We consider the following Problem:

  Strict Trs:
    {  exp(x, 0()) -> s(0())
     , exp(x, s(y)) -> *(x, exp(x, y))
     , *(0(), y) -> 0()
     , *(s(x), y) -> +(y, *(x, y))
     , -(0(), y) -> 0()
     , -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^2))

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {  exp(x, 0()) -> s(0())
       , exp(x, s(y)) -> *(x, exp(x, y))
       , *(0(), y) -> 0()
       , *(s(x), y) -> +(y, *(x, y))
       , -(0(), y) -> 0()
       , -(x, 0()) -> x
       , -(s(x), s(y)) -> -(x, y)}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^2))
  
  Proof:
    The weightgap principle applies, where following rules are oriented strictly:
    
    TRS Component:
      {  -(0(), y) -> 0()
       , -(s(x), s(y)) -> -(x, y)}
    
    Interpretation of nonconstant growth:
    -------------------------------------
      The following argument positions are usable:
        Uargs(exp) = {}, Uargs(s) = {}, Uargs(*) = {2}, Uargs(+) = {2},
        Uargs(-) = {}
      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       exp(x1, x2) = [0 0] x1 + [0 0] x2 + [1]
                     [0 0]      [0 0]      [1]
       0() = [0]
             [0]
       s(x1) = [0 0] x1 + [1]
               [1 1]      [1]
       *(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                   [1 1]      [0 0]      [1]
       +(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                   [1 1]      [0 0]      [1]
       -(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                   [0 0]      [0 0]      [1]
    
    The strictly oriented rules are moved into the weak component.
    
    We consider the following Problem:
    
      Strict Trs:
        {  exp(x, 0()) -> s(0())
         , exp(x, s(y)) -> *(x, exp(x, y))
         , *(0(), y) -> 0()
         , *(s(x), y) -> +(y, *(x, y))
         , -(x, 0()) -> x}
      Weak Trs:
        {  -(0(), y) -> 0()
         , -(s(x), s(y)) -> -(x, y)}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^2))
    
    Proof:
      The weightgap principle applies, where following rules are oriented strictly:
      
      TRS Component: {*(0(), y) -> 0()}
      
      Interpretation of nonconstant growth:
      -------------------------------------
        The following argument positions are usable:
          Uargs(exp) = {}, Uargs(s) = {}, Uargs(*) = {2}, Uargs(+) = {2},
          Uargs(-) = {}
        We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
        Interpretation Functions:
         exp(x1, x2) = [0 0] x1 + [0 0] x2 + [1]
                       [1 1]      [0 0]      [1]
         0() = [0]
               [0]
         s(x1) = [0 0] x1 + [1]
                 [1 1]      [1]
         *(x1, x2) = [0 0] x1 + [1 0] x2 + [2]
                     [1 1]      [0 0]      [1]
         +(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                     [1 1]      [0 0]      [1]
         -(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                     [0 0]      [0 0]      [1]
      
      The strictly oriented rules are moved into the weak component.
      
      We consider the following Problem:
      
        Strict Trs:
          {  exp(x, 0()) -> s(0())
           , exp(x, s(y)) -> *(x, exp(x, y))
           , *(s(x), y) -> +(y, *(x, y))
           , -(x, 0()) -> x}
        Weak Trs:
          {  *(0(), y) -> 0()
           , -(0(), y) -> 0()
           , -(s(x), s(y)) -> -(x, y)}
        StartTerms: basic terms
        Strategy: innermost
      
      Certificate: YES(?,O(n^2))
      
      Proof:
        The weightgap principle applies, where following rules are oriented strictly:
        
        TRS Component: {exp(x, 0()) -> s(0())}
        
        Interpretation of nonconstant growth:
        -------------------------------------
          The following argument positions are usable:
            Uargs(exp) = {}, Uargs(s) = {}, Uargs(*) = {2}, Uargs(+) = {2},
            Uargs(-) = {}
          We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
          Interpretation Functions:
           exp(x1, x2) = [0 0] x1 + [0 0] x2 + [1]
                         [0 0]      [0 0]      [1]
           0() = [0]
                 [0]
           s(x1) = [0 0] x1 + [0]
                   [1 1]      [0]
           *(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                       [0 0]      [0 0]      [1]
           +(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                       [1 1]      [0 0]      [1]
           -(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                       [0 0]      [0 0]      [1]
        
        The strictly oriented rules are moved into the weak component.
        
