MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            f(x,a(b(y))) -> f(a(b(b(x))),y)
            f(a(x),y) -> f(x,a(y))
            f(b(x),y) -> f(x,b(y))
        - Signature:
            {f/2} / {a/1,b/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,b}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak innermost dependency pairs:
        
        Strict DPs
          f#(x,a(b(y))) -> c_1(f#(a(b(b(x))),y))
          f#(a(x),y) -> c_2(f#(x,a(y)))
          f#(b(x),y) -> c_3(f#(x,b(y)))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(x,a(b(y))) -> c_1(f#(a(b(b(x))),y))
            f#(a(x),y) -> c_2(f#(x,a(y)))
            f#(b(x),y) -> c_3(f#(x,b(y)))
        - Strict TRS:
            f(x,a(b(y))) -> f(a(b(b(x))),y)
            f(a(x),y) -> f(x,a(y))
            f(b(x),y) -> f(x,b(y))
        - Signature:
            {f/2,f#/2} / {a/1,b/1,c_1/1,c_2/1,c_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#} and constructors {a,b}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          f#(x,a(b(y))) -> c_1(f#(a(b(b(x))),y))
          f#(a(x),y) -> c_2(f#(x,a(y)))
          f#(b(x),y) -> c_3(f#(x,b(y)))
* Step 3: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(x,a(b(y))) -> c_1(f#(a(b(b(x))),y))
          f#(a(x),y) -> c_2(f#(x,a(y)))
          f#(b(x),y) -> c_3(f#(x,b(y)))
      - Signature:
          {f/2,f#/2} / {a/1,b/1,c_1/1,c_2/1,c_3/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {f#} and constructors {a,b}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE