MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            ack(0(),y) -> s(y)
            ack(s(x),0()) -> ack(x,s(0()))
            ack(s(x),s(y)) -> ack(x,ack(s(x),y))
        - Signature:
            {ack/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ack} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          ack#(0(),y) -> c_1()
          ack#(s(x),0()) -> c_2(ack#(x,s(0())))
          ack#(s(x),s(y)) -> c_3(ack#(x,ack(s(x),y)),ack#(s(x),y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            ack#(0(),y) -> c_1()
            ack#(s(x),0()) -> c_2(ack#(x,s(0())))
            ack#(s(x),s(y)) -> c_3(ack#(x,ack(s(x),y)),ack#(s(x),y))
        - Weak TRS:
            ack(0(),y) -> s(y)
            ack(s(x),0()) -> ack(x,s(0()))
            ack(s(x),s(y)) -> ack(x,ack(s(x),y))
        - Signature:
            {ack/2,ack#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ack#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {2,3}.
        Here rules are labelled as follows:
          1: ack#(0(),y) -> c_1()
          2: ack#(s(x),0()) -> c_2(ack#(x,s(0())))
          3: ack#(s(x),s(y)) -> c_3(ack#(x,ack(s(x),y)),ack#(s(x),y))
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            ack#(s(x),0()) -> c_2(ack#(x,s(0())))
            ack#(s(x),s(y)) -> c_3(ack#(x,ack(s(x),y)),ack#(s(x),y))
        - Weak DPs:
            ack#(0(),y) -> c_1()
        - Weak TRS:
            ack(0(),y) -> s(y)
            ack(s(x),0()) -> ack(x,s(0()))
            ack(s(x),s(y)) -> ack(x,ack(s(x),y))
        - Signature:
            {ack/2,ack#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ack#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:ack#(s(x),0()) -> c_2(ack#(x,s(0())))
             -->_1 ack#(s(x),s(y)) -> c_3(ack#(x,ack(s(x),y)),ack#(s(x),y)):2
             -->_1 ack#(0(),y) -> c_1():3
          
          2:S:ack#(s(x),s(y)) -> c_3(ack#(x,ack(s(x),y)),ack#(s(x),y))
             -->_1 ack#(0(),y) -> c_1():3
             -->_2 ack#(s(x),s(y)) -> c_3(ack#(x,ack(s(x),y)),ack#(s(x),y)):2
             -->_1 ack#(s(x),s(y)) -> c_3(ack#(x,ack(s(x),y)),ack#(s(x),y)):2
             -->_2 ack#(s(x),0()) -> c_2(ack#(x,s(0()))):1
             -->_1 ack#(s(x),0()) -> c_2(ack#(x,s(0()))):1
          
          3:W:ack#(0(),y) -> c_1()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: ack#(0(),y) -> c_1()
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          ack#(s(x),0()) -> c_2(ack#(x,s(0())))
          ack#(s(x),s(y)) -> c_3(ack#(x,ack(s(x),y)),ack#(s(x),y))
      - Weak TRS:
          ack(0(),y) -> s(y)
          ack(s(x),0()) -> ack(x,s(0()))
          ack(s(x),s(y)) -> ack(x,ack(s(x),y))
      - Signature:
          {ack/2,ack#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {ack#} and constructors {0,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE