MAYBE

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   b#(x1) -> c#(x1)
   b#(c(x1)) -> a#(x1)
   b#(c(x1)) -> b#(a(x1))
   b#(c(x1)) -> c#(b(a(x1)))
  TRS:
   a(x1) -> x1
   a(a(x1)) -> b(x1)
   b(x1) -> c(x1)
   b(c(x1)) -> c(b(a(x1)))
   c(x1) -> x1
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    b#(x1) -> c#(x1)
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> b#(a(x1))
    b#(c(x1)) -> c#(b(a(x1)))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> b(x1)
    b(x1) -> c(x1)
    b(c(x1)) -> c(b(a(x1)))
    c(x1) -> x1
   graph:
    b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> c#(b(a(x1)))
    b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1))
    b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> b#(a(x1)) -> b#(x1) -> c#(x1)
    b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(a(x1)))
    a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(a(x1))
    a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1)
    a#(a(x1)) -> b#(x1) -> b#(x1) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 9/25
    DPs:
     b#(c(x1)) -> b#(a(x1))
     b#(c(x1)) -> a#(x1)
     a#(a(x1)) -> b#(x1)
    TRS:
     a(x1) -> x1
     a(a(x1)) -> b(x1)
     b(x1) -> c(x1)
     b(c(x1)) -> c(b(a(x1)))
     c(x1) -> x1
    Open