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TRS Standard pair #487066707
details
property
value
status
complete
benchmark
23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n186.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.463994 seconds
cpu usage
0.806128
user time
0.568791
system time
0.237337
max virtual memory
96176.0
max residence set size
60368.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: g(0(),f(x,x)) -> x g(x,s(y)) -> g(f(x,y),0()) g(s(x),y) -> g(f(x,y),0()) g(f(x,y),0()) -> f(g(x,0()),g(y,0())) Proof: Matrix Interpretation Processor: dim=1 interpretation: [f](x0, x1) = x0 + 2x1 + 4, [s](x0) = 4x0 + 4, [0] = 0, [g](x0, x1) = x0 + 4x1 orientation: g(0(),f(x,x)) = 12x + 16 >= x = x g(x,s(y)) = x + 16y + 16 >= x + 2y + 4 = g(f(x,y),0()) g(s(x),y) = 4x + 4y + 4 >= x + 2y + 4 = g(f(x,y),0()) g(f(x,y),0()) = x + 2y + 4 >= x + 2y + 4 = f(g(x,0()),g(y,0())) problem: g(s(x),y) -> g(f(x,y),0()) g(f(x,y),0()) -> f(g(x,0()),g(y,0())) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [0] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [1 0 0] [1] [s](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [0] = [0] [0], [1 0 0] [1 0 0] [0] [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] g(s(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = g(f(x,y),0()) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] g(f(x,y),0()) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = f(g(x,0()),g(y,0())) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] problem: g(f(x,y),0()) -> f(g(x,0()),g(y,0())) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [f](x0, x1) = [0 0 0]x0 + x1 + [0] [0 0 1] [1], [0] [0] = [0] [0], [1 0 1] [1 0 0] [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 1 1] [0 0 0] orientation: [1 1 1] [1 0 1] [1] [1 0 1] [1 0 1] [0] g(f(x,y),0()) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = f(g(x,0()),g(y,0())) [1 1 1] [1 1 1] [1] [1 1 1] [1 1 1] [1] problem: Qed
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