MAYBE

Problem:
 c(c(b(c(x)))) -> b(a(0(),c(x)))
 c(c(x)) -> b(c(b(c(x))))
 a(0(),x) -> c(c(x))

Proof:
 DP Processor:
  DPs:
   c#(c(b(c(x)))) -> a#(0(),c(x))
   c#(c(x)) -> c#(b(c(x)))
   a#(0(),x) -> c#(x)
   a#(0(),x) -> c#(c(x))
  TRS:
   c(c(b(c(x)))) -> b(a(0(),c(x)))
   c(c(x)) -> b(c(b(c(x))))
   a(0(),x) -> c(c(x))
  EDG Processor:
   DPs:
    c#(c(b(c(x)))) -> a#(0(),c(x))
    c#(c(x)) -> c#(b(c(x)))
    a#(0(),x) -> c#(x)
    a#(0(),x) -> c#(c(x))
   TRS:
    c(c(b(c(x)))) -> b(a(0(),c(x)))
    c(c(x)) -> b(c(b(c(x))))
    a(0(),x) -> c(c(x))
   graph:
    a#(0(),x) -> c#(c(x)) -> c#(c(b(c(x)))) -> a#(0(),c(x))
    a#(0(),x) -> c#(c(x)) -> c#(c(x)) -> c#(b(c(x)))
    a#(0(),x) -> c#(x) -> c#(c(b(c(x)))) -> a#(0(),c(x))
    a#(0(),x) -> c#(x) -> c#(c(x)) -> c#(b(c(x)))
    c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(x)
    c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(c(x))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 6/16
    DPs:
     a#(0(),x) -> c#(c(x))
     c#(c(b(c(x)))) -> a#(0(),c(x))
     a#(0(),x) -> c#(x)
    TRS:
     c(c(b(c(x)))) -> b(a(0(),c(x)))
     c(c(x)) -> b(c(b(c(x))))
     a(0(),x) -> c(c(x))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [a#](x0, x1) = x1 + 1,
      
      [c#](x0) = x0,
      
      [a](x0, x1) = x0 + x1 + 1,
      
      [0] = 1,
      
      [b](x0) = x0,
      
      [c](x0) = x0 + 1
     orientation:
      a#(0(),x) = x + 1 >= x + 1 = c#(c(x))
      
      c#(c(b(c(x)))) = x + 2 >= x + 2 = a#(0(),c(x))
      
      a#(0(),x) = x + 1 >= x = c#(x)
      
      c(c(b(c(x)))) = x + 3 >= x + 3 = b(a(0(),c(x)))
      
      c(c(x)) = x + 2 >= x + 2 = b(c(b(c(x))))
      
      a(0(),x) = x + 2 >= x + 2 = c(c(x))
     problem:
      DPs:
       a#(0(),x) -> c#(c(x))
       c#(c(b(c(x)))) -> a#(0(),c(x))
      TRS:
       c(c(b(c(x)))) -> b(a(0(),c(x)))
       c(c(x)) -> b(c(b(c(x))))
       a(0(),x) -> c(c(x))
     Open