0.00/0.06 YES 0.00/0.06 Input TRS: 0.00/0.06 AC symbols: plus times 0.00/0.06 1: plus(x,0()) -> x 0.00/0.06 2: plus(x,i(x)) -> 0() 0.00/0.06 3: i(0()) -> 0() 0.00/0.06 4: i(i(x)) -> x 0.00/0.06 5: i(plus(x,y)) -> plus(i(x),i(y)) 0.00/0.06 6: times(x,1()) -> x 0.00/0.06 7: times(x,0()) -> 0() 0.00/0.06 8: times(x,i(y)) -> i(times(x,y)) 0.00/0.06 9: times(x,plus(y,z)) -> plus(times(x,y),times(x,z)) 0.00/0.06 Number of strict rules: 9 0.00/0.06 Direct POLO(bPol) ... failed. 0.00/0.06 Uncurrying ... failed. 0.00/0.06 Dependency Pairs: 0.00/0.06 #1: #times(x,plus(y,z)) -> #plus(times(x,y),times(x,z)) 0.00/0.06 #2: #times(x,plus(y,z)) -> #times(x,y) 0.00/0.06 #3: #times(x,plus(y,z)) -> #times(x,z) 0.00/0.06 #4: #times(x,times(y,z)) ->= #times(times(x,y),z) 0.00/0.06 #5: #times(x,times(y,z)) ->= #times(x,y) 0.00/0.06 #6: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.06 #7: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.06 #8: #i(plus(x,y)) -> #plus(i(x),i(y)) 0.00/0.06 #9: #i(plus(x,y)) -> #i(x) 0.00/0.06 #10: #i(plus(x,y)) -> #i(y) 0.00/0.06 #11: #times(x,i(y)) -> #i(times(x,y)) 0.00/0.06 #12: #times(x,i(y)) -> #times(x,y) 0.00/0.06 Number of SCCs: 3, DPs: 9 0.00/0.06 SCC { #9 #10 } 0.00/0.06 POLO(Sum)... succeeded. 0.00/0.06 1 w: 0 0.00/0.06 #plus w: 0 0.00/0.06 #times w: 0 0.00/0.06 0 w: 0 0.00/0.06 times w: 0 0.00/0.06 i w: 0 0.00/0.06 plus w: x1 + x2 + 1 0.00/0.06 #i w: x1 0.00/0.06 USABLE RULES: { } 0.00/0.06 Removed DPs: #9 #10 0.00/0.06 Number of SCCs: 2, DPs: 7 0.00/0.06 SCC { #6 #7 } 0.00/0.06 only weak rules. 0.00/0.06 Number of SCCs: 1, DPs: 5 0.00/0.06 SCC { #2..5 #12 } 0.00/0.06 POLO(Sum)... POLO(max)... QLPOS... succeeded. 0.00/0.06 1 s: [] p: 0 0.00/0.06 #plus s: {} p: 1 0.00/0.06 #times s: {1,2} p: 3 0.00/0.06 0 s: [] p: 0 0.00/0.06 times s: {1,2} p: 3 0.00/0.06 i s: [1] p: 2 0.00/0.06 plus s: {1,2} p: 1 0.00/0.06 #i s: [] p: 0 0.00/0.06 USABLE RULES: { 1..11 } 0.00/0.06 Removed DPs: #2 #3 #5 #12 0.00/0.06 Number of SCCs: 1, DPs: 1 0.00/0.06 SCC { #4 } 0.00/0.06 only weak rules. 0.00/0.06 Number of SCCs: 0, DPs: 0 0.00/0.06 Next Dependency Pairs: 0.00/0.06 #13: #plus(plus(x,i(x)),_1) -> #plus(0(),_1) 0.00/0.06 #14: #times(times(x,1()),_1) -> #times(x,_1) 0.00/0.06 #15: #times(times(x,plus(y,z)),_1) -> #times(plus(times(x,y),times(x,z)),_1) 0.00/0.06 #16: #times(x,times(y,z)) ->= #times(times(x,y),z) 0.00/0.06 #17: #times(x,times(y,z)) ->= #times(x,y) 0.00/0.06 #18: #times(times(x,0()),_1) -> #times(0(),_1) 0.00/0.06 #19: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.06 #20: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.06 #21: #plus(plus(x,0()),_1) -> #plus(x,_1) 0.00/0.06 #22: #times(times(x,i(y)),_1) -> #times(i(times(x,y)),_1) 0.00/0.06 Number of SCCs: 2, DPs: 10 0.00/0.06 SCC { #14..18 #22 } 0.00/0.06 POLO(Sum)... POLO(max)... QLPOS... succeeded. 0.00/0.06 1 s: [] p: 4 0.00/0.06 #plus s: {} p: 1 0.00/0.06 #times s: {1,2} p: 3 0.00/0.06 0 s: [] p: 0 0.00/0.06 times s: {1,2} p: 3 0.00/0.06 i s: [1] p: 2 0.00/0.06 plus s: {1,2} p: 1 0.00/0.06 #i s: [] p: 0 0.00/0.06 USABLE RULES: { 1..11 } 0.00/0.06 Removed DPs: #14 #15 #17 #18 #22 0.00/0.06 Number of SCCs: 2, DPs: 5 0.00/0.06 SCC { #16 } 0.00/0.06 only weak rules. 0.00/0.06 Number of SCCs: 1, DPs: 4 0.00/0.06 SCC { #13 #19..21 } 0.00/0.06 POLO(Sum)... succeeded. 0.00/0.06 1 w: 1 0.00/0.06 #plus w: x1 + x2 0.00/0.06 #times w: 0 0.00/0.06 0 w: 1 0.00/0.06 times w: x1 + x2 + 1 0.00/0.06 i w: x1 + 1 0.00/0.06 plus w: x1 + x2 + 1 0.00/0.06 #i w: 0 0.00/0.06 USABLE RULES: { 1..4 10 } 0.00/0.06 Removed DPs: #13 #20 #21 0.00/0.06 Number of SCCs: 1, DPs: 1 0.00/0.06 SCC { #19 } 0.00/0.06 only weak rules. 0.00/0.06 Number of SCCs: 0, DPs: 0 0.00/0.06 EOF