MAYBE

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

Proof:
 DP Processor:
  DPs:
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> c#(c(x1))
   b#(b(x1)) -> c#(c(c(x1)))
   b#(b(x1)) -> c#(c(c(c(x1))))
   c#(c(x1)) -> b#(x1)
   c#(c(x1)) -> c#(b(x1))
   c#(c(x1)) -> a#(c(b(x1)))
  TRS:
   a(a(x1)) -> x1
   b(b(x1)) -> c(c(c(c(x1))))
   c(c(x1)) -> a(c(b(x1)))
  TDG Processor:
   DPs:
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> c#(c(x1))
    b#(b(x1)) -> c#(c(c(x1)))
    b#(b(x1)) -> c#(c(c(c(x1))))
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> c#(b(x1))
    c#(c(x1)) -> a#(c(b(x1)))
   TRS:
    a(a(x1)) -> x1
    b(b(x1)) -> c(c(c(c(x1))))
    c(c(x1)) -> a(c(b(x1)))
   graph:
    c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(c(b(x1)))
    c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(x1))
    c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(c(c(x1))))
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(c(x1)))
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(x1))
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> c#(c(c(c(x1)))) -> c#(c(x1)) -> a#(c(b(x1)))
    b#(b(x1)) -> c#(c(c(c(x1)))) -> c#(c(x1)) -> c#(b(x1))
    b#(b(x1)) -> c#(c(c(c(x1)))) -> c#(c(x1)) -> b#(x1)
    b#(b(x1)) -> c#(c(c(x1))) -> c#(c(x1)) -> a#(c(b(x1)))
    b#(b(x1)) -> c#(c(c(x1))) -> c#(c(x1)) -> c#(b(x1))
    b#(b(x1)) -> c#(c(c(x1))) -> c#(c(x1)) -> b#(x1)
    b#(b(x1)) -> c#(c(x1)) -> c#(c(x1)) -> a#(c(b(x1)))
    b#(b(x1)) -> c#(c(x1)) -> c#(c(x1)) -> c#(b(x1))
    b#(b(x1)) -> c#(c(x1)) -> c#(c(x1)) -> b#(x1)
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> a#(c(b(x1)))
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(x1))
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 6
    #arcs: 19/49
    DPs:
     c#(c(x1)) -> c#(b(x1))
     c#(c(x1)) -> b#(x1)
     b#(b(x1)) -> c#(x1)
     b#(b(x1)) -> c#(c(x1))
     b#(b(x1)) -> c#(c(c(x1)))
     b#(b(x1)) -> c#(c(c(c(x1))))
    TRS:
     a(a(x1)) -> x1
     b(b(x1)) -> c(c(c(c(x1))))
     c(c(x1)) -> a(c(b(x1)))
    Open