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TRS Standard pair #487067707
details
property
value
status
complete
benchmark
2.01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.420443 seconds
cpu usage
0.674729
user time
0.516454
system time
0.158275
max virtual memory
96176.0
max residence set size
58668.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: i(0()) -> 0() +(0(),y) -> y +(x,0()) -> x i(i(x)) -> x +(i(x),x) -> 0() +(x,i(x)) -> 0() i(+(x,y)) -> +(i(x),i(y)) +(x,+(y,z)) -> +(+(x,y),z) +(+(x,i(y)),y) -> x +(+(x,y),i(y)) -> x Proof: Matrix Interpretation Processor: dim=1 interpretation: [i](x0) = x0, [0] = 1, [+](x0, x1) = x0 + 4x1 + 1 orientation: i(0()) = 1 >= 1 = 0() +(0(),y) = 4y + 2 >= y = y +(x,0()) = x + 5 >= x = x i(i(x)) = x >= x = x +(i(x),x) = 5x + 1 >= 1 = 0() +(x,i(x)) = 5x + 1 >= 1 = 0() i(+(x,y)) = x + 4y + 1 >= x + 4y + 1 = +(i(x),i(y)) +(x,+(y,z)) = x + 4y + 16z + 5 >= x + 4y + 4z + 2 = +(+(x,y),z) +(+(x,i(y)),y) = x + 8y + 2 >= x = x +(+(x,y),i(y)) = x + 8y + 2 >= x = x problem: i(0()) -> 0() i(i(x)) -> x +(i(x),x) -> 0() +(x,i(x)) -> 0() i(+(x,y)) -> +(i(x),i(y)) Matrix Interpretation Processor: dim=1 interpretation: [i](x0) = 4x0 + 5, [0] = 3, [+](x0, x1) = 2x0 + x1 + 5 orientation: i(0()) = 17 >= 3 = 0() i(i(x)) = 16x + 25 >= x = x +(i(x),x) = 9x + 15 >= 3 = 0() +(x,i(x)) = 6x + 10 >= 3 = 0() i(+(x,y)) = 8x + 4y + 25 >= 8x + 4y + 20 = +(i(x),i(y)) problem: Qed
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