YES

Problem:
 a12(a12(a12(a12(x1)))) -> x1
 a13(a13(a13(a13(x1)))) -> x1
 a14(a14(a14(a14(x1)))) -> x1
 a15(a15(a15(a15(x1)))) -> x1
 a16(a16(a16(a16(x1)))) -> x1
 a23(a23(a23(a23(x1)))) -> x1
 a24(a24(a24(a24(x1)))) -> x1
 a25(a25(a25(a25(x1)))) -> x1
 a26(a26(a26(a26(x1)))) -> x1
 a34(a34(a34(a34(x1)))) -> x1
 a35(a35(a35(a35(x1)))) -> x1
 a36(a36(a36(a36(x1)))) -> x1
 a45(a45(a45(a45(x1)))) -> x1
 a46(a46(a46(a46(x1)))) -> x1
 a56(a56(a56(a56(x1)))) -> x1
 a13(a13(x1)) -> a12(a12(a23(a23(a12(a12(x1))))))
 a14(a14(x1)) -> a12(a12(a23(a23(a34(a34(a23(a23(a12(a12(x1))))))))))
 a15(a15(x1)) -> a12(a12(a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(a12(a12(x1))))))))))))))
 a16(a16(x1)) ->
 a12(a12(a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(a12(a12(x1))))))))))))))))))
 a24(a24(x1)) -> a23(a23(a34(a34(a23(a23(x1))))))
 a25(a25(x1)) -> a23(a23(a34(a34(a45(a45(a34(a34(a23(a23(x1))))))))))
 a26(a26(x1)) -> a23(a23(a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(a23(a23(x1))))))))))))))
 a35(a35(x1)) -> a34(a34(a45(a45(a34(a34(x1))))))
 a36(a36(x1)) -> a34(a34(a45(a45(a56(a56(a45(a45(a34(a34(x1))))))))))
 a46(a46(x1)) -> a45(a45(a56(a56(a45(a45(x1))))))
 a12(a12(a23(a23(a12(a12(a23(a23(a12(a12(a23(a23(x1)))))))))))) -> x1
 a23(a23(a34(a34(a23(a23(a34(a34(a23(a23(a34(a34(x1)))))))))))) -> x1
 a34(a34(a45(a45(a34(a34(a45(a45(a34(a34(a45(a45(x1)))))))))))) -> x1
 a45(a45(a56(a56(a45(a45(a56(a56(a45(a45(a56(a56(x1)))))))))))) -> x1
 a12(a12(a34(a34(x1)))) -> a34(a34(a12(a12(x1))))
 a12(a12(a45(a45(x1)))) -> a45(a45(a12(a12(x1))))
 a12(a12(a56(a56(x1)))) -> a56(a56(a12(a12(x1))))
 a23(a23(a45(a45(x1)))) -> a45(a45(a23(a23(x1))))
 a23(a23(a56(a56(x1)))) -> a56(a56(a23(a23(x1))))
 a34(a34(a56(a56(x1)))) -> a56(a56(a34(a34(x1))))

Proof:
 WPO Processor:
  algebra: Sum
  weight function:
   w0 = 0
   w(a24) = w(a16) = w(a13) = 1
   w(a56) = w(a46) = w(a45) = w(a36) = w(a35) = w(a34) = w(a26) = w(a25) = w(
   a23) = w(a15) = w(a14) = w(a12) = 0
  status function:
   st(a56) = st(a46) = st(a45) = st(a36) = st(a35) = st(a34) = st(a26) = st(
   a25) = st(a24) = st(a23) = st(a16) = st(a15) = st(a14) = st(a13) = st(
   a12) = [0]
  precedence:
   a26 > a25 ~ a15 ~ a14 > a23 > a36 ~ a35 ~ a12 > a46 ~ a34 > a56 ~ a45 ~ a24 ~ a16 ~ a13
  problem:
   
  Qed