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TRS Standard pair #487073006
details
property
value
status
complete
benchmark
thiemann18.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n187.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.306964 seconds
cpu usage
0.083991
user time
0.051473
system time
0.032518
max virtual memory
113188.0
max residence set size
6860.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: 1: eq(0(),0()) -> true() 2: eq(0(),s(m)) -> false() 3: eq(s(n),0()) -> false() 4: eq(s(n),s(m)) -> eq(n,m) 5: le(0(),m) -> true() 6: le(s(n),0()) -> false() 7: le(s(n),s(m)) -> le(n,m) 8: min(cons(x,nil())) -> x 9: min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x))) 10: if_min(true(),cons(n,cons(m,x))) -> min(cons(n,x)) 11: if_min(false(),cons(n,cons(m,x))) -> min(cons(m,x)) 12: replace(n,m,nil()) -> nil() 13: replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x)) 14: if_replace(true(),n,m,cons(k,x)) -> cons(m,x) 15: if_replace(false(),n,m,cons(k,x)) -> cons(k,replace(n,m,x)) 16: empty(nil()) -> true() 17: empty(cons(n,x)) -> false() 18: head(cons(n,x)) -> n 19: tail(nil()) -> nil() 20: tail(cons(n,x)) -> x 21: sort(x) -> sortIter(x,nil()) 22: sortIter(x,y) -> if(empty(x),x,y,append(y,cons(min(x),nil()))) 23: if(true(),x,y,z) -> y 24: if(false(),x,y,z) -> sortIter(replace(min(x),head(x),tail(x)),z) Number of strict rules: 24 Direct POLO(bPol) ... failed. Uncurrying min 1: eq(0(),0()) -> true() 2: eq(0(),s(m)) -> false() 3: eq(s(n),0()) -> false() 4: eq(s(n),s(m)) -> eq(n,m) 5: le(0(),m) -> true() 6: le(s(n),0()) -> false() 7: le(s(n),s(m)) -> le(n,m) 8: min^1_cons(x,nil()) -> x 9: min^1_cons(n,cons(m,x)) -> if_min(le(n,m),cons(n,cons(m,x))) 10: if_min(true(),cons(n,cons(m,x))) -> min^1_cons(n,x) 11: if_min(false(),cons(n,cons(m,x))) -> min^1_cons(m,x) 12: replace(n,m,nil()) -> nil() 13: replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x)) 14: if_replace(true(),n,m,cons(k,x)) -> cons(m,x) 15: if_replace(false(),n,m,cons(k,x)) -> cons(k,replace(n,m,x)) 16: empty(nil()) -> true() 17: empty(cons(n,x)) -> false() 18: head(cons(n,x)) -> n 19: tail(nil()) -> nil() 20: tail(cons(n,x)) -> x 21: sort(x) -> sortIter(x,nil()) 22: sortIter(x,y) -> if(empty(x),x,y,append(y,cons(min(x),nil()))) 23: if(true(),x,y,z) -> y 24: if(false(),x,y,z) -> sortIter(replace(min(x),head(x),tail(x)),z) 25: min(cons(_1,_2)) ->= min^1_cons(_1,_2) Number of strict rules: 24 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #replace(n,m,cons(k,x)) -> #if_replace(eq(n,k),n,m,cons(k,x)) #2: #replace(n,m,cons(k,x)) -> #eq(n,k) #3: #min^1_cons(n,cons(m,x)) -> #if_min(le(n,m),cons(n,cons(m,x))) #4: #min^1_cons(n,cons(m,x)) -> #le(n,m) #5: #if_min(false(),cons(n,cons(m,x))) -> #min^1_cons(m,x) #6: #if(false(),x,y,z) -> #sortIter(replace(min(x),head(x),tail(x)),z) #7: #if(false(),x,y,z) -> #replace(min(x),head(x),tail(x)) #8: #if(false(),x,y,z) -> #min(x) #9: #if(false(),x,y,z) -> #head(x) #10: #if(false(),x,y,z) -> #tail(x) #11: #min(cons(_1,_2)) ->? #min^1_cons(_1,_2) #12: #le(s(n),s(m)) -> #le(n,m) #13: #if_min(true(),cons(n,cons(m,x))) -> #min^1_cons(n,x) #14: #sortIter(x,y) -> #if(empty(x),x,y,append(y,cons(min(x),nil()))) #15: #sortIter(x,y) -> #empty(x) #16: #sortIter(x,y) -> #min(x) #17: #sort(x) -> #sortIter(x,nil()) #18: #if_replace(false(),n,m,cons(k,x)) -> #replace(n,m,x) #19: #eq(s(n),s(m)) -> #eq(n,m) Number of SCCs: 5, DPs: 9 SCC { #12 } POLO(Sum)... succeeded. le w: 0 #empty w: 0 s w: x1 + 1 #le w: x1 + x2 #if_min w: 0 min^1_cons w: 0 eq w: 0 false w: 0 #min w: 0 #head w: 0 sortIter w: 0 #sortIter w: 0 true w: 0 #eq w: 0 #sort w: 0 tail w: 0 append w: 0 0 w: 0 if w: 0 if_replace w: 0 nil w: 0
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