details

property	value
status	complete
benchmark	2.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	Mixed_TRS

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.46935 seconds
cpu usage	0.826283
user time	0.612638
system time	0.213645
max virtual memory	96176.0
max residence set size	59532.0

stage attributes

key	value
starexec-result	YES

output

YES Problem: f(a(),f(f(a(),a()),x)) -> f(f(a(),a()),f(a(),f(a(),x))) Proof: Extended Uncurrying Processor: application symbol: f symbol table: a ==> a0/0 a1/1 a2/2 uncurry-rules: f(a1(x2),x3) -> a2(x2,x3) f(a0(),x2) -> a1(x2) eta-rules: f(f(a(),f(f(a(),a()),x)),x1) -> f(f(f(a(),a()),f(a(),f(a(),x))),x1) problem: a1(a2(a0(),x)) -> a2(a0(),a1(a1(x))) a2(a2(a0(),x),x1) -> f(a2(a0(),a1(a1(x))),x1) f(a1(x2),x3) -> a2(x2,x3) f(a0(),x2) -> a1(x2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [a2](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [1 0 0] [0 0 1] , [1 0 0] [1 0 0] [f](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [1 0 0] [0 0 1] , [1 0 0] [a1](x0) = [0 0 1]x0 [0 0 1] , [1] [a0] = [0] [0] orientation: [1 0 0] [1] [1 0 0] [1] a1(a2(a0(),x)) = [0 0 1]x + [1] >= [0 0 1]x + [0] = a2(a0(),a1(a1(x))) [0 0 1] [1] [0 0 1] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] a2(a2(a0(),x),x1) = [0 0 0]x + [0 0 1]x1 + [0] >= [0 0 0]x + [0 0 1]x1 + [0] = f(a2(a0(),a1(a1(x))),x1) [1 0 0] [0 0 1] [1] [1 0 0] [0 0 1] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] f(a1(x2),x3) = [0 0 0]x2 + [0 0 1]x3 >= [0 0 0]x2 + [0 0 1]x3 = a2(x2,x3) [1 0 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1] [1 0 0] f(a0(),x2) = [0 0 1]x2 + [0] >= [0 0 1]x2 = a1(x2) [0 0 1] [1] [0 0 1] problem: a1(a2(a0(),x)) -> a2(a0(),a1(a1(x))) a2(a2(a0(),x),x1) -> f(a2(a0(),a1(a1(x))),x1) f(a1(x2),x3) -> a2(x2,x3) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [1 0 0] [0] [a2](x0, x1) = [0 0 0]x0 + [0 1 1]x1 + [1] [0 0 0] [0 1 1] [1], [1 0 0] [1 0 0] [1] [f](x0, x1) = [0 0 0]x0 + [0 1 1]x1 + [1] [0 0 0] [0 1 1] [1], [1 1 0] [a1](x0) = [0 0 1]x0 [0 1 0] , [0] [a0] = [0] [0] orientation: [1 1 1] [1] [1 1 1] [0] a1(a2(a0(),x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = a2(a0(),a1(a1(x))) [0 1 1] [1] [0 1 1] [1] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [1] a2(a2(a0(),x),x1) = [0 0 0]x + [0 1 1]x1 + [1] >= [0 0 0]x + [0 1 1]x1 + [1] = f(a2(a0(),a1(a1(x))),x1) [0 0 0] [0 1 1] [1] [0 0 0] [0 1 1] [1] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [0] f(a1(x2),x3) = [0 0 0]x2 + [0 1 1]x3 + [1] >= [0 0 0]x2 + [0 1 1]x3 + [1] = a2(x2,x3) [0 0 0] [0 1 1] [1] [0 0 0] [0 1 1] [1] problem: a2(a2(a0(),x),x1) -> f(a2(a0(),a1(a1(x))),x1) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [1 0 0] [0] [a2](x0, x1) = [1 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 0] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 popout

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all output return to TRS Standard