        We consider the following Problem:
        
          Strict Trs:
            {  exp(x, s(y)) -> *(x, exp(x, y))
             , *(s(x), y) -> +(y, *(x, y))
             , -(x, 0()) -> x}
          Weak Trs:
            {  exp(x, 0()) -> s(0())
             , *(0(), y) -> 0()
             , -(0(), y) -> 0()
             , -(s(x), s(y)) -> -(x, y)}
          StartTerms: basic terms
          Strategy: innermost
        
        Certificate: YES(?,O(n^2))
        
        Proof:
          The weightgap principle applies, where following rules are oriented strictly:
          
          TRS Component: {-(x, 0()) -> x}
          
          Interpretation of nonconstant growth:
          -------------------------------------
            The following argument positions are usable:
              Uargs(exp) = {}, Uargs(s) = {}, Uargs(*) = {2}, Uargs(+) = {2},
              Uargs(-) = {}
            We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
            Interpretation Functions:
             exp(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                           [0 0]      [0 0]      [1]
             0() = [0]
                   [0]
             s(x1) = [1 0] x1 + [0]
                     [0 1]      [1]
             *(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                         [0 0]      [0 0]      [1]
             +(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                         [0 1]      [0 0]      [1]
             -(x1, x2) = [1 0] x1 + [0 0] x2 + [1]
                         [0 1]      [0 0]      [1]
          
          The strictly oriented rules are moved into the weak component.
          
          We consider the following Problem:
          
            Strict Trs:
              {  exp(x, s(y)) -> *(x, exp(x, y))
               , *(s(x), y) -> +(y, *(x, y))}
            Weak Trs:
              {  -(x, 0()) -> x
               , exp(x, 0()) -> s(0())
               , *(0(), y) -> 0()
               , -(0(), y) -> 0()
               , -(s(x), s(y)) -> -(x, y)}
            StartTerms: basic terms
            Strategy: innermost
          
          Certificate: YES(?,O(n^2))
          
          Proof:
            The weightgap principle applies, where following rules are oriented strictly:
            
            TRS Component: {exp(x, s(y)) -> *(x, exp(x, y))}
            
            Interpretation of nonconstant growth:
            -------------------------------------
              The following argument positions are usable:
                Uargs(exp) = {}, Uargs(s) = {}, Uargs(*) = {2}, Uargs(+) = {2},
                Uargs(-) = {}
              We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
              Interpretation Functions:
               exp(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                             [0 0]      [0 0]      [1]
               0() = [0]
                     [0]
               s(x1) = [1 0] x1 + [1]
                       [0 1]      [1]
               *(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                           [0 0]      [0 0]      [1]
               +(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                           [1 0]      [0 0]      [1]
               -(x1, x2) = [1 0] x1 + [0 0] x2 + [1]
                           [0 1]      [0 0]      [1]
            
            The strictly oriented rules are moved into the weak component.
            
            We consider the following Problem:
            
              Strict Trs: {*(s(x), y) -> +(y, *(x, y))}
              Weak Trs:
                {  exp(x, s(y)) -> *(x, exp(x, y))
                 , -(x, 0()) -> x
                 , exp(x, 0()) -> s(0())
                 , *(0(), y) -> 0()
                 , -(0(), y) -> 0()
                 , -(s(x), s(y)) -> -(x, y)}
              StartTerms: basic terms
              Strategy: innermost
            
            Certificate: YES(?,O(n^2))
            
            Proof:
              We consider the following Problem:
              
                Strict Trs: {*(s(x), y) -> +(y, *(x, y))}
                Weak Trs:
                  {  exp(x, s(y)) -> *(x, exp(x, y))
                   , -(x, 0()) -> x
                   , exp(x, 0()) -> s(0())
                   , *(0(), y) -> 0()
                   , -(0(), y) -> 0()
                   , -(s(x), s(y)) -> -(x, y)}
                StartTerms: basic terms
                Strategy: innermost
              
              Certificate: YES(?,O(n^2))
              
              Proof:
                The following argument positions are usable:
                  Uargs(exp) = {}, Uargs(s) = {}, Uargs(*) = {2}, Uargs(+) = {2},
                  Uargs(-) = {}
                We have the following restricted  polynomial interpretation:
                Interpretation Functions:
                 [exp](x1, x2) = 3 + x1 + 2*x1*x2 + x2^2
                 [0]() = 2
                 [s](x1) = 2 + x1
                 [*](x1, x2) = 2 + 3*x1 + x2
                 [+](x1, x2) = 2 + x2
                 [-](x1, x2) = 1 + 2*x1 + 2*x2

Hurray, we answered YES(?,O(n^2))