MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
            hd(cons(X,Y)) -> X
            incr(cons(X,Y)) -> cons(s(X),incr(Y))
            nats() -> adx(zeros())
            tl(cons(X,Y)) -> Y
            zeros() -> cons(0(),zeros())
        - Signature:
            {adx/1,hd/1,incr/1,nats/0,tl/1,zeros/0} / {0/0,cons/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {adx,hd,incr,nats,tl,zeros} and constructors {0,cons,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y))
          hd#(cons(X,Y)) -> c_2()
          incr#(cons(X,Y)) -> c_3(incr#(Y))
          nats#() -> c_4(adx#(zeros()),zeros#())
          tl#(cons(X,Y)) -> c_5()
          zeros#() -> c_6(zeros#())
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y))
            hd#(cons(X,Y)) -> c_2()
            incr#(cons(X,Y)) -> c_3(incr#(Y))
            nats#() -> c_4(adx#(zeros()),zeros#())
            tl#(cons(X,Y)) -> c_5()
            zeros#() -> c_6(zeros#())
        - Weak TRS:
            adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
            hd(cons(X,Y)) -> X
            incr(cons(X,Y)) -> cons(s(X),incr(Y))
            nats() -> adx(zeros())
            tl(cons(X,Y)) -> Y
            zeros() -> cons(0(),zeros())
        - Signature:
            {adx/1,hd/1,incr/1,nats/0,tl/1,zeros/0,adx#/1,hd#/1,incr#/1,nats#/0,tl#/1,zeros#/0} / {0/0,cons/2,s/1,c_1/2
            ,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {adx#,hd#,incr#,nats#,tl#,zeros#} and constructors {0,cons
            ,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
          incr(cons(X,Y)) -> cons(s(X),incr(Y))
          zeros() -> cons(0(),zeros())
          adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y))
          hd#(cons(X,Y)) -> c_2()
          incr#(cons(X,Y)) -> c_3(incr#(Y))
          nats#() -> c_4(adx#(zeros()),zeros#())
          tl#(cons(X,Y)) -> c_5()
          zeros#() -> c_6(zeros#())
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y))
            hd#(cons(X,Y)) -> c_2()
            incr#(cons(X,Y)) -> c_3(incr#(Y))
            nats#() -> c_4(adx#(zeros()),zeros#())
            tl#(cons(X,Y)) -> c_5()
            zeros#() -> c_6(zeros#())
        - Weak TRS:
            adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
            incr(cons(X,Y)) -> cons(s(X),incr(Y))
            zeros() -> cons(0(),zeros())
        - Signature:
            {adx/1,hd/1,incr/1,nats/0,tl/1,zeros/0,adx#/1,hd#/1,incr#/1,nats#/0,tl#/1,zeros#/0} / {0/0,cons/2,s/1,c_1/2
            ,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {adx#,hd#,incr#,nats#,tl#,zeros#} and constructors {0,cons
            ,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,5}
        by application of
          Pre({2,5}) = {}.
        Here rules are labelled as follows:
          1: adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y))
          2: hd#(cons(X,Y)) -> c_2()
          3: incr#(cons(X,Y)) -> c_3(incr#(Y))
          4: nats#() -> c_4(adx#(zeros()),zeros#())
          5: tl#(cons(X,Y)) -> c_5()
          6: zeros#() -> c_6(zeros#())
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y))
            incr#(cons(X,Y)) -> c_3(incr#(Y))
            nats#() -> c_4(adx#(zeros()),zeros#())
            zeros#() -> c_6(zeros#())
        - Weak DPs:
            hd#(cons(X,Y)) -> c_2()
            tl#(cons(X,Y)) -> c_5()
        - Weak TRS:
            adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
            incr(cons(X,Y)) -> cons(s(X),incr(Y))
            zeros() -> cons(0(),zeros())
        - Signature:
            {adx/1,hd/1,incr/1,nats/0,tl/1,zeros/0,adx#/1,hd#/1,incr#/1,nats#/0,tl#/1,zeros#/0} / {0/0,cons/2,s/1,c_1/2
            ,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {adx#,hd#,incr#,nats#,tl#,zeros#} and constructors {0,cons
            ,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y))
             -->_1 incr#(cons(X,Y)) -> c_3(incr#(Y)):2
             -->_2 adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y)):1
          
