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TRS Standard pair #487072597
details
property
value
status
complete
benchmark
7.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
Beerendonk_07
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.952645 seconds
cpu usage
2.70392
user time
2.03741
system time
0.666517
max virtual memory
3687460.0
max residence set size
69592.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: cond(true(),x) -> cond(odd(x),p(p(p(x)))) odd(0()) -> false() odd(s(0())) -> true() odd(s(s(x))) -> odd(x) p(0()) -> 0() p(s(x)) -> x Proof: DP Processor: DPs: cond#(true(),x) -> p#(x) cond#(true(),x) -> p#(p(x)) cond#(true(),x) -> p#(p(p(x))) cond#(true(),x) -> odd#(x) cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) odd#(s(s(x))) -> odd#(x) TRS: cond(true(),x) -> cond(odd(x),p(p(p(x)))) odd(0()) -> false() odd(s(0())) -> true() odd(s(s(x))) -> odd(x) p(0()) -> 0() p(s(x)) -> x TDG Processor: DPs: cond#(true(),x) -> p#(x) cond#(true(),x) -> p#(p(x)) cond#(true(),x) -> p#(p(p(x))) cond#(true(),x) -> odd#(x) cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) odd#(s(s(x))) -> odd#(x) TRS: cond(true(),x) -> cond(odd(x),p(p(p(x)))) odd(0()) -> false() odd(s(0())) -> true() odd(s(s(x))) -> odd(x) p(0()) -> 0() p(s(x)) -> x graph: odd#(s(s(x))) -> odd#(x) -> odd#(s(s(x))) -> odd#(x) cond#(true(),x) -> odd#(x) -> odd#(s(s(x))) -> odd#(x) cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) -> cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) -> cond#(true(),x) -> odd#(x) cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) -> cond#(true(),x) -> p#(p(p(x))) cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) -> cond#(true(),x) -> p#(p(x)) cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) -> cond#(true(),x) -> p#(x) SCC Processor: #sccs: 2 #rules: 2 #arcs: 7/36 DPs: cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) TRS: cond(true(),x) -> cond(odd(x),p(p(p(x)))) odd(0()) -> false() odd(s(0())) -> true() odd(s(s(x))) -> odd(x) p(0()) -> 0() p(s(x)) -> x Usable Rule Processor: DPs: cond#(true(),x) -> cond#(odd(x),p(p(p(x)))) TRS: p(0()) -> 0() p(s(x)) -> x odd(0()) -> false() odd(s(0())) -> true() odd(s(s(x))) -> odd(x) Arctic Interpretation Processor: dimension: 1 usable rules: p(0()) -> 0() p(s(x)) -> x odd(0()) -> false() odd(s(0())) -> true() odd(s(s(x))) -> odd(x) interpretation: [0] = 0, [p](x0) = -1x0 + 0, [false] = 0, [true] = 2, [cond#](x0, x1) = 4x0 + 5x1 + 0, [s](x0) = 2x0, [odd](x0) = x0 orientation: cond#(true(),x) = 5x + 6 >= 4x + 5 = cond#(odd(x),p(p(p(x))))
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