YES Input TRS: AC symbols: or and C symbols: eq neq 1: eq(x,x) -> true() 2: not(eq(x,y)) -> neq(x,y) 3: not(neq(x,y)) -> eq(x,y) 4: not(true()) -> false() 5: not(false()) -> true() 6: not(not(x)) -> x 7: not(and(x,y)) -> or(not(x),not(y)) 8: not(or(x,y)) -> and(not(x),not(y)) 9: neq(x,x) -> false() 10: or(and(x,y),z) -> and(or(x,z),or(y,z)) 11: or(x,x) -> x 12: or(x,true()) -> true() 13: or(x,false()) -> x 14: and(x,x) -> x 15: and(x,true()) -> x 16: and(x,false()) -> false() 17: and(x,or(x,y)) -> x Number of strict rules: 17 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #not(eq(x,y)) -> #neq(x,y) #2: #not(and(x,y)) -> #or(not(x),not(y)) #3: #not(and(x,y)) -> #not(x) #4: #not(and(x,y)) -> #not(y) #5: #or(and(x,y),z) -> #and(or(x,z),or(y,z)) #6: #or(and(x,y),z) -> #or(x,z) #7: #or(and(x,y),z) -> #or(y,z) #8: #and(x,and(y,z)) ->= #and(and(x,y),z) #9: #and(x,and(y,z)) ->= #and(x,y) #10: #not(neq(x,y)) -> #eq(x,y) #11: #not(or(x,y)) -> #and(not(x),not(y)) #12: #not(or(x,y)) -> #not(x) #13: #not(or(x,y)) -> #not(y) #14: #or(x,or(y,z)) ->= #or(or(x,y),z) #15: #or(x,or(y,z)) ->= #or(x,y) Number of SCCs: 3, DPs: 10 SCC { #8 #9 } only weak rules. Number of SCCs: 2, DPs: 8 SCC { #3 #4 #12 #13 } POLO(Sum)... succeeded. neq w: 0 and w: x1 + x2 + 1 eq w: 0 false w: 0 true w: 0 #eq w: 0 #not w: x1 #neq w: 0 or w: x1 + x2 + 1 #or w: 0 #and w: 0 not w: 0 USABLE RULES: { } Removed DPs: #3 #4 #12 #13 Number of SCCs: 1, DPs: 4 SCC { #6 #7 #14 #15 } POLO(Sum)... POLO(max)... QLPOS... succeeded. neq s: {} p: 0 and s: {1,2} p: 1 eq s: {} p: 0 false s: [] p: 0 true s: [] p: 0 #eq s: {} p: 0 #not s: [] p: 0 #neq s: {} p: 0 or s: {1,2} p: 2 #or s: {1,2} p: 2 #and s: {} p: 1 not s: [] p: 0 USABLE RULES: { 10..19 } Removed DPs: #6 #7 #15 Number of SCCs: 1, DPs: 1 SCC { #14 } only weak rules. Number of SCCs: 0, DPs: 0 Next Dependency Pairs: #16: #or(or(x,false()),_1) -> #or(x,_1) #17: #or(or(x,x),_1) -> #or(x,_1) #18: #or(or(x,true()),_1) -> #or(true(),_1) #19: #and(and(x,x),_1) -> #and(x,_1) #20: #or(or(and(x,y),z),_1) -> #or(and(or(x,z),or(y,z)),_1) #21: #and(and(x,or(x,y)),_1) -> #and(x,_1) #22: #and(x,and(y,z)) ->= #and(and(x,y),z) #23: #and(x,and(y,z)) ->= #and(x,y) #24: #and(and(x,false()),_1) -> #and(false(),_1) #25: #and(and(x,true()),_1) -> #and(x,_1) #26: #or(x,or(y,z)) ->= #or(or(x,y),z) #27: #or(x,or(y,z)) ->= #or(x,y) Number of SCCs: 2, DPs: 12 SCC { #19 #21..25 } POLO(Sum)... succeeded. neq w: 0 and w: x1 + x2 + 1 eq w: 0 false w: 1 true w: 7758 #eq w: 0 #not w: 0 #neq w: 0 or w: x1 + x2 + 1 #or w: 0 #and w: x1 + x2 not w: 0 USABLE RULES: { 14..17 19 } Removed DPs: #19 #21 #23..25 Number of SCCs: 2, DPs: 7 SCC { #22 } only weak rules. Number of SCCs: 1, DPs: 6 SCC { #16..18 #20 #26 #27 } POLO(Sum)... POLO(max)... QLPOS... succeeded. neq s: {} p: 0 and s: {1,2} p: 1 eq s: {} p: 0 false s: [] p: 0 true s: [] p: 3 #eq s: {} p: 0 #not s: [] p: 0 #neq s: {} p: 0 or s: {1,2} p: 2 #or s: {1,2} p: 2 #and s: {} p: 1 not s: [] p: 0 USABLE RULES: { 10..19 } Removed DPs: #16..18 #20 #27 Number of SCCs: 1, DPs: 1 SCC { #26 } only weak rules. Number of SCCs: 0, DPs: 0