MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            2ndsneg(0(),Z) -> rnil()
            2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z))
            2ndspos(0(),Z) -> rnil()
            2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z))
            from(X) -> cons(X,from(s(X)))
            pi(X) -> 2ndspos(X,from(0()))
            plus(0(),Y) -> Y
            plus(s(X),Y) -> s(plus(X,Y))
            square(X) -> times(X,X)
            times(0(),Y) -> 0()
            times(s(X),Y) -> plus(Y,times(X,Y))
        - Signature:
            {2ndsneg/2,2ndspos/2,from/1,pi/1,plus/2,square/1,times/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0
            ,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2ndsneg,2ndspos,from,pi,plus,square
            ,times} and constructors {0,cons,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          2ndsneg#(0(),Z) -> c_1()
          2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
          2ndspos#(0(),Z) -> c_3()
          2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
          from#(X) -> c_5(from#(s(X)))
          pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
          plus#(0(),Y) -> c_7()
          plus#(s(X),Y) -> c_8(plus#(X,Y))
          square#(X) -> c_9(times#(X,X))
          times#(0(),Y) -> c_10()
          times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            2ndsneg#(0(),Z) -> c_1()
            2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
            2ndspos#(0(),Z) -> c_3()
            2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
            from#(X) -> c_5(from#(s(X)))
            pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
            plus#(0(),Y) -> c_7()
            plus#(s(X),Y) -> c_8(plus#(X,Y))
            square#(X) -> c_9(times#(X,X))
            times#(0(),Y) -> c_10()
            times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
        - Weak TRS:
            2ndsneg(0(),Z) -> rnil()
            2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z))
            2ndspos(0(),Z) -> rnil()
            2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z))
            from(X) -> cons(X,from(s(X)))
            pi(X) -> 2ndspos(X,from(0()))
            plus(0(),Y) -> Y
            plus(s(X),Y) -> s(plus(X,Y))
            square(X) -> times(X,X)
            times(0(),Y) -> 0()
            times(s(X),Y) -> plus(Y,times(X,Y))
        - Signature:
            {2ndsneg/2,2ndspos/2,from/1,pi/1,plus/2,square/1,times/2,2ndsneg#/2,2ndspos#/2,from#/1,pi#/1,plus#/2
            ,square#/1,times#/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1
            ,c_6/2,c_7/0,c_8/1,c_9/1,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2ndsneg#,2ndspos#,from#,pi#,plus#,square#
            ,times#} and constructors {0,cons,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          from(X) -> cons(X,from(s(X)))
          plus(0(),Y) -> Y
          plus(s(X),Y) -> s(plus(X,Y))
          times(0(),Y) -> 0()
          times(s(X),Y) -> plus(Y,times(X,Y))
          2ndsneg#(0(),Z) -> c_1()
          2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
          2ndspos#(0(),Z) -> c_3()
          2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
          from#(X) -> c_5(from#(s(X)))
          pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
          plus#(0(),Y) -> c_7()
          plus#(s(X),Y) -> c_8(plus#(X,Y))
          square#(X) -> c_9(times#(X,X))
          times#(0(),Y) -> c_10()
          times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            2ndsneg#(0(),Z) -> c_1()
            2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
            2ndspos#(0(),Z) -> c_3()
            2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
            from#(X) -> c_5(from#(s(X)))
            pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
            plus#(0(),Y) -> c_7()
            plus#(s(X),Y) -> c_8(plus#(X,Y))
            square#(X) -> c_9(times#(X,X))
            times#(0(),Y) -> c_10()
            times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
        - Weak TRS:
            from(X) -> cons(X,from(s(X)))
            plus(0(),Y) -> Y
            plus(s(X),Y) -> s(plus(X,Y))
            times(0(),Y) -> 0()
            times(s(X),Y) -> plus(Y,times(X,Y))
        - Signature:
            {2ndsneg/2,2ndspos/2,from/1,pi/1,plus/2,square/1,times/2,2ndsneg#/2,2ndspos#/2,from#/1,pi#/1,plus#/2
            ,square#/1,times#/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1
            ,c_6/2,c_7/0,c_8/1,c_9/1,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2ndsneg#,2ndspos#,from#,pi#,plus#,square#
            ,times#} and constructors {0,cons,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,7,10}
        by application of
          Pre({1,3,7,10}) = {2,4,6,8,9,11}.
        Here rules are labelled as follows:
          1: 2ndsneg#(0(),Z) -> c_1()
          2: 2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
          3: 2ndspos#(0(),Z) -> c_3()
          4: 2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
          5: from#(X) -> c_5(from#(s(X)))
          6: pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
          7: plus#(0(),Y) -> c_7()
          8: plus#(s(X),Y) -> c_8(plus#(X,Y))
          9: square#(X) -> c_9(times#(X,X))
          10: times#(0(),Y) -> c_10()
          11: times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
            2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
            from#(X) -> c_5(from#(s(X)))
            pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
            plus#(s(X),Y) -> c_8(plus#(X,Y))
            square#(X) -> c_9(times#(X,X))
            times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
        - Weak DPs:
            2ndsneg#(0(),Z) -> c_1()
            2ndspos#(0(),Z) -> c_3()
            plus#(0(),Y) -> c_7()
            times#(0(),Y) -> c_10()
        - Weak TRS:
            from(X) -> cons(X,from(s(X)))
            plus(0(),Y) -> Y
            plus(s(X),Y) -> s(plus(X,Y))
            times(0(),Y) -> 0()
            times(s(X),Y) -> plus(Y,times(X,Y))
        - Signature:
            {2ndsneg/2,2ndspos/2,from/1,pi/1,plus/2,square/1,times/2,2ndsneg#/2,2ndspos#/2,from#/1,pi#/1,plus#/2
            ,square#/1,times#/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1
            ,c_6/2,c_7/0,c_8/1,c_9/1,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2ndsneg#,2ndspos#,from#,pi#,plus#,square#
            ,times#} and constructors {0,cons,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
             -->_1 2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z)):2
             -->_1 2ndspos#(0(),Z) -> c_3():9
          
