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TRS Equational pair #487092805
details
property
value
status
complete
benchmark
boolean_rings.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.070509 seconds
cpu usage
0.04311
user time
0.028448
system time
0.014662
max virtual memory
113188.0
max residence set size
6244.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: AC symbols: or xor and 1: xor(F(),x) -> x 2: xor(neg(x),x) -> F() 3: and(T(),x) -> x 4: and(F(),x) -> F() 5: and(x,x) -> x 6: and(xor(x,y),z) -> xor(and(x,z),and(y,z)) 7: xor(x,x) -> F() 8: impl(x,y) -> xor(and(x,y),xor(T(),x)) 9: or(x,y) -> xor(and(x,y),xor(x,y)) 10: equiv(x,y) -> xor(xor(T(),y),x) 11: neg(x) -> xor(T(),x) Number of strict rules: 11 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #and(xor(x,y),z) -> #xor(and(x,z),and(y,z)) #2: #and(xor(x,y),z) -> #and(x,z) #3: #and(xor(x,y),z) -> #and(y,z) #4: #xor(x,xor(y,z)) ->= #xor(xor(x,y),z) #5: #xor(x,xor(y,z)) ->= #xor(x,y) #6: #or(x,y) -> #xor(and(x,y),xor(x,y)) #7: #or(x,y) -> #and(x,y) #8: #or(x,y) -> #xor(x,y) #9: #neg(x) -> #xor(T(),x) #10: #or(x,or(y,z)) ->= #or(or(x,y),z) #11: #or(x,or(y,z)) ->= #or(x,y) #12: #and(x,and(y,z)) ->= #and(and(x,y),z) #13: #and(x,and(y,z)) ->= #and(x,y) #14: #equiv(x,y) -> #xor(xor(T(),y),x) #15: #equiv(x,y) -> #xor(T(),y) #16: #impl(x,y) -> #xor(and(x,y),xor(T(),x)) #17: #impl(x,y) -> #and(x,y) #18: #impl(x,y) -> #xor(T(),x) Number of SCCs: 3, DPs: 8 SCC { #10 #11 } only weak rules. Number of SCCs: 2, DPs: 6 SCC { #4 #5 } only weak rules. Number of SCCs: 1, DPs: 4 SCC { #2 #3 #12 #13 } POLO(Sum)... POLO(max)... QLPOS... succeeded. T s: [] p: 0 F s: [] p: 0 and s: {1,2} p: 2 #impl s: 1 equiv s: 1 or s: {} p: 0 neg s: [] p: 0 impl s: [1,2] p: 0 #xor s: {} p: 1 #equiv s: [1,2] p: 0 #or s: {} p: 0 #neg s: [] p: 0 xor s: {1,2} p: 1 #and s: {1,2} p: 2 USABLE RULES: { 1..7 13 14 } Removed DPs: #2 #3 #13 Number of SCCs: 1, DPs: 1 SCC { #12 } only weak rules. Number of SCCs: 0, DPs: 0 Next Dependency Pairs: #19: #xor(xor(neg(x),x),_1) -> #xor(F(),_1) #20: #and(and(xor(x,y),z),_1) -> #and(xor(and(x,z),and(y,z)),_1) #21: #xor(x,xor(y,z)) ->= #xor(xor(x,y),z) #22: #xor(x,xor(y,z)) ->= #xor(x,y) #23: #or(or(x,y),_1) -> #or(xor(and(x,y),xor(x,y)),_1) #24: #or(x,or(y,z)) ->= #or(or(x,y),z) #25: #or(x,or(y,z)) ->= #or(x,y) #26: #and(x,and(y,z)) ->= #and(and(x,y),z) #27: #and(x,and(y,z)) ->= #and(x,y) #28: #xor(xor(x,x),_1) -> #xor(F(),_1) #29: #and(and(x,x),_1) -> #and(x,_1) #30: #and(and(T(),x),_1) -> #and(x,_1) #31: #xor(xor(F(),x),_1) -> #xor(x,_1) #32: #and(and(F(),x),_1) -> #and(F(),_1) Number of SCCs: 3, DPs: 14 SCC { #23..25 } POLO(Sum)... POLO(max)... QLPOS... succeeded. T s: [] p: 0 F s: [] p: 0 and s: {1,2} p: 2 #impl s: 1 equiv s: 1 or s: {1,2} p: 3 neg s: [] p: 0 impl s: [1,2] p: 0 #xor s: {} p: 1 #equiv s: [1,2] p: 0 #or s: {1,2} p: 3 #neg s: [] p: 0 xor s: {1,2} p: 1 #and s: {1,2} p: 2 USABLE RULES: { 1..7 9 12..14 } Removed DPs: #23 #25 Number of SCCs: 3, DPs: 12
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