YES

Problem:
 a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
 a(c(b(x1))) -> a(a(b(c(b(a(x1))))))

Proof:
 DP Processor:
  DPs:
   a#(b(a(a(x1)))) -> a#(b(a(x1)))
   a#(c(b(x1))) -> a#(x1)
   a#(c(b(x1))) -> a#(b(c(b(a(x1)))))
   a#(c(b(x1))) -> a#(a(b(c(b(a(x1))))))
  TRS:
   a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
   a(c(b(x1))) -> a(a(b(c(b(a(x1))))))
  EDG Processor:
   DPs:
    a#(b(a(a(x1)))) -> a#(b(a(x1)))
    a#(c(b(x1))) -> a#(x1)
    a#(c(b(x1))) -> a#(b(c(b(a(x1)))))
    a#(c(b(x1))) -> a#(a(b(c(b(a(x1))))))
   TRS:
    a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
    a(c(b(x1))) -> a(a(b(c(b(a(x1))))))
   graph:
    a#(c(b(x1))) -> a#(x1) -> a#(b(a(a(x1)))) -> a#(b(a(x1)))
    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> a#(x1)
    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> a#(b(c(b(a(x1)))))
    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> a#(a(b(c(b(a(x1))))))
    a#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(a(x1)))
   CDG Processor:
    DPs:
     a#(b(a(a(x1)))) -> a#(b(a(x1)))
     a#(c(b(x1))) -> a#(x1)
     a#(c(b(x1))) -> a#(b(c(b(a(x1)))))
     a#(c(b(x1))) -> a#(a(b(c(b(a(x1))))))
    TRS:
     a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
     a(c(b(x1))) -> a(a(b(c(b(a(x1))))))
    graph:
     a#(c(b(x1))) -> a#(x1) -> a#(b(a(a(x1)))) -> a#(b(a(x1)))
     a#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(a(x1)))
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 2/16
     DPs:
      a#(b(a(a(x1)))) -> a#(b(a(x1)))
     TRS:
      a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
      a(c(b(x1))) -> a(a(b(c(b(a(x1))))))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [a#](x0) = x0 + 0,
       
       [c](x0) = 12x0 + 0,
       
       [b](x0) = -12x0 + 0,
       
       [a](x0) = 1x0 + 12
      orientation:
       a#(b(a(a(x1)))) = -10x1 + 1 >= -11x1 + 0 = a#(b(a(x1)))
       
       a(b(a(a(x1)))) = -9x1 + 12 >= -10x1 + 12 = c(b(a(b(a(x1)))))
       
       a(c(b(x1))) = 1x1 + 13 >= -9x1 + 13 = a(a(b(c(b(a(x1))))))
      problem:
       DPs:
        
       TRS:
        a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
        a(c(b(x1))) -> a(a(b(c(b(a(x1))))))
      Qed