NO

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

Proof:
 Church Rosser Transformation Processor:
  strict:
   
  weak:
   
  critical peaks: 20
   c(b(c(x99))) <-0|0[]- c(c(a(x99))) -2|[]-> a(c(a(x99)))
   a(b(c(x100))) <-0|0[]- a(c(a(x100))) -3|[]-> c(b(a(x100)))
   c(b(c(x101))) <-0|0[]- c(c(a(x101))) -6|[]-> c(b(a(x101)))
   c(b(b(x102))) <-1|0[]- c(c(b(x102))) -2|[]-> a(c(b(x102)))
   a(b(b(x103))) <-1|0[]- a(c(b(x103))) -3|[]-> c(b(b(x103)))
   c(b(b(x104))) <-1|0[]- c(c(b(x104))) -6|[]-> c(b(b(x104)))
   c(a(c(x105))) <-2|0[]- c(c(c(x105))) -2|[]-> a(c(c(x105)))
   a(a(c(x106))) <-2|0[]- a(c(c(x106))) -3|[]-> c(b(c(x106)))
   a(c(x)) <-2|[]- c(c(x)) -6|[]-> c(b(x))
   c(a(c(x108))) <-2|0[]- c(c(c(x108))) -6|[]-> c(b(c(x108)))
   c(c(b(x109))) <-3|0[]- c(a(c(x109))) -0|[]-> b(c(c(x109)))
   b(c(b(x110))) <-3|0[]- b(a(c(x110))) -4|[]-> c(b(c(x110)))
   c(c(b(x111))) <-4|0[]- c(b(a(x111))) -1|[]-> b(b(a(x111)))
   b(c(b(x112))) <-4|0[]- b(b(a(x112))) -5|[]-> a(c(a(x112)))
   c(a(c(x113))) <-5|0[]- c(b(b(x113))) -1|[]-> b(b(b(x113)))
   b(a(c(x114))) <-5|0[]- b(b(b(x114))) -5|[]-> a(c(b(x114)))
   c(b(x)) <-6|[]- c(c(x)) -2|[]-> a(c(x))
   c(c(b(x116))) <-6|0[]- c(c(c(x116))) -2|[]-> a(c(c(x116)))
   a(c(b(x117))) <-6|0[]- a(c(c(x117))) -3|[]-> c(b(c(x117)))
   c(c(b(x118))) <-6|0[]- c(c(c(x118))) -6|[]-> c(b(c(x118)))
  Redundant Rules Transformation:
   c(a(x)) -> b(c(x))
   c(b(x)) -> b(b(x))
   c(c(x)) -> a(c(x))
   a(c(x)) -> c(b(x))
   b(a(x)) -> c(b(x))
   b(b(x)) -> a(c(x))
   c(c(x)) -> c(b(x))
   c(b(x)) -> a(c(x))
   a(c(x)) -> b(b(x))
   b(a(x)) -> b(b(x))
   b(b(x)) -> c(b(x))
   c(c(x)) -> b(b(x))
   Nonconfluence Processor:
    terms: a(b(c(f205()))) *<- a(c(a(f205()))) ->* b(c(b(f205())))
    Qed
    
    first automaton:
     final states: {1482}
     transitions:
      a(1485) -> 1482*
      c(1483) -> 1484*
      b(1484) -> 1485*
      f205() -> 1483*
    
    second automaton:
     final states: {1490}
     transitions:
      a(1493) -> 1490*
      a(19949) -> 1493*
      c(1491) -> 19949*
      c(1493) -> 1490*
      c(1492) -> 1493*
      c(19949) -> 1493*
      c(33296) -> 1490*
      b(33296) -> 1490*
      b(19949) -> 33296*
      b(1491) -> 1492*
      b(1493) -> 1490*
      b(1492) -> 1493*
      f205() -> 1491*