Problem:
 g(a()) -> f(g(a()))
 g(b()) -> c()
 a() -> b()
 f(x) -> h(x,x)
 h(x,y) -> c()

Proof:
 Church Rosser Transformation Processor (critical pair closing system, Thm 2.11):
  g(b()) -> c()
  f(x24) -> h(x24,x24)
  h(x28,x26) -> c()
  critical peaks: joinable
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [c] = 0,
    
    [g](x0) = x0,
    
    [b] = 4,
    
    [h](x0, x1) = 2x0 + 2x1,
    
    [f](x0) = 4x0
   orientation:
    g(b()) = 4 >= 0 = c()
    
    f(x24) = 4x24 >= 4x24 = h(x24,x24)
    
    h(x28,x26) = 2x26 + 2x28 >= 0 = c()
   problem:
    f(x24) -> h(x24,x24)
    h(x28,x26) -> c()
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [c] = 0,
     
     [h](x0, x1) = 2x0 + 4x1,
     
     [f](x0) = 6x0 + 4
    orientation:
     f(x24) = 6x24 + 4 >= 6x24 = h(x24,x24)
     
     h(x28,x26) = 4x26 + 2x28 >= 0 = c()
    problem:
     h(x28,x26) -> c()
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [c] = 0,
      
      [h](x0, x1) = 4x0 + 4x1 + 4
     orientation:
      h(x28,x26) = 4x26 + 4x28 + 4 >= 0 = c()
     problem:
      
     Qed