YES Input TRS: 1: 0(0(1(2(1(x1))))) -> 1(0(1(1(0(x1))))) 2: 0(3(1(2(4(x1))))) -> 0(5(1(4(x1)))) 3: 4(3(0(1(1(x1))))) -> 5(4(5(2(x1)))) 4: 4(3(4(2(2(x1))))) -> 0(5(0(2(x1)))) 5: 2(1(1(4(0(2(x1)))))) -> 1(1(5(3(5(x1))))) 6: 2(2(4(1(3(4(2(x1))))))) -> 2(3(2(4(3(5(x1)))))) 7: 4(0(5(4(2(4(0(x1))))))) -> 0(1(2(2(2(2(0(x1))))))) 8: 4(2(4(2(5(1(0(1(5(x1))))))))) -> 5(0(3(1(0(2(2(5(x1)))))))) 9: 5(2(4(5(0(3(0(2(3(x1))))))))) -> 5(3(2(1(0(1(3(4(0(x1))))))))) 10: 1(4(1(3(2(3(3(1(2(1(x1)))))))))) -> 1(5(3(2(4(5(1(3(4(x1))))))))) 11: 4(0(4(2(3(4(5(1(1(5(1(x1))))))))))) -> 5(4(3(2(2(3(2(1(2(4(0(x1))))))))))) 12: 4(5(2(2(5(4(4(3(4(5(4(x1))))))))))) -> 5(2(3(2(5(0(0(0(5(4(x1)))))))))) 13: 4(3(4(4(0(3(0(3(2(3(2(1(x1)))))))))))) -> 5(5(5(5(5(0(2(2(4(4(2(0(x1)))))))))))) 14: 5(3(4(4(3(3(5(2(5(2(1(1(4(2(x1)))))))))))))) -> 5(4(0(5(2(5(5(3(1(0(3(3(5(x1))))))))))))) 15: 0(5(1(0(3(3(2(5(5(4(0(5(5(5(2(x1))))))))))))))) -> 1(0(1(3(4(5(3(3(3(2(2(3(3(5(2(x1))))))))))))))) 16: 4(5(3(2(1(1(5(2(2(3(4(3(2(3(1(x1))))))))))))))) -> 0(1(3(5(0(1(3(4(0(3(5(4(3(1(x1)))))))))))))) 17: 5(0(1(0(1(1(5(1(1(5(5(2(1(1(0(x1))))))))))))))) -> 5(1(5(1(1(1(3(0(3(3(3(3(1(0(x1)))))))))))))) 18: 5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> 5(4(1(4(0(2(1(2(2(5(3(5(3(4(4(x1))))))))))))))) 19: 2(4(1(0(2(3(2(3(5(3(1(2(3(1(1(4(x1)))))))))))))))) -> 2(2(2(1(4(5(0(1(0(3(1(3(5(1(2(x1))))))))))))))) 20: 0(1(1(3(2(2(0(0(0(5(0(2(4(3(3(0(1(x1))))))))))))))))) -> 5(4(1(1(0(5(2(0(2(3(3(3(0(5(0(1(x1)))))))))))))))) 21: 2(1(1(5(3(1(3(4(3(5(3(3(2(4(3(1(4(x1))))))))))))))))) -> 1(0(1(0(0(2(1(3(2(2(0(3(0(5(2(4(x1)))))))))))))))) 22: 2(4(3(5(0(2(5(5(1(5(0(4(4(4(1(4(3(x1))))))))))))))))) -> 2(0(5(2(2(0(5(4(1(3(2(4(1(4(1(1(0(x1))))))))))))))))) 23: 0(4(5(4(5(0(2(3(1(2(4(5(3(5(0(4(3(3(2(x1))))))))))))))))))) -> 1(0(2(4(5(5(2(2(4(2(1(1(4(0(1(2(3(0(2(5(x1)))))))))))))))))))) 24: 4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> 0(5(5(2(0(5(2(4(2(5(2(5(2(0(1(5(2(3(3(0(x1)))))))))))))))))))) 25: 3(1(2(4(3(4(3(2(0(3(2(3(4(3(4(5(4(3(4(1(1(x1))))))))))))))))))))) -> 3(4(0(0(2(4(5(0(0(4(3(5(4(3(0(3(2(2(1(1(x1)))))))))))))))))))) Number of strict rules: 25 Direct POLO(bPol) ... removes: 4 8 3 16 21 19 17 22 5 10 7 20 25 14 12 23 9 13 6 2 1 w: x1 + 7 4 w: x1 + 8 5 w: x1 + 8 3 w: x1 + 9 0 w: x1 + 9 2 w: x1 + 7 Number of strict rules: 5 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #4(0(4(2(3(4(5(1(1(5(1(x1))))))))))) -> #5(4(3(2(2(3(2(1(2(4(0(x1))))))))))) #2: #4(0(4(2(3(4(5(1(1(5(1(x1))))))))))) -> #4(3(2(2(3(2(1(2(4(0(x1)))))))))) #3: #4(0(4(2(3(4(5(1(1(5(1(x1))))))))))) -> #4(0(x1)) #4: #4(0(4(2(3(4(5(1(1(5(1(x1))))))))))) -> #0(x1) #5: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #0(5(5(2(0(5(2(4(2(5(2(5(2(0(1(5(2(3(3(0(x1)))))))))))))))))))) #6: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #5(5(2(0(5(2(4(2(5(2(5(2(0(1(5(2(3(3(0(x1))))))))))))))))))) #7: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #5(2(0(5(2(4(2(5(2(5(2(0(1(5(2(3(3(0(x1)))))))))))))))))) #8: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #0(5(2(4(2(5(2(5(2(0(1(5(2(3(3(0(x1)))))))))))))))) #9: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #5(2(4(2(5(2(5(2(0(1(5(2(3(3(0(x1))))))))))))))) #10: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #4(2(5(2(5(2(0(1(5(2(3(3(0(x1))))))))))))) #11: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #5(2(5(2(0(1(5(2(3(3(0(x1))))))))))) #12: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #5(2(0(1(5(2(3(3(0(x1))))))))) #13: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #0(1(5(2(3(3(0(x1))))))) #14: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #5(2(3(3(0(x1))))) #15: #4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> #0(x1) #16: #0(0(1(2(1(x1))))) -> #0(1(1(0(x1)))) #17: #0(0(1(2(1(x1))))) -> #0(x1) #18: #0(5(1(0(3(3(2(5(5(4(0(5(5(5(2(x1))))))))))))))) -> #0(1(3(4(5(3(3(3(2(2(3(3(5(2(x1)))))))))))))) #19: #0(5(1(0(3(3(2(5(5(4(0(5(5(5(2(x1))))))))))))))) -> #4(5(3(3(3(2(2(3(3(5(2(x1))))))))))) #20: #0(5(1(0(3(3(2(5(5(4(0(5(5(5(2(x1))))))))))))))) -> #5(3(3(3(2(2(3(3(5(2(x1)))))))))) #21: #5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> #5(4(1(4(0(2(1(2(2(5(3(5(3(4(4(x1))))))))))))))) #22: #5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> #4(1(4(0(2(1(2(2(5(3(5(3(4(4(x1)))))))))))))) #23: #5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> #4(0(2(1(2(2(5(3(5(3(4(4(x1)))))))))))) #24: #5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> #0(2(1(2(2(5(3(5(3(4(4(x1))))))))))) #25: #5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> #5(3(5(3(4(4(x1)))))) #26: #5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> #5(3(4(4(x1)))) #27: #5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> #4(4(x1)) #28: #5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> #4(x1) Number of SCCs: 2, DPs: 2 SCC { #17 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 + 1 4 w: 0 5 w: 0 3 w: 0 #4 w: 0 0 w: x1 #5 w: 0 2 w: x1 + 23675 USABLE RULES: { } Removed DPs: #17 Number of SCCs: 1, DPs: 1 SCC { #3 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 + 1 4 w: x1 + 41935 5 w: x1 + 17887 3 w: x1 + 59821 #4 w: x1 0 w: x1 + 83869 #5 w: 0 2 w: x1 + 1 USABLE RULES: { 1 11 15 18 24 } Removed DPs: #3 Number of SCCs: 0, DPs: 0