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TRS Relative pair #487081777
details
property
value
status
complete
benchmark
#3.10_rand.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
INVY_15
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.672206 seconds
cpu usage
0.68
user time
0.62
system time
0.06
max virtual memory
331748.0
max residence set size
9328.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: 1: eq(0(),0()) -> true() 2: eq(0(),s(x)) -> false() 3: eq(s(x),0()) -> false() 4: eq(s(x),s(y)) -> eq(x,y) 5: le(0(),y) -> true() 6: le(s(x),0()) -> false() 7: le(s(x),s(y)) -> le(x,y) 8: app(nil(),y) -> y 9: app(add(n,x),y) -> add(n,app(x,y)) 10: min(add(n,nil())) -> n 11: min(add(n,add(m,x))) -> if_min(le(n,m),add(n,add(m,x))) 12: if_min(true(),add(n,add(m,x))) -> min(add(n,x)) 13: if_min(false(),add(n,add(m,x))) -> min(add(m,x)) 14: rm(n,nil()) -> nil() 15: rm(n,add(m,x)) -> if_rm(eq(n,m),n,add(m,x)) 16: if_rm(true(),n,add(m,x)) -> rm(n,x) 17: if_rm(false(),n,add(m,x)) -> add(m,rm(n,x)) 18: minsort(nil(),nil()) -> nil() 19: minsort(add(n,x),y) -> if_minsort(eq(n,min(add(n,x))),add(n,x),y) 20: if_minsort(true(),add(n,x),y) -> add(n,minsort(app(rm(n,x),y),nil())) 21: if_minsort(false(),add(n,x),y) -> minsort(x,add(n,y)) 22: rand(x) ->= x 23: rand(x) ->= rand(s(x)) Number of strict rules: 21 Direct POLO(bPol) ... failed. Uncurrying min 1: eq(0(),0()) -> true() 2: eq(0(),s(x)) -> false() 3: eq(s(x),0()) -> false() 4: eq(s(x),s(y)) -> eq(x,y) 5: le(0(),y) -> true() 6: le(s(x),0()) -> false() 7: le(s(x),s(y)) -> le(x,y) 8: app(nil(),y) -> y 9: app(add(n,x),y) -> add(n,app(x,y)) 10: min^1_add(n,nil()) -> n 11: min^1_add(n,add(m,x)) -> if_min(le(n,m),add(n,add(m,x))) 12: if_min(true(),add(n,add(m,x))) -> min^1_add(n,x) 13: if_min(false(),add(n,add(m,x))) -> min^1_add(m,x) 14: rm(n,nil()) -> nil() 15: rm(n,add(m,x)) -> if_rm(eq(n,m),n,add(m,x)) 16: if_rm(true(),n,add(m,x)) -> rm(n,x) 17: if_rm(false(),n,add(m,x)) -> add(m,rm(n,x)) 18: minsort(nil(),nil()) -> nil() 19: minsort(add(n,x),y) -> if_minsort(eq(n,min^1_add(n,x)),add(n,x),y) 20: if_minsort(true(),add(n,x),y) -> add(n,minsort(app(rm(n,x),y),nil())) 21: if_minsort(false(),add(n,x),y) -> minsort(x,add(n,y)) 22: rand(x) ->= x 23: rand(x) ->= rand(s(x)) 24: min(add(_1,_2)) ->= min^1_add(_1,_2) Number of strict rules: 21 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #if_min(false(),add(n,add(m,x))) -> #min^1_add(m,x) #2: #app(add(n,x),y) -> #app(x,y) #3: #min^1_add(n,add(m,x)) -> #if_min(le(n,m),add(n,add(m,x))) #4: #min^1_add(n,add(m,x)) -> #le(n,m) #5: #min(add(_1,_2)) ->? #min^1_add(_1,_2) #6: #if_min(true(),add(n,add(m,x))) -> #min^1_add(n,x) #7: #if_minsort(true(),add(n,x),y) -> #minsort(app(rm(n,x),y),nil()) #8: #if_minsort(true(),add(n,x),y) -> #app(rm(n,x),y) #9: #if_minsort(true(),add(n,x),y) -> #rm(n,x) #10: #le(s(x),s(y)) -> #le(x,y) #11: #if_rm(false(),n,add(m,x)) -> #rm(n,x) #12: #minsort(add(n,x),y) -> #if_minsort(eq(n,min^1_add(n,x)),add(n,x),y) #13: #minsort(add(n,x),y) -> #eq(n,min^1_add(n,x)) #14: #minsort(add(n,x),y) -> #min^1_add(n,x) #15: #if_minsort(false(),add(n,x),y) -> #minsort(x,add(n,y)) #16: #if_rm(true(),n,add(m,x)) -> #rm(n,x) #17: #rm(n,add(m,x)) -> #if_rm(eq(n,m),n,add(m,x)) #18: #rm(n,add(m,x)) -> #eq(n,m) #19: #eq(s(x),s(y)) -> #eq(x,y) Number of SCCs: 6, DPs: 12 SCC { #19 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. le s: [2,1] p: 1 w: max(x1 + 1, x2 + 4) if_rm s: 3 s s: [1] p: 0 w: x1 #le s: [2,1] p: 0 w: max(x1 + 1, x2 + 1) #if_rm s: 3 #if_min s: [2] p: 0 w: max(x2 + 1) eq s: [] p: 3 w: max(x1 + 5, x2 + 7) false s: [] p: 1 w: 6 #min s: 1 min^1_add s: [] p: 2 w: max(x1 + 4, x2) true s: [] p: 1 w: 3 rand s: [] p: 0 w: x1 + 1 #eq s: [1] p: 1 w: max(x1 + 1) 0 s: [] p: 1 w: 3 nil s: [] p: 3 w: 4 #app s: 1 #if_minsort s: [3,1] p: 0 w: max(x1 + 1, x2 + 1, x3 + 1) min s: [] p: 0 w: x1 + 1 #min^1_add s: 1 #minsort s: [2,1] p: 0 w: max(x1 + 1, x2 + 1) add s: [] p: 3 w: max(x1 + 4, x2) if_min s: [] p: 2 w: max(x1, x2) if_minsort s: [] p: 4 w: max(x2, x3)
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