0.00/0.08 YES 0.00/0.08 Input TRS: 0.00/0.08 AC symbols: plus times 0.00/0.08 1: p(s(x)) -> x 0.00/0.08 2: plus(x,0()) -> x 0.00/0.08 3: plus(x,s(y)) -> s(plus(x,y)) 0.00/0.08 4: times(x,0()) -> 0() 0.00/0.08 5: times(x,s(y)) -> plus(x,times(x,y)) 0.00/0.08 6: minus(x,0()) -> x 0.00/0.08 7: minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) 0.00/0.08 8: div(0(),s(y)) -> 0() 0.00/0.08 9: div(s(x),s(y)) -> s(div(minus(x,y),s(y))) 0.00/0.08 Number of strict rules: 9 0.00/0.08 Direct POLO(bPol) ... failed. 0.00/0.08 Uncurrying p 0.00/0.08 AC symbols: plus times 0.00/0.08 1: p^1_s(x) -> x 0.00/0.08 2: plus(x,0()) -> x 0.00/0.08 3: plus(x,s(y)) -> s(plus(x,y)) 0.00/0.08 4: times(x,0()) -> 0() 0.00/0.08 5: times(x,s(y)) -> plus(x,times(x,y)) 0.00/0.08 6: minus(x,0()) -> x 0.00/0.08 7: minus(s(x),s(y)) -> minus(p^1_s(x),p^1_s(y)) 0.00/0.08 8: div(0(),s(y)) -> 0() 0.00/0.08 9: div(s(x),s(y)) -> s(div(minus(x,y),s(y))) 0.00/0.08 10: p(s(_1)) ->= p^1_s(_1) 0.00/0.08 Number of strict rules: 9 0.00/0.08 Direct POLO(bPol) ... failed. 0.00/0.08 Dependency Pairs: 0.00/0.08 #1: #div(s(x),s(y)) -> #div(minus(x,y),s(y)) 0.00/0.08 #2: #div(s(x),s(y)) -> #minus(x,y) 0.00/0.08 #3: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.08 #4: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.08 #5: #times(x,times(y,z)) ->= #times(times(x,y),z) 0.00/0.08 #6: #times(x,times(y,z)) ->= #times(x,y) 0.00/0.08 #7: #minus(s(x),s(y)) -> #minus(p^1_s(x),p^1_s(y)) 0.00/0.08 #8: #minus(s(x),s(y)) -> #p^1_s(x) 0.00/0.08 #9: #minus(s(x),s(y)) -> #p^1_s(y) 0.00/0.08 #10: #p(s(_1)) ->? #p^1_s(_1) 0.00/0.08 #11: #times(x,s(y)) -> #plus(x,times(x,y)) 0.00/0.08 #12: #times(x,s(y)) -> #times(x,y) 0.00/0.08 #13: #plus(x,s(y)) -> #plus(x,y) 0.00/0.08 Number of SCCs: 4, DPs: 8 0.00/0.08 SCC { #7 } 0.00/0.08 POLO(Sum)... succeeded. 0.00/0.08 #div w: 0 0.00/0.08 s w: x1 + 2 0.00/0.08 #p^1_s w: 0 0.00/0.08 minus w: 0 0.00/0.08 #plus w: 0 0.00/0.08 div w: 0 0.00/0.08 p^1_s w: x1 + 1 0.00/0.08 #p w: 0 0.00/0.08 p w: 0 0.00/0.08 #times w: 0 0.00/0.08 0 w: 0 0.00/0.08 times w: 0 0.00/0.08 #minus w: x1 + x2 0.00/0.08 plus w: 0 0.00/0.08 USABLE RULES: { 1 } 0.00/0.08 Removed DPs: #7 0.00/0.08 Number of SCCs: 3, DPs: 7 0.00/0.08 SCC { #1 } 0.00/0.08 POLO(Sum)... succeeded. 0.00/0.08 #div w: x1 0.00/0.08 s w: x1 + 2 0.00/0.08 #p^1_s w: 0 0.00/0.08 minus w: x1 + 1 0.00/0.08 #plus w: 0 0.00/0.08 div w: 0 0.00/0.08 p^1_s w: x1 + 1 0.00/0.08 #p w: 0 0.00/0.08 p w: 0 0.00/0.08 #times w: 0 0.00/0.08 0 w: 1 0.00/0.08 times w: 0 0.00/0.08 #minus w: x1 + x2 0.00/0.08 plus w: 0 0.00/0.08 USABLE RULES: { 1 6 7 } 0.00/0.08 Removed DPs: #1 0.00/0.08 Number of SCCs: 2, DPs: 6 0.00/0.08 SCC { #5 #6 #12 } 0.00/0.08 POLO(Sum)... POLO(max)... QLPOS... succeeded. 0.00/0.08 #div s: [] p: 0 0.00/0.08 s s: [1] p: 0 0.00/0.08 #p^1_s s: [] p: 0 0.00/0.08 minus s: [] p: 0 0.00/0.08 #plus s: {} p: 1 0.00/0.08 div s: [] p: 0 0.00/0.08 p^1_s s: [] p: 0 0.00/0.08 #p s: [] p: 0 0.00/0.08 p s: [] p: 0 0.00/0.08 #times s: {1,2} p: 2 0.00/0.08 0 s: [] p: 0 0.00/0.08 times s: {1,2} p: 2 0.00/0.08 #minus s: [] p: 0 0.00/0.08 plus s: {1,2} p: 1 0.00/0.08 USABLE RULES: { 2..5 11 12 } 0.00/0.08 Removed DPs: #6 #12 0.00/0.08 Number of SCCs: 2, DPs: 4 0.00/0.08 SCC { #5 } 0.00/0.08 only weak rules. 