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TRS Standard pair #487073097
details
property
value
status
complete
benchmark
kabasci05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n180.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
2.58056 seconds
cpu usage
8.85989
user time
7.04224
system time
1.81765
max virtual memory
5750884.0
max residence set size
92056.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) max(x,0()) -> x max(0(),y) -> y max(s(x),s(y)) -> s(max(x,y)) minus(x,0()) -> x minus(s(x),s(y)) -> s(minus(x,y)) gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y))) transform(x) -> s(s(x)) transform(cons(x,y)) -> cons(cons(x,x),x) transform(cons(x,y)) -> y transform(s(x)) -> s(s(transform(x))) cons(x,y) -> y cons(x,cons(y,s(z))) -> cons(y,x) cons(cons(x,z),s(y)) -> transform(x) Proof: DP Processor: DPs: min#(s(x),s(y)) -> min#(x,y) max#(s(x),s(y)) -> max#(x,y) minus#(s(x),s(y)) -> minus#(x,y) gcd#(s(x),s(y)) -> min#(x,y) gcd#(s(x),s(y)) -> transform#(y) gcd#(s(x),s(y)) -> min#(x,transform(y)) gcd#(s(x),s(y)) -> max#(x,y) gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,transform(y))) gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y))) transform#(cons(x,y)) -> cons#(x,x) transform#(cons(x,y)) -> cons#(cons(x,x),x) transform#(s(x)) -> transform#(x) cons#(x,cons(y,s(z))) -> cons#(y,x) cons#(cons(x,z),s(y)) -> transform#(x) TRS: min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) max(x,0()) -> x max(0(),y) -> y max(s(x),s(y)) -> s(max(x,y)) minus(x,0()) -> x minus(s(x),s(y)) -> s(minus(x,y)) gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y))) transform(x) -> s(s(x)) transform(cons(x,y)) -> cons(cons(x,x),x) transform(cons(x,y)) -> y transform(s(x)) -> s(s(transform(x))) cons(x,y) -> y cons(x,cons(y,s(z))) -> cons(y,x) cons(cons(x,z),s(y)) -> transform(x) TDG Processor: DPs: min#(s(x),s(y)) -> min#(x,y) max#(s(x),s(y)) -> max#(x,y) minus#(s(x),s(y)) -> minus#(x,y) gcd#(s(x),s(y)) -> min#(x,y) gcd#(s(x),s(y)) -> transform#(y) gcd#(s(x),s(y)) -> min#(x,transform(y)) gcd#(s(x),s(y)) -> max#(x,y) gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,transform(y))) gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y))) transform#(cons(x,y)) -> cons#(x,x) transform#(cons(x,y)) -> cons#(cons(x,x),x) transform#(s(x)) -> transform#(x) cons#(x,cons(y,s(z))) -> cons#(y,x) cons#(cons(x,z),s(y)) -> transform#(x) TRS: min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) max(x,0()) -> x max(0(),y) -> y max(s(x),s(y)) -> s(max(x,y)) minus(x,0()) -> x minus(s(x),s(y)) -> s(minus(x,y)) gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y))) transform(x) -> s(s(x)) transform(cons(x,y)) -> cons(cons(x,x),x) transform(cons(x,y)) -> y transform(s(x)) -> s(s(transform(x))) cons(x,y) -> y cons(x,cons(y,s(z))) -> cons(y,x) cons(cons(x,z),s(y)) -> transform(x) graph: cons#(cons(x,z),s(y)) -> transform#(x) -> transform#(s(x)) -> transform#(x) cons#(cons(x,z),s(y)) -> transform#(x) -> transform#(cons(x,y)) -> cons#(cons(x,x),x) cons#(cons(x,z),s(y)) -> transform#(x) -> transform#(cons(x,y)) -> cons#(x,x) cons#(x,cons(y,s(z))) -> cons#(y,x) -> cons#(cons(x,z),s(y)) -> transform#(x) cons#(x,cons(y,s(z))) -> cons#(y,x) -> cons#(x,cons(y,s(z))) -> cons#(y,x) transform#(cons(x,y)) -> cons#(cons(x,x),x) -> cons#(cons(x,z),s(y)) -> transform#(x)
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