'Weak Dependency Graph [60.0]'
------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    innermost runtime-complexity with respect to
  Rules: {h(f(x, y)) -> f(y, f(h(h(x)), a()))}

Details:         
  We have computed the following set of weak (innermost) dependency pairs:
   {h^#(f(x, y)) -> c_0(h^#(h(x)))}
  
  The usable rules are:
   {h(f(x, y)) -> f(y, f(h(h(x)), a()))}
  
  The estimated dependency graph contains the following edges:
   {h^#(f(x, y)) -> c_0(h^#(h(x)))}
     ==> {h^#(f(x, y)) -> c_0(h^#(h(x)))}
  
  We consider the following path(s):
   1) {h^#(f(x, y)) -> c_0(h^#(h(x)))}
      
      The usable rules for this path are the following:
      {h(f(x, y)) -> f(y, f(h(h(x)), a()))}
      
        We have applied the subprocessor on the union of usable rules and weak (innermost) dependency pairs.
        
          'Weight Gap Principle'
          ----------------------
          Answer:           YES(?,O(n^1))
          Input Problem:    innermost runtime-complexity with respect to
            Rules:
              {  h(f(x, y)) -> f(y, f(h(h(x)), a()))
               , h^#(f(x, y)) -> c_0(h^#(h(x)))}
          
          Details:         
            We apply the weight gap principle, strictly orienting the rules
            {h^#(f(x, y)) -> c_0(h^#(h(x)))}
            and weakly orienting the rules
            {}
            using the following strongly linear interpretation:
              Processor 'Matrix Interpretation' oriented the following rules strictly:
              
              {h^#(f(x, y)) -> c_0(h^#(h(x)))}
              
              Details:
                 Interpretation Functions:
                  h(x1) = [1] x1 + [1]
                  f(x1, x2) = [1] x1 + [1] x2 + [8]
                  a() = [8]
                  h^#(x1) = [1] x1 + [0]
                  c_0(x1) = [1] x1 + [0]
              
            Finally we apply the subprocessor
            'fastest of 'combine', 'Bounds with default enrichment', 'Bounds with default enrichment''
            ------------------------------------------------------------------------------------------
            Answer:           YES(?,O(n^1))
            Input Problem:    innermost relative runtime-complexity with respect to
              Strict Rules: {h(f(x, y)) -> f(y, f(h(h(x)), a()))}
              Weak Rules: {h^#(f(x, y)) -> c_0(h^#(h(x)))}
            
            Details:         
              The problem was solved by processor 'Bounds with default enrichment':
              'Bounds with default enrichment'
              --------------------------------
              Answer:           YES(?,O(n^1))
              Input Problem:    innermost relative runtime-complexity with respect to
                Strict Rules: {h(f(x, y)) -> f(y, f(h(h(x)), a()))}
                Weak Rules: {h^#(f(x, y)) -> c_0(h^#(h(x)))}
              
              Details:         
                The problem is Match-bounded by 2.
                The enriched problem is compatible with the following automaton:
                {  h_0(2) -> 6
                 , h_0(3) -> 6
                 , h_1(2) -> 10
                 , h_1(3) -> 10
                 , h_1(10) -> 8
                 , h_2(2) -> 15
                 , h_2(3) -> 15
                 , h_2(15) -> 13
                 , f_0(2, 2) -> 2
                 , f_0(2, 3) -> 2
                 , f_0(3, 2) -> 2
                 , f_0(3, 3) -> 2
                 , f_1(2, 7) -> 6
                 , f_1(2, 7) -> 10
                 , f_1(2, 7) -> 15
                 , f_1(3, 7) -> 6
                 , f_1(3, 7) -> 10
                 , f_1(3, 7) -> 15
                 , f_1(8, 9) -> 7
                 , f_2(7, 12) -> 8
                 , f_2(7, 12) -> 13
                 , f_2(13, 14) -> 12
                 , a_0() -> 3
                 , a_1() -> 9
                 , a_2() -> 14
                 , h^#_0(2) -> 4
                 , h^#_0(3) -> 4
                 , h^#_0(6) -> 5
                 , h^#_1(10) -> 11
                 , c_0_0(5) -> 4
                 , c_0_1(11) -> 5
                 , c_0_1(11) -> 11}