YES

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

Proof:
 WPO Processor:
  algebra: Sum
  weight function:
   w0 = 0
   w(a46) = w(a36) = w(a26) = w(a24) = w(a16) = 2
   w(a56) = 1
   w(a45) = w(a35) = w(a34) = w(a25) = w(a23) = w(a15) = w(a14) = w(a13) = 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:
   a15 ~ a13 > a25 ~ a14 > a23 ~ a12 > a35 > a34 > a56 ~ a46 ~ a45 ~ a36 ~ a26 ~ a24 ~ a16
  problem:
   
  Qed