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TRS Standard pair #487068772
details
property
value
status
complete
benchmark
z26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n190.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.58298 seconds
cpu usage
1.50897
user time
1.21488
system time
0.294088
max virtual memory
96176.0
max residence set size
66788.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) f(a(x),a(y)) -> a(f(x,y)) f(b(x),b(y)) -> b(f(x,y)) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [a](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [1 0 0] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 1] , [1 0 0] [b](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 2] [1 0 2] [1] [1 0 1] [1 0 1] [0] a(a(f(x,y))) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) [0 0 1] [0 0 1] [2] [0 0 0] [0 0 0] [2] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] f(a(x),a(y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = a(f(x,y)) [0 0 1] [0 0 1] [2] [0 0 1] [0 0 1] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] f(b(x),b(y)) = [0 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = b(f(x,y)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: f(a(x),a(y)) -> a(f(x,y)) f(b(x),b(y)) -> b(f(x,y)) Matrix Interpretation Processor: dim=1 interpretation: [a](x0) = 2x0 + 1, [f](x0, x1) = x0 + x1 + 1, [b](x0) = x0 + 7 orientation: f(a(x),a(y)) = 2x + 2y + 3 >= 2x + 2y + 3 = a(f(x,y)) f(b(x),b(y)) = x + y + 15 >= x + y + 8 = b(f(x,y)) problem: f(a(x),a(y)) -> a(f(x,y)) Matrix Interpretation Processor: dim=1 interpretation: [a](x0) = x0 + 5, [f](x0, x1) = x0 + x1 + 3 orientation: f(a(x),a(y)) = x + y + 13 >= x + y + 8 = a(f(x,y)) problem: Qed
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