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TRS Standard pair #487067042
details
property
value
status
complete
benchmark
#4.26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n187.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.922655 seconds
cpu usage
2.5618
user time
1.9689
system time
0.592898
max virtual memory
4855916.0
max residence set size
68632.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: p(0()) -> 0() p(s(x)) -> x le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,y) -> if(le(x,y),x,y) if(true(),x,y) -> 0() if(false(),x,y) -> s(minus(p(x),y)) Proof: DP Processor: DPs: le#(s(x),s(y)) -> le#(x,y) minus#(x,y) -> le#(x,y) minus#(x,y) -> if#(le(x,y),x,y) if#(false(),x,y) -> p#(x) if#(false(),x,y) -> minus#(p(x),y) TRS: p(0()) -> 0() p(s(x)) -> x le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,y) -> if(le(x,y),x,y) if(true(),x,y) -> 0() if(false(),x,y) -> s(minus(p(x),y)) TDG Processor: DPs: le#(s(x),s(y)) -> le#(x,y) minus#(x,y) -> le#(x,y) minus#(x,y) -> if#(le(x,y),x,y) if#(false(),x,y) -> p#(x) if#(false(),x,y) -> minus#(p(x),y) TRS: p(0()) -> 0() p(s(x)) -> x le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,y) -> if(le(x,y),x,y) if(true(),x,y) -> 0() if(false(),x,y) -> s(minus(p(x),y)) graph: if#(false(),x,y) -> minus#(p(x),y) -> minus#(x,y) -> if#(le(x,y),x,y) if#(false(),x,y) -> minus#(p(x),y) -> minus#(x,y) -> le#(x,y) minus#(x,y) -> if#(le(x,y),x,y) -> if#(false(),x,y) -> minus#(p(x),y) minus#(x,y) -> if#(le(x,y),x,y) -> if#(false(),x,y) -> p#(x) minus#(x,y) -> le#(x,y) -> le#(s(x),s(y)) -> le#(x,y) le#(s(x),s(y)) -> le#(x,y) -> le#(s(x),s(y)) -> le#(x,y) SCC Processor: #sccs: 2 #rules: 3 #arcs: 6/25 DPs: if#(false(),x,y) -> minus#(p(x),y) minus#(x,y) -> if#(le(x,y),x,y) TRS: p(0()) -> 0() p(s(x)) -> x le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,y) -> if(le(x,y),x,y) if(true(),x,y) -> 0() if(false(),x,y) -> s(minus(p(x),y)) Usable Rule Processor: DPs: if#(false(),x,y) -> minus#(p(x),y) minus#(x,y) -> if#(le(x,y),x,y) TRS: p(0()) -> 0() p(s(x)) -> x le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) Matrix Interpretation Processor: dim=1 usable rules: p(0()) -> 0() p(s(x)) -> x le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) interpretation: [true] = 0, [p](x0) = 1/2x0, [le](x0, x1) = x0, [false] = 1, [minus#](x0, x1) = x0 + 1/2, [0] = 0,
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