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TRS Standard pair #487067412
details
property
value
status
complete
benchmark
#3.15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.455847 seconds
cpu usage
0.788193
user time
0.575819
system time
0.212374
max virtual memory
96176.0
max residence set size
60048.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: average(s(x),y) -> average(x,s(y)) average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 1 1] [1 0 0] [average](x0, x1) = [0 1 1]x0 + [0 0 0]x1 [0 1 1] [0 0 0] , [1 0 0] [s](x0) = [0 0 1]x0 [0 1 0] , [0] [0] = [0] [1] orientation: [1 1 1] [1 0 0] [1 1 1] [1 0 0] average(s(x),y) = [0 1 1]x + [0 0 0]y >= [0 1 1]x + [0 0 0]y = average(x,s(y)) [0 1 1] [0 0 0] [0 1 1] [0 0 0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] average(x,s(s(s(y)))) = [0 1 1]x + [0 0 0]y >= [0 1 1]x + [0 0 0]y = s(average(s(x),y)) [0 1 1] [0 0 0] [0 1 1] [0 0 0] [1] [0] average(0(),0()) = [1] >= [0] = 0() [1] [1] [1] [0] average(0(),s(0())) = [1] >= [0] = 0() [1] [1] [1] [0] average(0(),s(s(0()))) = [1] >= [1] = s(0()) [1] [0] problem: average(s(x),y) -> average(x,s(y)) average(x,s(s(s(y)))) -> s(average(s(x),y)) Matrix Interpretation Processor: dim=1 interpretation: [average](x0, x1) = 4x0 + 4x1 + 6, [s](x0) = x0 + 1 orientation: average(s(x),y) = 4x + 4y + 10 >= 4x + 4y + 10 = average(x,s(y)) average(x,s(s(s(y)))) = 4x + 4y + 18 >= 4x + 4y + 11 = s(average(s(x),y)) problem: average(s(x),y) -> average(x,s(y)) Matrix Interpretation Processor: dim=3 interpretation: [1 1 1] [1 0 0] [average](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [s](x0) = [0 1 1]x0 + [0] [0 0 0] [1] orientation: [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] average(s(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = average(x,s(y)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] problem: Qed
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