Problem:
 a__g(X) -> a__h(X)
 a__c() -> d()
 a__h(d()) -> a__g(c())
 mark(g(X)) -> a__g(X)
 mark(h(X)) -> a__h(X)
 mark(c()) -> a__c()
 mark(d()) -> d()
 a__g(X) -> g(X)
 a__h(X) -> h(X)
 a__c() -> c()

Proof:
 Complexity Transformation Processor:
  strict:
   a__g(X) -> a__h(X)
   a__c() -> d()
   a__h(d()) -> a__g(c())
   mark(g(X)) -> a__g(X)
   mark(h(X)) -> a__h(X)
   mark(c()) -> a__c()
   mark(d()) -> d()
   a__g(X) -> g(X)
   a__h(X) -> h(X)
   a__c() -> c()
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [h](x0) = x0 + 12,
     
     [mark](x0) = x0 + 6,
     
     [g](x0) = x0 + 12,
     
     [c] = 4,
     
     [d] = 0,
     
     [a__c] = 5,
     
     [a__h](x0) = x0,
     
     [a__g](x0) = x0 + 8
    orientation:
     a__g(X) = X + 8 >= X = a__h(X)
     
     a__c() = 5 >= 0 = d()
     
     a__h(d()) = 0 >= 12 = a__g(c())
     
     mark(g(X)) = X + 18 >= X + 8 = a__g(X)
     
     mark(h(X)) = X + 18 >= X = a__h(X)
     
     mark(c()) = 10 >= 5 = a__c()
     
     mark(d()) = 6 >= 0 = d()
     
     a__g(X) = X + 8 >= X + 12 = g(X)
     
     a__h(X) = X >= X + 12 = h(X)
     
     a__c() = 5 >= 4 = c()
    problem:
     strict:
      a__h(d()) -> a__g(c())
      a__g(X) -> g(X)
      a__h(X) -> h(X)
     weak:
      a__g(X) -> a__h(X)
      a__c() -> d()
      mark(g(X)) -> a__g(X)
      mark(h(X)) -> a__h(X)
      mark(c()) -> a__c()
      mark(d()) -> d()
      a__c() -> c()
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [h](x0) = x0 + 7,
       
       [mark](x0) = x0 + 1,
       
       [g](x0) = x0 + 7,
       
       [c] = 0,
       
       [d] = 1,
       
       [a__c] = 1,
       
       [a__h](x0) = x0 + 8,
       
       [a__g](x0) = x0 + 8
      orientation:
       a__h(d()) = 9 >= 8 = a__g(c())
       
       a__g(X) = X + 8 >= X + 7 = g(X)
       
       a__h(X) = X + 8 >= X + 7 = h(X)
       
       a__g(X) = X + 8 >= X + 8 = a__h(X)
       
       a__c() = 1 >= 1 = d()
       
       mark(g(X)) = X + 8 >= X + 8 = a__g(X)
       
       mark(h(X)) = X + 8 >= X + 8 = a__h(X)
       
       mark(c()) = 1 >= 1 = a__c()
       
       mark(d()) = 2 >= 1 = d()
       
       a__c() = 1 >= 0 = c()
      problem:
       strict:
        
       weak:
        a__h(d()) -> a__g(c())
        a__g(X) -> g(X)
        a__h(X) -> h(X)
        a__g(X) -> a__h(X)
        a__c() -> d()
        mark(g(X)) -> a__g(X)
        mark(h(X)) -> a__h(X)
        mark(c()) -> a__c()
        mark(d()) -> d()
        a__c() -> c()
      Qed