MAYBE
TRS:
 {   a__f(X1, X2, X3) -> f(X1, X2, X3),
    a__f(b(), X, c()) -> a__f(X, a__c(), X),
               a__c() -> b(),
               a__c() -> c(),
            mark(b()) -> b(),
            mark(c()) -> a__c(),
  mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)}
 DP:
  Strict:
   {  a__f#(b(), X, c()) -> a__f#(X, a__c(), X),
      a__f#(b(), X, c()) -> a__c#(),
              mark#(c()) -> a__c#(),
    mark#(f(X1, X2, X3)) -> a__f#(X1, mark(X2), X3),
    mark#(f(X1, X2, X3)) -> mark#(X2)}
  Weak:
  {   a__f(X1, X2, X3) -> f(X1, X2, X3),
     a__f(b(), X, c()) -> a__f(X, a__c(), X),
                a__c() -> b(),
                a__c() -> c(),
             mark(b()) -> b(),
             mark(c()) -> a__c(),
   mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)}
  EDG:
   {(mark#(f(X1, X2, X3)) -> mark#(X2), mark#(f(X1, X2, X3)) -> mark#(X2))
    (mark#(f(X1, X2, X3)) -> mark#(X2), mark#(f(X1, X2, X3)) -> a__f#(X1, mark(X2), X3))
    (mark#(f(X1, X2, X3)) -> mark#(X2), mark#(c()) -> a__c#())
    (mark#(f(X1, X2, X3)) -> a__f#(X1, mark(X2), X3), a__f#(b(), X, c()) -> a__f#(X, a__c(), X))
    (mark#(f(X1, X2, X3)) -> a__f#(X1, mark(X2), X3), a__f#(b(), X, c()) -> a__c#())
    (a__f#(b(), X, c()) -> a__f#(X, a__c(), X), a__f#(b(), X, c()) -> a__f#(X, a__c(), X))
    (a__f#(b(), X, c()) -> a__f#(X, a__c(), X), a__f#(b(), X, c()) -> a__c#())}
   SCCS:
    Scc:
     {mark#(f(X1, X2, X3)) -> mark#(X2)}
    Scc:
     {a__f#(b(), X, c()) -> a__f#(X, a__c(), X)}
    SCC:
     Strict:
      {mark#(f(X1, X2, X3)) -> mark#(X2)}
     Weak:
     {   a__f(X1, X2, X3) -> f(X1, X2, X3),
        a__f(b(), X, c()) -> a__f(X, a__c(), X),
                   a__c() -> b(),
                   a__c() -> c(),
                mark(b()) -> b(),
                mark(c()) -> a__c(),
      mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)}
     SPSC:
      Simple Projection:
       pi(mark#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {a__f#(b(), X, c()) -> a__f#(X, a__c(), X)}
     Weak:
     {   a__f(X1, X2, X3) -> f(X1, X2, X3),
        a__f(b(), X, c()) -> a__f(X, a__c(), X),
                   a__c() -> b(),
                   a__c() -> c(),
                mark(b()) -> b(),
                mark(c()) -> a__c(),
      mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)}
     Fail