YES Input TRS: 1: 2(7(x1)) -> 1(8(x1)) 2: 2(8(1(x1))) -> 8(x1) 3: 2(8(x1)) -> 4(x1) 4: 5(9(x1)) -> 0(x1) 5: 4(x1) -> 5(2(3(x1))) 6: 5(3(x1)) -> 6(0(x1)) 7: 2(8(x1)) -> 7(x1) 8: 4(7(x1)) -> 1(3(x1)) 9: 5(2(6(x1))) -> 6(2(4(x1))) 10: 9(7(x1)) -> 7(5(x1)) 11: 7(2(x1)) -> 4(x1) 12: 7(0(x1)) -> 9(3(x1)) 13: 6(9(x1)) -> 9(x1) 14: 9(5(9(x1))) -> 5(7(x1)) 15: 4(x1) -> 9(6(6(x1))) 16: 9(x1) -> 6(7(x1)) 17: 6(2(x1)) -> 7(7(x1)) 18: 2(4(x1)) -> 0(7(x1)) 19: 6(6(x1)) -> 3(x1) 20: 0(3(x1)) -> 5(3(x1)) Number of strict rules: 20 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #5(3(x1)) -> #6(0(x1)) #2: #5(3(x1)) -> #0(x1) #3: #5(2(6(x1))) -> #6(2(4(x1))) #4: #5(2(6(x1))) -> #2(4(x1)) #5: #5(2(6(x1))) -> #4(x1) #6: #7(2(x1)) -> #4(x1) #7: #7(0(x1)) -> #9(3(x1)) #8: #9(5(9(x1))) -> #5(7(x1)) #9: #9(5(9(x1))) -> #7(x1) #10: #0(3(x1)) -> #5(3(x1)) #11: #2(8(x1)) -> #7(x1) #12: #9(7(x1)) -> #7(5(x1)) #13: #9(7(x1)) -> #5(x1) #14: #4(x1) -> #5(2(3(x1))) #15: #4(x1) -> #2(3(x1)) #16: #6(2(x1)) -> #7(7(x1)) #17: #6(2(x1)) -> #7(x1) #18: #9(x1) -> #6(7(x1)) #19: #9(x1) -> #7(x1) #20: #2(8(x1)) -> #4(x1) #21: #4(x1) -> #9(6(6(x1))) #22: #4(x1) -> #6(6(x1)) #23: #4(x1) -> #6(x1) #24: #5(9(x1)) -> #0(x1) #25: #2(4(x1)) -> #0(7(x1)) #26: #2(4(x1)) -> #7(x1) Number of SCCs: 2, DPs: 16 SCC { #2 #10 } POLO(Sum)... succeeded. 7 w: 0 #0 w: x1 + 1 1 w: 0 4 w: 0 #7 w: 0 5 w: 0 3 w: x1 + 2 #6 w: 0 #2 w: 0 9 w: 0 8 w: 0 #4 w: 0 #9 w: 0 0 w: 0 #5 w: x1 2 w: 0 6 w: 0 USABLE RULES: { } Removed DPs: #2 #10 Number of SCCs: 1, DPs: 14 SCC { #3..7 #9 #12 #13 #16 #17 #19 #21 #23 #26 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. 7 w: [0,0;0,1] * x1 + [27879;0] #0 w: [0;0] 1 w: [0,0;0,1] * x1 4 w: [0,0;0,1] * x1 + [27879;0] #7 w: [0,1;0,0] * x1 + [27878;27879] 5 w: [0,0;0,1] * x1 + [27879;0] 3 w: [0;0] #6 w: [0,1;0,0] * x1 + [27878;27879] #2 w: [1,1;1,0] * x1 9 w: [0,0;0,1] * x1 + [27879;0] 8 w: [0,0;0,1] * x1 + [1;1] #4 w: [0,1;0,0] * x1 + [27878;27879] #9 w: [0,1;0,0] * x1 + [27878;27879] 0 w: [27879;0] #5 w: [0,1;0,0] * x1 + [27878;27879] 2 w: [0,1;1,1] * x1 + [27879;0] 6 w: [0,0;0,1] * x1 + [27879;0] USABLE RULES: { 1 4..6 8..20 } Removed DPs: #4 #5 #26 Number of SCCs: 1, DPs: 11 SCC { #3 #6 #7 #9 #12 #13 #16 #17 #19 #21 #23 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. 7 w: [1,1;0,0] * x1 #0 w: [0;0] 1 w: [0,0;0,1] * x1 4 w: [1,0;0,0] * x1 + [1;0] #7 w: [1,1;0,0] * x1 + [27877;27879] 5 w: [1,0;0,0] * x1 + [1;0] 3 w: [0;0] #6 w: [1,0;0,0] * x1 + [27879;27879] #2 w: [0;0] 9 w: [1,1;0,0] * x1 + [1;0] 8 w: [0,0;0,1] * x1 + [1;1] #4 w: [1,0;0,0] * x1 + [27879;27879] #9 w: [1,1;0,0] * x1 + [27878;27879] 0 w: [1;0] #5 w: [0,1;0,0] * x1 + [178;27879] 2 w: [1,1;1,1] * x1 + [0;27703] 6 w: [1,0;0,0] * x1 USABLE RULES: { 1 4..6 8..20 } Removed DPs: #3 #6 #9 #13 #16 #17 #19 #21 Number of SCCs: 0, DPs: 0