g(g(x)) -> f(f(x)) Proof: Matrix Interpretation Processor: dim=2 interpretation: [0] [g](x0) = x0 + [1], [0] [f](x0) = x0 + [1], [2 1] [2 1] [2 1] [0] [t](x0, x1, x2) = [0 0]x0 + [0 0]x1 + [0 0]x2 + [1] orientation: [2 1] [2 1] [2 1] [3] [2 1] [2 1] [2 1] [2] t(f(x),g(y),f(z)) = [0 0]x + [0 0]y + [0 0]z + [1] >= [0 0]x + [0 0]y + [0 0]z + [1] = t(z,g(x),g(y)) [2 1] [2 1] [2 1] [3] [2 1] [2 1] [2 1] [2] t(g(x),g(y),f(z)) = [0 0]x + [0 0]y + [0 0]z + [1] >= [0 0]x + [0 0]y + [0 0]z + [1] = t(f(y),f(z),x) [0] [0] f(g(x)) = x + [2] >= x + [2] = g(f(x)) [0] [0] g(f(x)) = x + [2] >= x + [2] = f(g(x)) [0] [0] f(f(x)) = x + [2] >= x + [2] = g(g(x)) [0] [0] g(g(x)) = x + [2] >= x + [2] = f(f(x)) problem: strict: weak: f(g(x)) -> g(f(x)) g(f(x)) -> f(g(x)) f(f(x)) -> g(g(x)) g(g(x)) -> f(f(x)) Qed
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