          2:S:2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
             -->_1 2ndsneg#(0(),Z) -> c_1():8
             -->_1 2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z)):1
          
          3:S:from#(X) -> c_5(from#(s(X)))
             -->_1 from#(X) -> c_5(from#(s(X))):3
          
          4:S:pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
             -->_1 2ndspos#(0(),Z) -> c_3():9
             -->_2 from#(X) -> c_5(from#(s(X))):3
             -->_1 2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z)):2
          
          5:S:plus#(s(X),Y) -> c_8(plus#(X,Y))
             -->_1 plus#(0(),Y) -> c_7():10
             -->_1 plus#(s(X),Y) -> c_8(plus#(X,Y)):5
          
          6:S:square#(X) -> c_9(times#(X,X))
             -->_1 times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y)):7
             -->_1 times#(0(),Y) -> c_10():11
          
          7:S:times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
             -->_2 times#(0(),Y) -> c_10():11
             -->_1 plus#(0(),Y) -> c_7():10
             -->_2 times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y)):7
             -->_1 plus#(s(X),Y) -> c_8(plus#(X,Y)):5
          
          8:W:2ndsneg#(0(),Z) -> c_1()
             
          
          9:W:2ndspos#(0(),Z) -> c_3()
             
          
          10:W:plus#(0(),Y) -> c_7()
             
          
          11:W:times#(0(),Y) -> c_10()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          11: times#(0(),Y) -> c_10()
          10: plus#(0(),Y) -> c_7()
          9: 2ndspos#(0(),Z) -> c_3()
          8: 2ndsneg#(0(),Z) -> c_1()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
            2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
            from#(X) -> c_5(from#(s(X)))
            pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
            plus#(s(X),Y) -> c_8(plus#(X,Y))
            square#(X) -> c_9(times#(X,X))
            times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
        - Weak TRS:
            from(X) -> cons(X,from(s(X)))
            plus(0(),Y) -> Y
            plus(s(X),Y) -> s(plus(X,Y))
            times(0(),Y) -> 0()
            times(s(X),Y) -> plus(Y,times(X,Y))
        - Signature:
            {2ndsneg/2,2ndspos/2,from/1,pi/1,plus/2,square/1,times/2,2ndsneg#/2,2ndspos#/2,from#/1,pi#/1,plus#/2
            ,square#/1,times#/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1
            ,c_6/2,c_7/0,c_8/1,c_9/1,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2ndsneg#,2ndspos#,from#,pi#,plus#,square#
            ,times#} and constructors {0,cons,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
           -->_1 2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z)):2
        
        2:S:2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
           -->_1 2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z)):1
        
        3:S:from#(X) -> c_5(from#(s(X)))
           -->_1 from#(X) -> c_5(from#(s(X))):3
        
        4:S:pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
           -->_2 from#(X) -> c_5(from#(s(X))):3
           -->_1 2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z)):2
        
        5:S:plus#(s(X),Y) -> c_8(plus#(X,Y))
           -->_1 plus#(s(X),Y) -> c_8(plus#(X,Y)):5
        
        6:S:square#(X) -> c_9(times#(X,X))
           -->_1 times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y)):7
        
