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TRS Standard pair #487068957
details
property
value
status
complete
benchmark
tower_sizeChange.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n173.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
76.4522 seconds
cpu usage
300.499
user time
297.623
system time
2.87608
max virtual memory
6357316.0
max residence set size
169928.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: tower(x) -> f(a(),x,s(0())) f(a(),0(),y) -> y f(a(),s(x),y) -> f(b(),y,s(x)) f(b(),y,x) -> f(a(),half(x),exp(y)) exp(0()) -> s(0()) exp(s(x)) -> double(exp(x)) double(0()) -> 0() double(s(x)) -> s(s(double(x))) half(0()) -> double(0()) half(s(0())) -> half(0()) half(s(s(x))) -> s(half(x)) Proof: Matrix Interpretation Processor: dim=1 interpretation: [f](x0, x1, x2) = 4x0 + 2x1 + 2x2 + 4, [double](x0) = x0, [a] = 0, [s](x0) = x0, [b] = 0, [tower](x0) = 2x0 + 5, [exp](x0) = x0, [half](x0) = x0, [0] = 0 orientation: tower(x) = 2x + 5 >= 2x + 4 = f(a(),x,s(0())) f(a(),0(),y) = 2y + 4 >= y = y f(a(),s(x),y) = 2x + 2y + 4 >= 2x + 2y + 4 = f(b(),y,s(x)) f(b(),y,x) = 2x + 2y + 4 >= 2x + 2y + 4 = f(a(),half(x),exp(y)) exp(0()) = 0 >= 0 = s(0()) exp(s(x)) = x >= x = double(exp(x)) double(0()) = 0 >= 0 = 0() double(s(x)) = x >= x = s(s(double(x))) half(0()) = 0 >= 0 = double(0()) half(s(0())) = 0 >= 0 = half(0()) half(s(s(x))) = x >= x = s(half(x)) problem: f(a(),s(x),y) -> f(b(),y,s(x)) f(b(),y,x) -> f(a(),half(x),exp(y)) exp(0()) -> s(0()) exp(s(x)) -> double(exp(x)) double(0()) -> 0() double(s(x)) -> s(s(double(x))) half(0()) -> double(0()) half(s(0())) -> half(0()) half(s(s(x))) -> s(half(x)) DP Processor: DPs: f#(a(),s(x),y) -> f#(b(),y,s(x)) f#(b(),y,x) -> exp#(y) f#(b(),y,x) -> half#(x) f#(b(),y,x) -> f#(a(),half(x),exp(y)) exp#(s(x)) -> exp#(x) exp#(s(x)) -> double#(exp(x)) double#(s(x)) -> double#(x) half#(0()) -> double#(0()) half#(s(0())) -> half#(0()) half#(s(s(x))) -> half#(x) TRS: f(a(),s(x),y) -> f(b(),y,s(x)) f(b(),y,x) -> f(a(),half(x),exp(y)) exp(0()) -> s(0()) exp(s(x)) -> double(exp(x)) double(0()) -> 0() double(s(x)) -> s(s(double(x))) half(0()) -> double(0()) half(s(0())) -> half(0()) half(s(s(x))) -> s(half(x)) TDG Processor: DPs: f#(a(),s(x),y) -> f#(b(),y,s(x)) f#(b(),y,x) -> exp#(y) f#(b(),y,x) -> half#(x) f#(b(),y,x) -> f#(a(),half(x),exp(y)) exp#(s(x)) -> exp#(x) exp#(s(x)) -> double#(exp(x)) double#(s(x)) -> double#(x) half#(0()) -> double#(0())
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