YES
Input TRS:
      1: C(x1) -> c(x1)
      2: c(c(x1)) -> x1
      3: b(b(x1)) -> B(x1)
      4: B(B(x1)) -> b(x1)
      5: c(B(c(b(c(x1))))) -> B(c(b(c(B(c(b(x1)))))))
      6: b(B(x1)) -> x1
      7: B(b(x1)) -> x1
      8: c(C(x1)) -> x1
      9: C(c(x1)) -> x1
Number of strict rules: 9
Direct POLO(bPol) ... removes: 8 1 9 2
      b 	w: x1
      c 	w: x1 + 282
      C 	w: x1 + 283
      B 	w: x1
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #c(B(c(b(c(x1))))) -> #B(c(b(c(B(c(b(x1)))))))
     #2: #c(B(c(b(c(x1))))) -> #c(b(c(B(c(b(x1))))))
     #3: #c(B(c(b(c(x1))))) -> #b(c(B(c(b(x1)))))
     #4: #c(B(c(b(c(x1))))) -> #c(B(c(b(x1))))
     #5: #c(B(c(b(c(x1))))) -> #B(c(b(x1)))
     #6: #c(B(c(b(c(x1))))) -> #c(b(x1))
     #7: #c(B(c(b(c(x1))))) -> #b(x1)
     #8: #b(b(x1)) -> #B(x1)
     #9: #B(B(x1)) -> #b(x1)
Number of SCCs: 2, DPs: 5
  SCC { #8 #9 }
POLO(Sum)... succeeded.
      b 	w: x1 + 1
      #B 	w: x1
      c 	w: 0
      C 	w: 0
      B 	w: x1 + 39
      #c 	w: 0
      #b 	w: x1
    USABLE RULES: { }
    Removed DPs: #8 #9
Number of SCCs: 1, DPs: 3
  SCC { #2 #4 #6 }
POLO(Sum)... succeeded.
      b 	w: x1
      #B 	w: 0
      c 	w: x1 + 2438
      C 	w: 0
      B 	w: x1
      #c 	w: x1
      #b 	w: 0
    USABLE RULES: { 3..7 }
    Removed DPs: #4 #6
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded.
      b 	w: [0,1;1,1] * x1 + [0;1]
      #B 	w: [0;0]
      c 	w: [1,0;0,0] * x1 + [0;14921]
      C 	w: [0;0]
      B 	w: [1,1;1,0] * x1 + [1;0]
      #c 	w: [1,0;0,0] * x1
      #b 	w: [0;0]
    USABLE RULES: { 3..7 }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0