        7:S:times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
           -->_2 times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y)):7
           -->_1 plus#(s(X),Y) -> c_8(plus#(X,Y)):5
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(6,square#(X) -> c_9(times#(X,X)))]
* Step 6: NaturalMI MAYBE
    + Considered Problem:
        - Strict DPs:
            2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
            2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
            from#(X) -> c_5(from#(s(X)))
            pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
            plus#(s(X),Y) -> c_8(plus#(X,Y))
            times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
        - Weak TRS:
            from(X) -> cons(X,from(s(X)))
            plus(0(),Y) -> Y
            plus(s(X),Y) -> s(plus(X,Y))
            times(0(),Y) -> 0()
            times(s(X),Y) -> plus(Y,times(X,Y))
        - Signature:
            {2ndsneg/2,2ndspos/2,from/1,pi/1,plus/2,square/1,times/2,2ndsneg#/2,2ndspos#/2,from#/1,pi#/1,plus#/2
            ,square#/1,times#/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1
            ,c_6/2,c_7/0,c_8/1,c_9/1,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2ndsneg#,2ndspos#,from#,pi#,plus#,square#
            ,times#} and constructors {0,cons,negrecip,posrecip,rcons,rnil,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_2) = {1},
          uargs(c_4) = {1},
          uargs(c_5) = {1},
          uargs(c_6) = {1,2},
          uargs(c_8) = {1},
          uargs(c_11) = {1,2}
        
        Following symbols are considered usable:
          {2ndsneg#,2ndspos#,from#,pi#,plus#,square#,times#}
        TcT has computed the following interpretation:
                 p(0) = [2]                  
           p(2ndsneg) = [1]                  
           p(2ndspos) = [1] x1 + [8] x2 + [1]
              p(cons) = [8]                  
              p(from) = [7] x1 + [8]         
          p(negrecip) = [1]                  
                p(pi) = [1] x1 + [2]         
              p(plus) = [1] x1 + [14]        
          p(posrecip) = [2]                  
             p(rcons) = [2]                  
              p(rnil) = [1]                  
                 p(s) = [2]                  
            p(square) = [2]                  
             p(times) = [4] x1 + [1]         
          p(2ndsneg#) = [0]                  
          p(2ndspos#) = [0]                  
             p(from#) = [0]                  
               p(pi#) = [2] x1 + [2]         
             p(plus#) = [0]                  
           p(square#) = [2] x1 + [2]         
            p(times#) = [0]                  
               p(c_1) = [1]                  
               p(c_2) = [1] x1 + [0]         
               p(c_3) = [0]                  
               p(c_4) = [1] x1 + [0]         
               p(c_5) = [8] x1 + [0]         
               p(c_6) = [4] x1 + [1] x2 + [1]
               p(c_7) = [4]                  
               p(c_8) = [1] x1 + [0]         
               p(c_9) = [1]                  
              p(c_10) = [8]                  
              p(c_11) = [8] x1 + [4] x2 + [0]
        
        Following rules are strictly oriented:
        pi#(X) = [2] X + [2]                          
               > [1]                                  
               = c_6(2ndspos#(X,from(0())),from#(0()))
        
        
        Following rules are (at-least) weakly oriented:
        2ndsneg#(s(N),cons(X,cons(Y,Z))) =  [0]                                  
                                         >= [0]                                  
                                         =  c_2(2ndspos#(N,Z))                   
        
        2ndspos#(s(N),cons(X,cons(Y,Z))) =  [0]                                  
                                         >= [0]                                  
                                         =  c_4(2ndsneg#(N,Z))                   
        
                                from#(X) =  [0]                                  
                                         >= [0]                                  
                                         =  c_5(from#(s(X)))                     
        
                           plus#(s(X),Y) =  [0]                                  
                                         >= [0]                                  
                                         =  c_8(plus#(X,Y))                      
        
                          times#(s(X),Y) =  [0]                                  
                                         >= [0]                                  
                                         =  c_11(plus#(Y,times(X,Y)),times#(X,Y))
        
* Step 7: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          2ndsneg#(s(N),cons(X,cons(Y,Z))) -> c_2(2ndspos#(N,Z))
          2ndspos#(s(N),cons(X,cons(Y,Z))) -> c_4(2ndsneg#(N,Z))
          from#(X) -> c_5(from#(s(X)))
          plus#(s(X),Y) -> c_8(plus#(X,Y))
          times#(s(X),Y) -> c_11(plus#(Y,times(X,Y)),times#(X,Y))
      - Weak DPs:
          pi#(X) -> c_6(2ndspos#(X,from(0())),from#(0()))
      - Weak TRS:
          from(X) -> cons(X,from(s(X)))
          plus(0(),Y) -> Y
          plus(s(X),Y) -> s(plus(X,Y))
          times(0(),Y) -> 0()
          times(s(X),Y) -> plus(Y,times(X,Y))
      - Signature:
          {2ndsneg/2,2ndspos/2,from/1,pi/1,plus/2,square/1,times/2,2ndsneg#/2,2ndspos#/2,from#/1,pi#/1,plus#/2
          ,square#/1,times#/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1
          ,c_6/2,c_7/0,c_8/1,c_9/1,c_10/0,c_11/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {2ndsneg#,2ndspos#,from#,pi#,plus#,square#
          ,times#} and constructors {0,cons,negrecip,posrecip,rcons,rnil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE