details

property	value
status	complete
benchmark	4.30.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n190.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.637793 seconds
cpu usage	1.48079
user time	1.14016
system time	0.34063
max virtual memory	1930624.0
max residence set size	65204.0

stage attributes

key	value
starexec-result	YES

output

YES Problem: f(nil()) -> nil() f(.(nil(),y)) -> .(nil(),f(y)) f(.(.(x,y),z)) -> f(.(x,.(y,z))) g(nil()) -> nil() g(.(x,nil())) -> .(g(x),nil()) g(.(x,.(y,z))) -> g(.(.(x,y),z)) Proof: Matrix Interpretation Processor: dim=1 interpretation: [f](x0) = x0, [g](x0) = 2x0 + 1, [nil] = 4, [.](x0, x1) = x0 + x1 orientation: f(nil()) = 4 >= 4 = nil() f(.(nil(),y)) = y + 4 >= y + 4 = .(nil(),f(y)) f(.(.(x,y),z)) = x + y + z >= x + y + z = f(.(x,.(y,z))) g(nil()) = 9 >= 4 = nil() g(.(x,nil())) = 2x + 9 >= 2x + 5 = .(g(x),nil()) g(.(x,.(y,z))) = 2x + 2y + 2z + 1 >= 2x + 2y + 2z + 1 = g(.(.(x,y),z)) problem: f(nil()) -> nil() f(.(nil(),y)) -> .(nil(),f(y)) f(.(.(x,y),z)) -> f(.(x,.(y,z))) g(.(x,.(y,z))) -> g(.(.(x,y),z)) Matrix Interpretation Processor: dim=1 interpretation: [f](x0) = 4x0 + 2, [g](x0) = x0, [nil] = 4, [.](x0, x1) = x0 + x1 orientation: f(nil()) = 18 >= 4 = nil() f(.(nil(),y)) = 4y + 18 >= 4y + 6 = .(nil(),f(y)) f(.(.(x,y),z)) = 4x + 4y + 4z + 2 >= 4x + 4y + 4z + 2 = f(.(x,.(y,z))) g(.(x,.(y,z))) = x + y + z >= x + y + z = g(.(.(x,y),z)) problem: f(.(.(x,y),z)) -> f(.(x,.(y,z))) g(.(x,.(y,z))) -> g(.(.(x,y),z)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [f](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [g](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [.](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 1] [0 0 0] [0] orientation: [1 1 1] [1 0 0] [1 0 0] [1] [1 1 1] [1 0 0] [1 0 0] f(.(.(x,y),z)) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z = f(.(x,.(y,z))) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1] g(.(x,.(y,z))) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] = g(.(.(x,y),z)) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] problem: g(.(x,.(y,z))) -> g(.(.(x,y),z)) Matrix Interpretation Processor: dim=1 interpretation: [g](x0) = x0 + 2, [.](x0, x1) = x0 + 4x1 + 1 orientation: g(.(x,.(y,z))) = x + 4y + 16z + 7 >= x + 4y + 4z + 4 = g(.(.(x,y),z)) problem: Qed popout

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all output return to TRS Standard