YES

Problem:
 b(c(x)) -> a(a(x))
 c(b(x)) -> a(c(x))
 a(b(x)) -> a(a(x))
 b(b(x)) -> a(b(x))
 b(c(x)) -> b(c(x))
 c(a(x)) -> a(b(x))
 a(c(x)) -> c(b(x))
 b(a(x)) -> c(a(x))

Proof:
 Church Rosser Transformation Processor (critical pair closing system, Thm 2.4):
  strict:
   
  weak:
   b(c(x)) -> a(a(x))
   c(b(x)) -> a(c(x))
   a(b(x)) -> a(a(x))
   b(b(x)) -> a(b(x))
   b(c(x)) -> b(c(x))
   c(a(x)) -> a(b(x))
   a(c(x)) -> c(b(x))
   b(a(x)) -> c(a(x))
  original problem:
   a(c(x154)) -> c(b(x154))
   b(c(x155)) -> a(a(x155))
   b(b(x168)) -> a(b(x168))
   c(a(x170)) -> a(b(x170))
   a(b(x172)) -> a(a(x172))
   b(a(x175)) -> c(a(x175))
   c(b(x189)) -> a(c(x189))
  critical peaks: 
   Shift Processor (no label):
    a(c(x154)) -> c(b(x154))
    b(c(x155)) -> a(a(x155))
    b(b(x168)) -> a(b(x168))
    c(a(x170)) -> a(b(x170))
    a(b(x172)) -> a(a(x172))
    b(a(x175)) -> c(a(x175))
    c(b(x189)) -> a(c(x189))
    AT confluence processor
     Complete TRS T' of input TRS:
     b(c(x155)) -> a(a(x155))
     b(b(x168)) -> a(b(x168))
     c(a(x170)) -> a(b(x170))
     a(b(x172)) -> a(a(x172))
     b(a(x175)) -> c(a(x175))
     c(c(b(x517))) -> a(a(a(x517)))
     a(c(c(x628))) -> a(a(a(x628)))
     a(c(b(x630))) -> a(a(a(x630)))
     a(a(c(x630))) -> a(a(a(x630)))
     a(c(x154)) -> c(b(x154))
     c(b(x189)) -> a(c(x189))
     
      T' = (P union S) with
     
      TRS P:a(c(x154)) -> c(b(x154))
            c(b(x189)) -> a(c(x189))
     
      TRS S:b(c(x155)) -> a(a(x155))
            b(b(x168)) -> a(b(x168))
            c(a(x170)) -> a(b(x170))
            a(b(x172)) -> a(a(x172))
            b(a(x175)) -> c(a(x175))
            c(c(b(x517))) -> a(a(a(x517)))
            a(c(c(x628))) -> a(a(a(x628)))
            a(c(b(x630))) -> a(a(a(x630)))
            a(a(c(x630))) -> a(a(a(x630)))
     
     S is linear and P is reversible.
     
      CP(S,S) = 
     b(a(a(x1348))) = a(b(c(x1348))), a(a(a(x1349))) = a(a(c(x1349))), 
     c(c(a(a(x1350)))) = a(a(a(c(x1350)))), a(c(a(a(x1351)))) = a(a(a(c(x1351)))), 
     b(a(b(x1352))) = a(b(b(x1352))), a(a(b(x1353))) = a(a(b(x1353))), 
     c(c(a(b(x1354)))) = a(a(a(b(x1354)))), a(c(a(b(x1355)))) = a(a(a(b(x1355)))), 
     b(a(b(x1356))) = a(a(a(x1356))), a(c(a(b(x1357)))) = a(a(a(a(x1357)))), 
     a(a(a(b(x1358)))) = a(a(a(a(x1358)))), c(a(a(x1359))) = a(b(b(x1359))), 
     b(a(a(x1360))) = c(a(b(x1360))), b(c(a(x1361))) = a(b(a(x1361))), 
     a(c(a(x1362))) = a(a(a(x1362))), c(c(c(a(x1363)))) = a(a(a(a(x1363)))), 
     a(c(c(a(x1364)))) = a(a(a(a(x1364)))), b(a(a(a(x1365)))) = a(a(c(b(x1365)))), 
     a(a(a(a(x1366)))) = a(a(a(b(x1366)))), a(c(a(a(a(x1367))))) = a(a(a(c(b(x1367))))), 
     a(a(a(a(a(x1368))))) = a(a(a(c(b(x1368))))), c(a(a(a(x1369)))) = 
     a(b(c(c(x1369)))), b(a(a(a(x1370)))) = c(a(c(c(x1370)))), a(a(a(a(x1371)))) = 
     a(a(a(c(x1371)))), c(a(a(a(x1372)))) = a(b(c(b(x1372)))), b(a(a(a(x1373)))) = 
     c(a(c(b(x1373)))), a(a(a(a(x1374)))) = a(a(a(b(x1374)))), c(a(a(a(x1375)))) = 
     a(b(a(c(x1375)))), b(a(a(a(x1376)))) = c(a(a(c(x1376))))
     
      CP(S,P union P^-1) = 
     c(a(a(x1449))) = a(c(c(x1449))), c(a(a(x1450))) = a(c(c(x1450))), 
     c(a(b(x1451))) = a(c(b(x1451))), c(a(b(x1452))) = a(c(b(x1452))), 
     a(a(b(x1453))) = c(b(a(x1453))), a(a(b(x1454))) = c(b(a(x1454))), 
     c(c(a(x1455))) = a(c(a(x1455))), c(c(a(x1456))) = a(c(a(x1456))), 
     a(a(a(a(x1457)))) = c(b(c(b(x1457)))), a(a(a(a(x1458)))) = c(b(c(b(x1458)))), 
     a(a(a(x1459))) = c(b(c(x1459))), a(a(a(x1460))) = c(b(c(x1460))), 
     a(a(a(x1461))) = c(b(b(x1461))), a(a(a(x1462))) = c(b(b(x1462)))
     
      CP(P union P^-1,S) = 
     c(c(b(x1551))) = a(b(c(x1551))), b(c(b(x1552))) = c(a(c(x1552))), 
     c(b(c(x628))) = a(a(a(x628))), c(b(b(x630))) = a(a(a(x630))), a(c(b(x630))) = 
     a(a(a(x630))), b(a(c(x1556))) = a(a(b(x1556))), c(a(c(x517))) = 
     a(a(a(x517))), a(c(a(c(x1558)))) = a(a(a(b(x1558)))), a(a(c(x630))) = 
     a(a(a(x630))), a(a(a(c(x1560)))) = a(a(a(b(x1560)))), b(a(c(x1561))) = 
     a(a(b(x1561))), a(c(a(c(x1563)))) = a(a(a(b(x1563)))), a(a(a(c(x1565)))) = 
     a(a(a(b(x1565)))), c(c(b(x1566))) = a(b(c(x1566))), b(c(b(x1567))) = 
     c(a(c(x1567)))
     
     
     We have to check termination of S:
     
     KBO Processor:
      weight function:
       w0 = 1
       w(a) = w(b) = w(c) = 1
      precedence:
       b > c > a
      problem:
       
      Qed