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TRS Standard pair #487067507
details
property
value
status
complete
benchmark
#3.5a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.860404 seconds
cpu usage
2.28263
user time
1.79251
system time
0.490125
max virtual memory
1164332.0
max residence set size
69352.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) pred(s(x)) -> x minus(x,0()) -> x minus(x,s(y)) -> pred(minus(x,y)) mod(0(),y) -> 0() mod(s(x),0()) -> 0() mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y)) if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y)) if_mod(false(),s(x),s(y)) -> s(x) Proof: DP Processor: DPs: le#(s(x),s(y)) -> le#(x,y) minus#(x,s(y)) -> minus#(x,y) minus#(x,s(y)) -> pred#(minus(x,y)) mod#(s(x),s(y)) -> le#(y,x) mod#(s(x),s(y)) -> if_mod#(le(y,x),s(x),s(y)) if_mod#(true(),s(x),s(y)) -> minus#(x,y) if_mod#(true(),s(x),s(y)) -> mod#(minus(x,y),s(y)) TRS: le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) pred(s(x)) -> x minus(x,0()) -> x minus(x,s(y)) -> pred(minus(x,y)) mod(0(),y) -> 0() mod(s(x),0()) -> 0() mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y)) if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y)) if_mod(false(),s(x),s(y)) -> s(x) TDG Processor: DPs: le#(s(x),s(y)) -> le#(x,y) minus#(x,s(y)) -> minus#(x,y) minus#(x,s(y)) -> pred#(minus(x,y)) mod#(s(x),s(y)) -> le#(y,x) mod#(s(x),s(y)) -> if_mod#(le(y,x),s(x),s(y)) if_mod#(true(),s(x),s(y)) -> minus#(x,y) if_mod#(true(),s(x),s(y)) -> mod#(minus(x,y),s(y)) TRS: le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) pred(s(x)) -> x minus(x,0()) -> x minus(x,s(y)) -> pred(minus(x,y)) mod(0(),y) -> 0() mod(s(x),0()) -> 0() mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y)) if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y)) if_mod(false(),s(x),s(y)) -> s(x) graph: if_mod#(true(),s(x),s(y)) -> mod#(minus(x,y),s(y)) -> mod#(s(x),s(y)) -> if_mod#(le(y,x),s(x),s(y)) if_mod#(true(),s(x),s(y)) -> mod#(minus(x,y),s(y)) -> mod#(s(x),s(y)) -> le#(y,x) if_mod#(true(),s(x),s(y)) -> minus#(x,y) -> minus#(x,s(y)) -> pred#(minus(x,y)) if_mod#(true(),s(x),s(y)) -> minus#(x,y) -> minus#(x,s(y)) -> minus#(x,y) mod#(s(x),s(y)) -> if_mod#(le(y,x),s(x),s(y)) -> if_mod#(true(),s(x),s(y)) -> mod#(minus(x,y),s(y)) mod#(s(x),s(y)) -> if_mod#(le(y,x),s(x),s(y)) -> if_mod#(true(),s(x),s(y)) -> minus#(x,y) mod#(s(x),s(y)) -> le#(y,x) -> le#(s(x),s(y)) -> le#(x,y) minus#(x,s(y)) -> minus#(x,y) -> minus#(x,s(y)) -> pred#(minus(x,y)) minus#(x,s(y)) -> minus#(x,y) -> minus#(x,s(y)) -> minus#(x,y) le#(s(x),s(y)) -> le#(x,y) -> le#(s(x),s(y)) -> le#(x,y) SCC Processor: #sccs: 3 #rules: 4 #arcs: 10/49 DPs: if_mod#(true(),s(x),s(y)) -> mod#(minus(x,y),s(y)) mod#(s(x),s(y)) -> if_mod#(le(y,x),s(x),s(y)) TRS: le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) pred(s(x)) -> x minus(x,0()) -> x minus(x,s(y)) -> pred(minus(x,y)) mod(0(),y) -> 0() mod(s(x),0()) -> 0() mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y)) if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y)) if_mod(false(),s(x),s(y)) -> s(x) Subterm Criterion Processor: simple projection: pi(pred) = 0 pi(minus) = 0 pi(mod#) = 0
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