0.00/0.05 YES 0.00/0.05 Input TRS: 0.00/0.05 AC symbols: plus times 0.00/0.05 1: times(x,0()) -> 0() 0.00/0.05 2: times(x,s(y)) -> plus(times(x,y),x) 0.00/0.05 3: plus(x,0()) -> x 0.00/0.05 4: plus(0(),x) -> x 0.00/0.05 5: plus(x,s(y)) -> s(plus(x,y)) 0.00/0.05 6: plus(s(x),y) -> s(plus(x,y)) 0.00/0.05 Number of strict rules: 6 0.00/0.05 Direct POLO(bPol) ... failed. 0.00/0.05 Uncurrying ... failed. 0.00/0.05 Dependency Pairs: 0.00/0.05 #1: #times(x,s(y)) -> #plus(times(x,y),x) 0.00/0.05 #2: #times(x,s(y)) -> #times(x,y) 0.00/0.05 #3: #plus(s(x),y) -> #plus(x,y) 0.00/0.05 #4: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.05 #5: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.05 #6: #plus(x,s(y)) -> #plus(x,y) 0.00/0.05 #7: #times(x,times(y,z)) ->= #times(times(x,y),z) 0.00/0.05 #8: #times(x,times(y,z)) ->= #times(x,y) 0.00/0.05 Number of SCCs: 2, DPs: 7 0.00/0.05 SCC { #2 #7 #8 } 0.00/0.05 POLO(Sum)... POLO(max)... QLPOS... succeeded. 0.00/0.05 s s: [1] p: 0 0.00/0.05 #plus s: {} p: 1 0.00/0.05 #times s: {1,2} p: 2 0.00/0.05 0 s: [] p: 0 0.00/0.05 times s: {1,2} p: 2 0.00/0.05 plus s: {1,2} p: 1 0.00/0.05 USABLE RULES: { 1..8 } 0.00/0.05 Removed DPs: #2 #8 0.00/0.05 Number of SCCs: 2, DPs: 5 0.00/0.05 SCC { #7 } 0.00/0.05 only weak rules. 0.00/0.05 Number of SCCs: 1, DPs: 4 0.00/0.05 SCC { #3..6 } 0.00/0.05 POLO(Sum)... succeeded. 0.00/0.05 s w: x1 + 1 0.00/0.05 #plus w: x1 + x2 0.00/0.05 #times w: 0 0.00/0.05 0 w: 1 0.00/0.05 times w: x1 + x2 + 1 0.00/0.05 plus w: x1 + x2 + 2 0.00/0.05 USABLE RULES: { 3..7 } 0.00/0.05 Removed DPs: #3 #5 #6 0.00/0.05 Number of SCCs: 1, DPs: 1 0.00/0.05 SCC { #4 } 0.00/0.05 only weak rules. 0.00/0.05 Number of SCCs: 0, DPs: 0 0.00/0.05 Next Dependency Pairs: 0.00/0.05 #9: #times(times(x,s(y)),_1) -> #times(plus(times(x,y),x),_1) 0.00/0.05 #10: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1) 0.00/0.05 #11: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.05 #12: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.05 #13: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1) 0.00/0.05 #14: #plus(plus(x,0()),_1) -> #plus(x,_1) 0.00/0.05 #15: #times(times(x,0()),_1) -> #times(0(),_1) 0.00/0.05 #16: #times(x,times(y,z)) ->= #times(times(x,y),z) 0.00/0.05 #17: #times(x,times(y,z)) ->= #times(x,y) 0.00/0.05 #18: #plus(plus(0(),x),_1) -> #plus(x,_1) 0.00/0.05 Number of SCCs: 2, DPs: 10 0.00/0.05 SCC { #9 #15..17 } 0.00/0.05 POLO(Sum)... POLO(max)... QLPOS... succeeded. 0.00/0.05 s s: [1] p: 0 0.00/0.05 #plus s: {} p: 1 0.00/0.05 #times s: {1,2} p: 2 0.00/0.05 0 s: [] p: 0 0.00/0.05 times s: {1,2} p: 2 0.00/0.05 plus s: {1,2} p: 1 0.00/0.05 USABLE RULES: { 1..8 } 0.00/0.05 Removed DPs: #9 #15 #17 0.00/0.05 Number of SCCs: 2, DPs: 7 0.00/0.05 SCC { #16 } 0.00/0.05 only weak rules. 0.00/0.05 Number of SCCs: 1, DPs: 6 0.00/0.05 SCC { #10..14 #18 } 0.00/0.05 POLO(Sum)... succeeded. 0.00/0.05 s w: 1 0.00/0.05 #plus w: x1 + x2 0.00/0.05 #times w: 0 0.00/0.05 0 w: 2 0.00/0.05 times w: 1 0.00/0.05 plus w: x1 + x2 + 1 0.00/0.05 USABLE RULES: { 3..7 } 0.00/0.05 Removed DPs: #10 #12..14 #18 0.00/0.05 Number of SCCs: 1, DPs: 1 0.00/0.05 SCC { #11 } 0.00/0.05 only weak rules. 0.00/0.05 Number of SCCs: 0, DPs: 0 0.00/0.05 EOF