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

Details:         
  We have computed the following set of weak (innermost) dependency pairs:
   {c^#(a(b(a(b(x1))))) -> c_0(c^#(a(b(c(a(x1))))))}
  
  The usable rules are:
   {c(a(b(a(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(x1)))))))))))))}
  
  The estimated dependency graph contains the following edges:
   {c^#(a(b(a(b(x1))))) -> c_0(c^#(a(b(c(a(x1))))))}
     ==> {c^#(a(b(a(b(x1))))) -> c_0(c^#(a(b(c(a(x1))))))}
  
  We consider the following path(s):
   1) {c^#(a(b(a(b(x1))))) -> c_0(c^#(a(b(c(a(x1))))))}
      
      The usable rules for this path are the following:
      {c(a(b(a(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(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(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(x1)))))))))))))
               , c^#(a(b(a(b(x1))))) -> c_0(c^#(a(b(c(a(x1))))))}
          
          Details:         
            We apply the weight gap principle, strictly orienting the rules
            {c^#(a(b(a(b(x1))))) -> c_0(c^#(a(b(c(a(x1))))))}
            and weakly orienting the rules
            {}
            using the following strongly linear interpretation:
              Processor 'Matrix Interpretation' oriented the following rules strictly:
              
              {c^#(a(b(a(b(x1))))) -> c_0(c^#(a(b(c(a(x1))))))}
              
              Details:
                 Interpretation Functions:
                  c(x1) = [1] x1 + [0]
                  a(x1) = [1] x1 + [0]
                  b(x1) = [1] x1 + [8]
                  c^#(x1) = [1] x1 + [0]
                  c_0(x1) = [1] x1 + [4]
              
            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:
                {c(a(b(a(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(x1)))))))))))))}
              Weak Rules: {c^#(a(b(a(b(x1))))) -> c_0(c^#(a(b(c(a(x1))))))}
            
            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:
                  {c(a(b(a(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(x1)))))))))))))}
                Weak Rules: {c^#(a(b(a(b(x1))))) -> c_0(c^#(a(b(c(a(x1))))))}
              
              Details:         
                The problem is Match-bounded by 2.
                The enriched problem is compatible with the following automaton:
                {  c_0(2) -> 8
                 , c_1(17) -> 16
                 , c_1(20) -> 19
                 , c_1(26) -> 25
                 , c_2(35) -> 34
                 , c_2(38) -> 37
                 , a_0(2) -> 2
                 , a_0(3) -> 2
                 , a_0(7) -> 6
                 , a_1(2) -> 20
                 , a_1(3) -> 20
                 , a_1(9) -> 8
                 , a_1(9) -> 19
                 , a_1(10) -> 26
                 , a_1(11) -> 10
                 , a_1(14) -> 13
                 , a_1(18) -> 17
                 , a_1(24) -> 23
                 , a_2(10) -> 38
                 , a_2(27) -> 16
                 , a_2(29) -> 28
                 , a_2(32) -> 31
                 , a_2(36) -> 35
                 , b_0(2) -> 3
                 , b_0(3) -> 3
                 , b_0(8) -> 7
                 , b_1(10) -> 9
                 , b_1(12) -> 11
                 , b_1(13) -> 12
                 , b_1(15) -> 14
                 , b_1(16) -> 15
                 , b_1(19) -> 18
                 , b_1(25) -> 24
                 , b_2(28) -> 27
                 , b_2(30) -> 29
                 , b_2(31) -> 30
                 , b_2(33) -> 32
                 , b_2(34) -> 33
                 , b_2(37) -> 36
                 , c^#_0(2) -> 4
                 , c^#_0(3) -> 4
                 , c^#_0(6) -> 5
                 , c^#_1(17) -> 21
                 , c^#_1(23) -> 22
                 , c^#_2(35) -> 39
                 , c_0_0(5) -> 4
                 , c_0_1(21) -> 4
                 , c_0_1(22) -> 5
                 , c_0_1(22) -> 21
                 , c_0_2(39) -> 21}