          2:S:incr#(cons(X,Y)) -> c_3(incr#(Y))
             -->_1 incr#(cons(X,Y)) -> c_3(incr#(Y)):2
          
          3:S:nats#() -> c_4(adx#(zeros()),zeros#())
             -->_2 zeros#() -> c_6(zeros#()):4
             -->_1 adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y)):1
          
          4:S:zeros#() -> c_6(zeros#())
             -->_1 zeros#() -> c_6(zeros#()):4
          
          5:W:hd#(cons(X,Y)) -> c_2()
             
          
          6:W:tl#(cons(X,Y)) -> c_5()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: tl#(cons(X,Y)) -> c_5()
          5: hd#(cons(X,Y)) -> c_2()
* Step 5: NaturalMI MAYBE
    + Considered Problem:
        - Strict DPs:
            adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y))
            incr#(cons(X,Y)) -> c_3(incr#(Y))
            nats#() -> c_4(adx#(zeros()),zeros#())
            zeros#() -> c_6(zeros#())
        - Weak TRS:
            adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
            incr(cons(X,Y)) -> cons(s(X),incr(Y))
            zeros() -> cons(0(),zeros())
        - Signature:
            {adx/1,hd/1,incr/1,nats/0,tl/1,zeros/0,adx#/1,hd#/1,incr#/1,nats#/0,tl#/1,zeros#/0} / {0/0,cons/2,s/1,c_1/2
            ,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {adx#,hd#,incr#,nats#,tl#,zeros#} and constructors {0,cons
            ,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
        The following argument positions are considered usable:
          uargs(c_1) = {1,2},
          uargs(c_3) = {1},
          uargs(c_4) = {1,2},
          uargs(c_6) = {1}
        
        Following symbols are considered usable:
          {adx#,hd#,incr#,nats#,tl#,zeros#}
        TcT has computed the following interpretation:
               p(0) = [8]                  
             p(adx) = [2]                  
            p(cons) = [2]                  
              p(hd) = [1]                  
            p(incr) = [6]                  
            p(nats) = [0]                  
               p(s) = [4]                  
              p(tl) = [4] x1 + [1]         
           p(zeros) = [0]                  
            p(adx#) = [0]                  
             p(hd#) = [1] x1 + [8]         
           p(incr#) = [0]                  
           p(nats#) = [2]                  
             p(tl#) = [1]                  
          p(zeros#) = [0]                  
             p(c_1) = [4] x1 + [4] x2 + [0]
             p(c_2) = [0]                  
             p(c_3) = [8] x1 + [0]         
             p(c_4) = [8] x1 + [2] x2 + [0]
             p(c_5) = [2]                  
             p(c_6) = [8] x1 + [0]         
        
        Following rules are strictly oriented:
        nats#() = [2]                        
                > [0]                        
                = c_4(adx#(zeros()),zeros#())
        
        
        Following rules are (at-least) weakly oriented:
         adx#(cons(X,Y)) =  [0]                               
                         >= [0]                               
                         =  c_1(incr#(cons(X,adx(Y))),adx#(Y))
        
        incr#(cons(X,Y)) =  [0]                               
                         >= [0]                               
                         =  c_3(incr#(Y))                     
        
                zeros#() =  [0]                               
                         >= [0]                               
                         =  c_6(zeros#())                     
        
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          adx#(cons(X,Y)) -> c_1(incr#(cons(X,adx(Y))),adx#(Y))
          incr#(cons(X,Y)) -> c_3(incr#(Y))
          zeros#() -> c_6(zeros#())
      - Weak DPs:
          nats#() -> c_4(adx#(zeros()),zeros#())
      - Weak TRS:
          adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
          incr(cons(X,Y)) -> cons(s(X),incr(Y))
          zeros() -> cons(0(),zeros())
      - Signature:
          {adx/1,hd/1,incr/1,nats/0,tl/1,zeros/0,adx#/1,hd#/1,incr#/1,nats#/0,tl#/1,zeros#/0} / {0/0,cons/2,s/1,c_1/2
          ,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {adx#,hd#,incr#,nats#,tl#,zeros#} and constructors {0,cons
          ,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE