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TRS Standard pair #487069322
details
property
value
status
complete
benchmark
gcd.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n177.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.953138 seconds
cpu usage
2.52249
user time
1.87586
system time
0.646636
max virtual memory
2228728.0
max residence set size
69352.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: minus(X,s(Y)) -> pred(minus(X,Y)) minus(X,0()) -> X pred(s(X)) -> X le(s(X),s(Y)) -> le(X,Y) le(s(X),0()) -> false() le(0(),Y) -> true() gcd(0(),Y) -> 0() gcd(s(X),0()) -> s(X) gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y)) if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y)) if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X)) Proof: DP Processor: DPs: minus#(X,s(Y)) -> minus#(X,Y) minus#(X,s(Y)) -> pred#(minus(X,Y)) le#(s(X),s(Y)) -> le#(X,Y) gcd#(s(X),s(Y)) -> le#(Y,X) gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) if#(true(),s(X),s(Y)) -> minus#(X,Y) if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) if#(false(),s(X),s(Y)) -> minus#(Y,X) if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X)) TRS: minus(X,s(Y)) -> pred(minus(X,Y)) minus(X,0()) -> X pred(s(X)) -> X le(s(X),s(Y)) -> le(X,Y) le(s(X),0()) -> false() le(0(),Y) -> true() gcd(0(),Y) -> 0() gcd(s(X),0()) -> s(X) gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y)) if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y)) if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X)) TDG Processor: DPs: minus#(X,s(Y)) -> minus#(X,Y) minus#(X,s(Y)) -> pred#(minus(X,Y)) le#(s(X),s(Y)) -> le#(X,Y) gcd#(s(X),s(Y)) -> le#(Y,X) gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) if#(true(),s(X),s(Y)) -> minus#(X,Y) if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) if#(false(),s(X),s(Y)) -> minus#(Y,X) if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X)) TRS: minus(X,s(Y)) -> pred(minus(X,Y)) minus(X,0()) -> X pred(s(X)) -> X le(s(X),s(Y)) -> le(X,Y) le(s(X),0()) -> false() le(0(),Y) -> true() gcd(0(),Y) -> 0() gcd(s(X),0()) -> s(X) gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y)) if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y)) if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X)) graph: if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) -> gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) -> gcd#(s(X),s(Y)) -> le#(Y,X) if#(true(),s(X),s(Y)) -> minus#(X,Y) -> minus#(X,s(Y)) -> pred#(minus(X,Y)) if#(true(),s(X),s(Y)) -> minus#(X,Y) -> minus#(X,s(Y)) -> minus#(X,Y) if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X)) -> gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X)) -> gcd#(s(X),s(Y)) -> le#(Y,X) if#(false(),s(X),s(Y)) -> minus#(Y,X) -> minus#(X,s(Y)) -> pred#(minus(X,Y)) if#(false(),s(X),s(Y)) -> minus#(Y,X) -> minus#(X,s(Y)) -> minus#(X,Y) gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) -> if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X)) gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) -> if#(false(),s(X),s(Y)) -> minus#(Y,X) gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) -> if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) -> if#(true(),s(X),s(Y)) -> minus#(X,Y) gcd#(s(X),s(Y)) -> le#(Y,X) -> le#(s(X),s(Y)) -> le#(X,Y) le#(s(X),s(Y)) -> le#(X,Y) -> 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) SCC Processor: #sccs: 3 #rules: 5 #arcs: 16/81 DPs: if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X))
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