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TRS Standard pair #487066982
details
property
value
status
complete
benchmark
#4.34.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n178.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.787734 seconds
cpu usage
1.83776
user time
1.47328
system time
0.364482
max virtual memory
1746012.0
max residence set size
69620.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) if(true(),x,y) -> x if(false(),x,y) -> y g(s(x),s(y)) -> if(f(x),s(x),s(y)) g(x,c(y)) -> g(x,g(s(c(y)),y)) Proof: Matrix Interpretation Processor: dim=2 interpretation: [2] [false] = [0], [2 0] [1] [c](x0) = [3 1]x0 + [3], [1 0] [0] [f](x0) = [0 0]x0 + [1], [2] [1] = [0], [1 0] [1] [s](x0) = [0 0]x0 + [0], [1] [0] = [0], [2 0] [1 1] [g](x0, x1) = [0 0]x0 + [0 0]x1, [1 0] [1 2] [1 2] [1] [if](x0, x1, x2) = [0 0]x0 + [0 1]x1 + [0 1]x2 + [0], [0] [true] = [1] orientation: [1] [0] f(0()) = [1] >= [1] = true() [2] [2] f(1()) = [1] >= [0] = false() [1 0] [1] [1 0] [0] f(s(x)) = [0 0]x + [1] >= [0 0]x + [1] = f(x) [1 2] [1 2] [1] if(true(),x,y) = [0 1]x + [0 1]y + [0] >= x = x [1 2] [1 2] [3] if(false(),x,y) = [0 1]x + [0 1]y + [0] >= y = y [2 0] [1 0] [3] [2 0] [1 0] [3] g(s(x),s(y)) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = if(f(x),s(x),s(y)) [2 0] [5 1] [4] [2 0] [5 1] [4] g(x,c(y)) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = g(x,g(s(c(y)),y)) problem: f(1()) -> false() g(s(x),s(y)) -> if(f(x),s(x),s(y)) g(x,c(y)) -> g(x,g(s(c(y)),y)) Matrix Interpretation Processor: dim=3 interpretation: [0] [false] = [0] [0], [1 1 0] [c](x0) = [1 1 1]x0 [1 1 1] , [1 0 0] [f](x0) = [1 0 1]x0 [0 0 0] , [1] [1] = [0] [1], [1 0 0] [s](x0) = [1 0 0]x0 [0 0 1] , [1 1 0] [1 1 1] [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1 0 1] [if](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] orientation: [1] [0] f(1()) = [2] >= [0] = false() [0] [0]
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