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TRS Standard pair #487073252
details
property
value
status
complete
benchmark
thiemann15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n190.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
1.21529 seconds
cpu usage
4.99212
user time
3.99696
system time
0.995158
max virtual memory
5014424.0
max residence set size
72744.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) inc(0()) -> 0() inc(s(x)) -> s(inc(x)) zero(0()) -> true() zero(s(x)) -> false() p(0()) -> 0() p(s(x)) -> x bits(x) -> bitIter(x,0()) bitIter(x,y) -> if(zero(x),x,inc(y)) if(true(),x,y) -> p(y) if(false(),x,y) -> bitIter(half(x),y) Proof: DP Processor: DPs: half#(s(s(x))) -> half#(x) inc#(s(x)) -> inc#(x) bits#(x) -> bitIter#(x,0()) bitIter#(x,y) -> inc#(y) bitIter#(x,y) -> zero#(x) bitIter#(x,y) -> if#(zero(x),x,inc(y)) if#(true(),x,y) -> p#(y) if#(false(),x,y) -> half#(x) if#(false(),x,y) -> bitIter#(half(x),y) TRS: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) inc(0()) -> 0() inc(s(x)) -> s(inc(x)) zero(0()) -> true() zero(s(x)) -> false() p(0()) -> 0() p(s(x)) -> x bits(x) -> bitIter(x,0()) bitIter(x,y) -> if(zero(x),x,inc(y)) if(true(),x,y) -> p(y) if(false(),x,y) -> bitIter(half(x),y) TDG Processor: DPs: half#(s(s(x))) -> half#(x) inc#(s(x)) -> inc#(x) bits#(x) -> bitIter#(x,0()) bitIter#(x,y) -> inc#(y) bitIter#(x,y) -> zero#(x) bitIter#(x,y) -> if#(zero(x),x,inc(y)) if#(true(),x,y) -> p#(y) if#(false(),x,y) -> half#(x) if#(false(),x,y) -> bitIter#(half(x),y) TRS: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) inc(0()) -> 0() inc(s(x)) -> s(inc(x)) zero(0()) -> true() zero(s(x)) -> false() p(0()) -> 0() p(s(x)) -> x bits(x) -> bitIter(x,0()) bitIter(x,y) -> if(zero(x),x,inc(y)) if(true(),x,y) -> p(y) if(false(),x,y) -> bitIter(half(x),y) graph: if#(false(),x,y) -> bitIter#(half(x),y) -> bitIter#(x,y) -> if#(zero(x),x,inc(y)) if#(false(),x,y) -> bitIter#(half(x),y) -> bitIter#(x,y) -> zero#(x) if#(false(),x,y) -> bitIter#(half(x),y) -> bitIter#(x,y) -> inc#(y) if#(false(),x,y) -> half#(x) -> half#(s(s(x))) -> half#(x) bitIter#(x,y) -> if#(zero(x),x,inc(y)) -> if#(false(),x,y) -> bitIter#(half(x),y) bitIter#(x,y) -> if#(zero(x),x,inc(y)) -> if#(false(),x,y) -> half#(x) bitIter#(x,y) -> if#(zero(x),x,inc(y)) -> if#(true(),x,y) -> p#(y) bitIter#(x,y) -> inc#(y) -> inc#(s(x)) -> inc#(x) bits#(x) -> bitIter#(x,0()) -> bitIter#(x,y) -> if#(zero(x),x,inc(y)) bits#(x) -> bitIter#(x,0()) -> bitIter#(x,y) -> zero#(x) bits#(x) -> bitIter#(x,0()) -> bitIter#(x,y) -> inc#(y) inc#(s(x)) -> inc#(x) -> inc#(s(x)) -> inc#(x) half#(s(s(x))) -> half#(x) -> half#(s(s(x))) -> half#(x) SCC Processor: #sccs: 3 #rules: 4 #arcs: 13/81 DPs: if#(false(),x,y) -> bitIter#(half(x),y) bitIter#(x,y) -> if#(zero(x),x,inc(y)) TRS: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) inc(0()) -> 0()
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