details

property	value
status	complete
benchmark	Ex6_11.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.712991 seconds
cpu usage	1.59609
user time	1.21286
system time	0.383228
max virtual memory	1746448.0
max residence set size	69048.0

stage attributes

key	value
starexec-result	YES

output

YES Problem: app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x)) Proof: Extended Uncurrying Processor: application symbol: app symbol table: G ==> G0/0 G1/1 F ==> F0/0 F1/1 F2/2 uncurry-rules: app(F1(x2),x3) -> F2(x2,x3) app(F0(),x2) -> F1(x2) app(G0(),x5) -> G1(x5) eta-rules: problem: F2(F2(f,x),x) -> F2(G1(F2(f,x)),app(f,x)) app(F1(x2),x3) -> F2(x2,x3) app(F0(),x2) -> F1(x2) app(G0(),x5) -> G1(x5) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [1] [F1](x0) = [1 1 0]x0 + [1] [0 1 0] [0], [1 0 0] [1 1 0] [app](x0, x1) = [0 1 0]x0 + [1 1 0]x1 [1 0 1] [0 1 0] , [1] [F0] = [1] [0], [1 1 0] [1 1 0] [1] [F2](x0, x1) = [1 1 0]x0 + [1 1 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [0] [G1](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1] [G0] = [1] [0] orientation: [2 2 0] [3 3 0] [3] [2 2 0] [3 3 0] [3] F2(F2(f,x),x) = [2 2 0]f + [3 3 0]x + [3] >= [2 2 0]f + [3 3 0]x + [3] = F2(G1(F2(f,x)),app(f,x)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1] app(F1(x2),x3) = [1 1 0]x2 + [1 1 0]x3 + [1] >= [1 1 0]x2 + [1 1 0]x3 + [1] = F2(x2,x3) [1 2 0] [0 1 0] [1] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] app(F0(),x2) = [1 1 0]x2 + [1] >= [1 1 0]x2 + [1] = F1(x2) [0 1 0] [1] [0 1 0] [0] [1 1 0] [1] [1 0 0] [0] app(G0(),x5) = [1 1 0]x5 + [1] >= [0 0 0]x5 + [1] = G1(x5) [0 1 0] [1] [0 0 0] [0] problem: F2(F2(f,x),x) -> F2(G1(F2(f,x)),app(f,x)) app(F1(x2),x3) -> F2(x2,x3) app(F0(),x2) -> F1(x2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [F1](x0) = [1 1 1]x0 + [1] [0 1 1] [1], [1 0 1] [1 0 0] [0] [app](x0, x1) = [0 1 0]x0 + [1 1 1]x1 + [1] [0 1 0] [0 1 1] [1], [0] [F0] = [0] [1], [1 0 1] [1 0 0] [0] [F2](x0, x1) = [0 1 1]x0 + [0 0 0]x1 + [1] [1 1 1] [0 0 0] [0], [1 0 0] [G1](x0) = [0 1 1]x0 [0 0 0] orientation: [2 1 2] [2 0 0] [0] [2 0 2] [2 0 0] [0] F2(F2(f,x),x) = [1 2 2]f + [0 0 0]x + [2] >= [1 2 2]f + [0 0 0]x + [2] = F2(G1(F2(f,x)),app(f,x)) [2 2 3] [1 0 0] [1] [2 2 3] [1 0 0] [1] [1 1 1] [1 0 0] [2] [1 0 1] [1 0 0] [0] app(F1(x2),x3) = [1 1 1]x2 + [1 1 1]x3 + [2] >= [0 1 1]x2 + [0 0 0]x3 + [1] = F2(x2,x3) [1 1 1] [0 1 1] [2] [1 1 1] [0 0 0] [0] popout

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