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TRS Standard pair #487067422
details
property
value
status
complete
benchmark
#3.12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.633843 seconds
cpu usage
1.43833
user time
1.1066
system time
0.331722
max virtual memory
1454904.0
max residence set size
66280.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: app(nil(),y) -> y app(add(n,x),y) -> add(n,app(x,y)) reverse(nil()) -> nil() reverse(add(n,x)) -> app(reverse(x),add(n,nil())) shuffle(nil()) -> nil() shuffle(add(n,x)) -> add(n,shuffle(reverse(x))) Proof: Matrix Interpretation Processor: dim=1 interpretation: [shuffle](x0) = x0 + 1, [app](x0, x1) = x0 + x1, [reverse](x0) = x0, [nil] = 0, [add](x0, x1) = x0 + x1 + 4 orientation: app(nil(),y) = y >= y = y app(add(n,x),y) = n + x + y + 4 >= n + x + y + 4 = add(n,app(x,y)) reverse(nil()) = 0 >= 0 = nil() reverse(add(n,x)) = n + x + 4 >= n + x + 4 = app(reverse(x),add(n,nil())) shuffle(nil()) = 1 >= 0 = nil() shuffle(add(n,x)) = n + x + 5 >= n + x + 5 = add(n,shuffle(reverse(x))) problem: app(nil(),y) -> y app(add(n,x),y) -> add(n,app(x,y)) reverse(nil()) -> nil() reverse(add(n,x)) -> app(reverse(x),add(n,nil())) shuffle(add(n,x)) -> add(n,shuffle(reverse(x))) Matrix Interpretation Processor: dim=1 interpretation: [shuffle](x0) = 4x0 + 7, [app](x0, x1) = x0 + x1, [reverse](x0) = x0, [nil] = 0, [add](x0, x1) = 2x0 + x1 + 1 orientation: app(nil(),y) = y >= y = y app(add(n,x),y) = 2n + x + y + 1 >= 2n + x + y + 1 = add(n,app(x,y)) reverse(nil()) = 0 >= 0 = nil() reverse(add(n,x)) = 2n + x + 1 >= 2n + x + 1 = app(reverse(x),add(n,nil())) shuffle(add(n,x)) = 8n + 4x + 11 >= 2n + 4x + 8 = add(n,shuffle(reverse(x))) problem: app(nil(),y) -> y app(add(n,x),y) -> add(n,app(x,y)) reverse(nil()) -> nil() reverse(add(n,x)) -> app(reverse(x),add(n,nil())) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [0] [app](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1] [1 0 0] [0 1 1] [0], [1 0 0] [1] [reverse](x0) = [1 0 0]x0 + [1] [1 0 1] [1], [0] [nil] = [0] [0], [1 0 1] [1 0 0] [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 1] orientation: [1 0 0] [0] app(nil(),y) = [0 1 0]y + [1] >= y = y [0 1 1] [0] [1 0 1] [1 0 0] [1 0 0] [0] [1 0 1] [1 0 0] [1 0 0] app(add(n,x),y) = [0 0 0]n + [0 0 0]x + [0 1 0]y + [1] >= [0 0 0]n + [0 0 0]x + [0 0 0]y = add(n,app(x,y)) [1 0 1] [1 0 0] [0 1 1] [0] [0 0 0] [1 0 0] [0 1 1] [1] [0] reverse(nil()) = [1] >= [0] = nil() [1] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1]
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