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TRS Equational pair #487092754
details
property
value
status
complete
benchmark
AC54.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.142154 seconds
cpu usage
0.069697
user time
0.03801
system time
0.031687
max virtual memory
113188.0
max residence set size
6864.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: AC symbols: plus 1: minus(x,0()) -> x 2: minus(s(x),s(y)) -> minus(x,y) 3: minus(minus(x,y),z) -> minus(x,plus(y,z)) 4: quot(0(),s(y)) -> 0() 5: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 6: plus(0(),y) -> y 7: plus(s(x),y) -> s(plus(x,y)) 8: app(nil(),k) -> k 9: app(l,nil()) -> l 10: app(cons(x,l),k) -> cons(x,app(l,k)) 11: sum(cons(x,nil())) -> cons(x,nil()) 12: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) 13: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) Number of strict rules: 13 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #minus(s(x),s(y)) -> #minus(x,y) #2: #sum(app(l,cons(x,cons(y,k)))) -> #sum(app(l,sum(cons(x,cons(y,k))))) #3: #sum(app(l,cons(x,cons(y,k)))) -> #app(l,sum(cons(x,cons(y,k)))) #4: #sum(app(l,cons(x,cons(y,k)))) -> #sum(cons(x,cons(y,k))) #5: #sum(cons(x,cons(y,l))) -> #sum(cons(plus(x,y),l)) #6: #sum(cons(x,cons(y,l))) -> #plus(x,y) #7: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) #8: #plus(x,plus(y,z)) ->= #plus(x,y) #9: #plus(s(x),y) -> #plus(x,y) #10: #app(cons(x,l),k) -> #app(l,k) #11: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y)) #12: #quot(s(x),s(y)) -> #minus(x,y) #13: #minus(minus(x,y),z) -> #minus(x,plus(y,z)) #14: #minus(minus(x,y),z) -> #plus(y,z) Number of SCCs: 6, DPs: 9 SCC { #10 } POLO(Sum)... succeeded. s w: 0 minus w: 0 #plus w: 0 sum w: 0 0 w: 0 quot w: 0 nil w: 0 #app w: x1 #minus w: 0 plus w: 0 cons w: x2 + 1 #quot w: 0 #sum w: 0 app w: 0 USABLE RULES: { } Removed DPs: #10 Number of SCCs: 5, DPs: 8 SCC { #11 } POLO(Sum)... succeeded. s w: x1 + 2 minus w: x1 + 1 #plus w: 0 sum w: 0 0 w: 1 quot w: 0 nil w: 0 #app w: 0 #minus w: 0 plus w: x1 + x2 + 23676 cons w: 1 #quot w: x1 #sum w: 0 app w: 0 USABLE RULES: { 1..3 } Removed DPs: #11 Number of SCCs: 4, DPs: 7 SCC { #5 } POLO(Sum)... succeeded. s w: x1 + 1 minus w: x1 + 1 #plus w: 0 sum w: 0 0 w: 1 quot w: 0 nil w: 0 #app w: 0 #minus w: 0 plus w: x1 + x2 + 1 cons w: x1 + x2 + 2 #quot w: x1 #sum w: x1 app w: 0 USABLE RULES: { 1..3 6 7 14 } Removed DPs: #5 Number of SCCs: 3, DPs: 6 SCC { #2 } POLO(Sum)... succeeded. s w: x1 + 1 minus w: x1 + 1 #plus w: 0 sum w: 3 0 w: 1 quot w: 0
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