Problem:
 c() -> f(n__g(n__c()))
 f(n__g(X)) -> g(activate(X))
 g(X) -> n__g(X)
 c() -> n__c()
 activate(n__g(X)) -> g(X)
 activate(n__c()) -> c()
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = x0,
   
   [activate](x0) = x0 + 1,
   
   [f](x0) = 4x0 + 1,
   
   [n__g](x0) = x0,
   
   [n__c] = 0,
   
   [c] = 1
  orientation:
   c() = 1 >= 1 = f(n__g(n__c()))
   
   f(n__g(X)) = 4X + 1 >= X + 1 = g(activate(X))
   
   g(X) = X >= X = n__g(X)
   
   c() = 1 >= 0 = n__c()
   
   activate(n__g(X)) = X + 1 >= X = g(X)
   
   activate(n__c()) = 1 >= 1 = c()
   
   activate(X) = X + 1 >= X = X
  problem:
   c() -> f(n__g(n__c()))
   f(n__g(X)) -> g(activate(X))
   g(X) -> n__g(X)
   activate(n__c()) -> c()
  Unfolding Processor:
   loop length: 3
   terms:
    c()
    f(n__g(n__c()))
    g(activate(n__c()))
   context: g([])
   substitution:
    
   Qed