0.00/0.03 YES 0.00/0.03 Input TRS: 0.00/0.03 AC symbols: ac1 ac2 0.00/0.03 1: ac1(a(),ac2(b(),c())) -> ac1(b(),f(ac2(a(),c()))) 0.00/0.03 2: ac2(a(),ac1(b(),c())) -> ac2(b(),f(ac1(a(),c()))) 0.00/0.03 Number of strict rules: 2 0.00/0.03 Direct POLO(bPol) ... failed. 0.00/0.03 Uncurrying ... failed. 0.00/0.03 Dependency Pairs: 0.00/0.03 #1: #ac2(a(),ac1(b(),c())) -> #ac2(b(),f(ac1(a(),c()))) 0.00/0.03 #2: #ac2(a(),ac1(b(),c())) -> #ac1(a(),c()) 0.00/0.03 #3: #ac1(x,ac1(y,z)) ->= #ac1(ac1(x,y),z) 0.00/0.03 #4: #ac1(x,ac1(y,z)) ->= #ac1(x,y) 0.00/0.03 #5: #ac1(a(),ac2(b(),c())) -> #ac1(b(),f(ac2(a(),c()))) 0.00/0.03 #6: #ac1(a(),ac2(b(),c())) -> #ac2(a(),c()) 0.00/0.03 #7: #ac2(x,ac2(y,z)) ->= #ac2(ac2(x,y),z) 0.00/0.03 #8: #ac2(x,ac2(y,z)) ->= #ac2(x,y) 0.00/0.03 Number of SCCs: 1, DPs: 8 0.00/0.03 SCC { #1..8 } 0.00/0.03 POLO(Sum)... succeeded. 0.00/0.03 a w: 1 0.00/0.03 #ac1 w: x1 + x2 0.00/0.03 b w: 1 0.00/0.03 c w: 0 0.00/0.03 f w: 1 0.00/0.03 ac1 w: x1 + x2 + 1 0.00/0.03 ac2 w: x1 + x2 + 1 0.00/0.03 #ac2 w: x1 + x2 0.00/0.03 USABLE RULES: { 1..4 } 0.00/0.03 Removed DPs: #1 #2 #4..6 #8 0.00/0.03 Number of SCCs: 2, DPs: 2 0.00/0.03 SCC { #7 } 0.00/0.03 only weak rules. 0.00/0.03 Number of SCCs: 1, DPs: 1 0.00/0.03 SCC { #3 } 0.00/0.03 only weak rules. 0.00/0.03 Number of SCCs: 0, DPs: 0 0.00/0.03 Next Dependency Pairs: 0.00/0.03 #9: #ac2(ac2(a(),ac1(b(),c())),_1) -> #ac2(ac2(b(),f(ac1(a(),c()))),_1) 0.00/0.03 #10: #ac1(x,ac1(y,z)) ->= #ac1(ac1(x,y),z) 0.00/0.03 #11: #ac1(x,ac1(y,z)) ->= #ac1(x,y) 0.00/0.03 #12: #ac1(ac1(a(),ac2(b(),c())),_1) -> #ac1(ac1(b(),f(ac2(a(),c()))),_1) 0.00/0.03 #13: #ac2(x,ac2(y,z)) ->= #ac2(ac2(x,y),z) 0.00/0.03 #14: #ac2(x,ac2(y,z)) ->= #ac2(x,y) 0.00/0.03 Number of SCCs: 2, DPs: 6 0.00/0.03 SCC { #9 #13 #14 } 0.00/0.03 POLO(Sum)... succeeded. 0.00/0.03 a w: 1 0.00/0.03 #ac1 w: x1 + x2 0.00/0.03 b w: 1 0.00/0.03 c w: 0 0.00/0.03 f w: 1 0.00/0.03 ac1 w: x1 + x2 + 1 0.00/0.03 ac2 w: x1 + x2 + 1 0.00/0.03 #ac2 w: x1 + x2 0.00/0.03 USABLE RULES: { 1..4 } 0.00/0.03 Removed DPs: #9 #14 0.00/0.03 Number of SCCs: 2, DPs: 4 0.00/0.03 SCC { #13 } 0.00/0.03 only weak rules. 0.00/0.03 Number of SCCs: 1, DPs: 3 0.00/0.03 SCC { #10..12 } 0.00/0.03 POLO(Sum)... succeeded. 0.00/0.03 a w: 1 0.00/0.03 #ac1 w: x1 + x2 0.00/0.03 b w: 1 0.00/0.03 c w: 0 0.00/0.03 f w: 1 0.00/0.03 ac1 w: x1 + x2 + 1 0.00/0.03 ac2 w: x1 + x2 + 1 0.00/0.03 #ac2 w: x1 + x2 0.00/0.03 USABLE RULES: { 1..4 } 0.00/0.03 Removed DPs: #11 #12 0.00/0.03 Number of SCCs: 1, DPs: 1 0.00/0.03 SCC { #10 } 0.00/0.03 only weak rules. 0.00/0.03 Number of SCCs: 0, DPs: 0 0.00/0.03 EOF