0.00/0.08 Number of SCCs: 1, DPs: 3 0.00/0.08 SCC { #3 #4 #13 } 0.00/0.08 POLO(Sum)... succeeded. 0.00/0.08 #div w: x1 0.00/0.08 s w: x1 + 2 0.00/0.08 #p^1_s w: 0 0.00/0.08 minus w: x1 + 1 0.00/0.08 #plus w: x1 + x2 0.00/0.08 div w: 0 0.00/0.08 p^1_s w: x1 + 1 0.00/0.08 #p w: 0 0.00/0.08 p w: 0 0.00/0.08 #times w: 0 0.00/0.08 0 w: 2 0.00/0.08 times w: 1 0.00/0.08 #minus w: x1 + x2 0.00/0.08 plus w: x1 + x2 + 1 0.00/0.08 USABLE RULES: { 1..3 6 7 11 } 0.00/0.08 Removed DPs: #4 #13 0.00/0.08 Number of SCCs: 1, DPs: 1 0.00/0.08 SCC { #3 } 0.00/0.08 only weak rules. 0.00/0.08 Number of SCCs: 0, DPs: 0 0.00/0.08 Next Dependency Pairs: 0.00/0.08 #14: #plus(plus(x,0()),_1) -> #plus(x,_1) 0.00/0.08 #15: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.08 #16: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.08 #17: #times(x,times(y,z)) ->= #times(times(x,y),z) 0.00/0.08 #18: #times(x,times(y,z)) ->= #times(x,y) 0.00/0.08 #19: #times(times(x,s(y)),_1) -> #times(plus(x,times(x,y)),_1) 0.00/0.08 #20: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1) 0.00/0.08 #21: #times(times(x,0()),_1) -> #times(0(),_1) 0.00/0.08 Number of SCCs: 2, DPs: 8 0.00/0.08 SCC { #17..19 #21 } 0.00/0.08 POLO(Sum)... POLO(max)... QLPOS... succeeded. 0.00/0.08 #div s: [] p: 0 0.00/0.08 s s: [1] p: 0 0.00/0.08 #p^1_s s: [] p: 0 0.00/0.08 minus s: [] p: 0 0.00/0.08 #plus s: {} p: 1 0.00/0.08 div s: [] p: 0 0.00/0.08 p^1_s s: [] p: 0 0.00/0.08 #p s: [] p: 0 0.00/0.08 p s: [] p: 0 0.00/0.08 #times s: {1,2} p: 2 0.00/0.08 0 s: [] p: 0 0.00/0.08 times s: {1,2} p: 2 0.00/0.08 #minus s: [] p: 0 0.00/0.08 plus s: {1,2} p: 1 0.00/0.08 USABLE RULES: { 2..5 11 12 } 0.00/0.08 Removed DPs: #18 #19 #21 0.00/0.08 Number of SCCs: 2, DPs: 5 0.00/0.08 SCC { #17 } 0.00/0.08 only weak rules. 0.00/0.08 Number of SCCs: 1, DPs: 4 0.00/0.08 SCC { #14..16 #20 } 0.00/0.08 POLO(Sum)... succeeded. 0.00/0.08 #div w: x1 0.00/0.08 s w: x1 + 1 0.00/0.08 #p^1_s w: 0 0.00/0.08 minus w: x1 + 1 0.00/0.08 #plus w: x1 + x2 0.00/0.08 div w: 0 0.00/0.08 p^1_s w: x1 + 1 0.00/0.08 #p w: 0 0.00/0.08 p w: 0 0.00/0.08 #times w: 0 0.00/0.08 0 w: 1 0.00/0.08 times w: x1 + x2 + 1 0.00/0.08 #minus w: x1 + x2 0.00/0.08 plus w: x1 + x2 + 2 0.00/0.08 USABLE RULES: { 1..3 6 7 11 } 0.00/0.08 Removed DPs: #14 #16 0.00/0.08 Number of SCCs: 1, DPs: 2 0.00/0.08 SCC { #15 #20 } 0.00/0.08 POLO(Sum)... succeeded. 0.00/0.08 #div w: 0 0.00/0.08 s w: 1 0.00/0.08 #p^1_s w: 0 0.00/0.08 minus w: x1 + 1 0.00/0.08 #plus w: x1 + x2 0.00/0.08 div w: 0 0.00/0.08 p^1_s w: x1 + 1 0.00/0.08 #p w: 0 0.00/0.08 p w: 0 0.00/0.08 #times w: 0 0.00/0.08 0 w: 1 0.00/0.08 times w: x1 + x2 + 1 0.00/0.08 #minus w: x1 + x2 0.00/0.08 plus w: x1 + x2 + 2 0.00/0.08 USABLE RULES: { 1..3 6 11 } 0.00/0.08 Removed DPs: #20 0.00/0.08 Number of SCCs: 1, DPs: 1 0.00/0.08 SCC { #15 } 0.00/0.08 only weak rules. 0.00/0.08 Number of SCCs: 0, DPs: 0 0.00/0.08 EOF