'Weak Dependency Graph [60.0]'
------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    innermost runtime-complexity with respect to
  Rules: {c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))}

Details:         
  We have computed the following set of weak (innermost) dependency pairs:
   {c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))}
  
  The usable rules are:
   {c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))}
  
  The estimated dependency graph contains the following edges:
   {c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))}
     ==> {c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))}
  
  We consider the following path(s):
   1) {c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))}
      
      The usable rules for this path are the following:
      {c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))}
      
        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:
              {  c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))
               , c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))}
          
          Details:         
            'fastest of 'combine', 'Bounds with default enrichment', 'Bounds with default enrichment''
            ------------------------------------------------------------------------------------------
            Answer:           YES(?,O(n^1))
            Input Problem:    innermost runtime-complexity with respect to
              Rules:
                {  c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))
                 , c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))}
            
            Details:         
              The problem was solved by processor 'Bounds with default enrichment':
              'Bounds with default enrichment'
              --------------------------------
              Answer:           YES(?,O(n^1))
              Input Problem:    innermost runtime-complexity with respect to
                Rules:
                  {  c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))
                   , c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))}
              
              Details:         
                The problem is Match-bounded by 2.
                The enriched problem is compatible with the following automaton:
                {  c_1(6) -> 14
                 , c_1(9) -> 8
                 , c_2(16) -> 24
                 , c_2(19) -> 18
                 , a_0(2) -> 2
                 , a_0(3) -> 2
                 , a_1(7) -> 6
                 , a_1(10) -> 9
                 , a_1(11) -> 8
                 , a_1(13) -> 12
                 , a_1(14) -> 13
                 , a_2(17) -> 16
                 , a_2(20) -> 19
                 , a_2(21) -> 14
                 , a_2(23) -> 22
                 , a_2(24) -> 23
                 , b_0(2) -> 3
                 , b_0(3) -> 3
                 , b_1(2) -> 10
                 , b_1(3) -> 10
                 , b_1(8) -> 7
                 , b_1(12) -> 11
                 , b_2(11) -> 20
                 , b_2(18) -> 17
                 , b_2(22) -> 21
                 , c^#_0(2) -> 4
                 , c^#_0(3) -> 4
                 , c^#_1(6) -> 5
                 , c^#_2(16) -> 15
                 , c_0_1(5) -> 4
                 , c_0_2(15) -> 5}