MAYBE

Problem:
 :(:(x,y),z) -> :(x,:(y,z))
 :(+(x,y),z) -> +(:(x,z),:(y,z))
 :(z,+(x,f(y))) -> :(g(z,y),+(x,a()))

Proof:
 DP Processor:
  DPs:
   :#(:(x,y),z) -> :#(y,z)
   :#(:(x,y),z) -> :#(x,:(y,z))
   :#(+(x,y),z) -> :#(y,z)
   :#(+(x,y),z) -> :#(x,z)
   :#(z,+(x,f(y))) -> :#(g(z,y),+(x,a()))
  TRS:
   :(:(x,y),z) -> :(x,:(y,z))
   :(+(x,y),z) -> +(:(x,z),:(y,z))
   :(z,+(x,f(y))) -> :(g(z,y),+(x,a()))
  Restore Modifier:
   DPs:
    :#(:(x,y),z) -> :#(y,z)
    :#(:(x,y),z) -> :#(x,:(y,z))
    :#(+(x,y),z) -> :#(y,z)
    :#(+(x,y),z) -> :#(x,z)
    :#(z,+(x,f(y))) -> :#(g(z,y),+(x,a()))
   TRS:
    :(:(x,y),z) -> :(x,:(y,z))
    :(+(x,y),z) -> +(:(x,z),:(y,z))
    :(z,+(x,f(y))) -> :(g(z,y),+(x,a()))
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 25/25
    DPs:
     :#(:(x,y),z) -> :#(y,z)
     :#(:(x,y),z) -> :#(x,:(y,z))
     :#(+(x,y),z) -> :#(y,z)
     :#(+(x,y),z) -> :#(x,z)
     :#(z,+(x,f(y))) -> :#(g(z,y),+(x,a()))
    TRS:
     :(:(x,y),z) -> :(x,:(y,z))
     :(+(x,y),z) -> +(:(x,z),:(y,z))
     :(z,+(x,f(y))) -> :(g(z,y),+(x,a()))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [:#](x0, x1) = x1,
      
      [a] = 0,
      
      [g](x0, x1) = 0,
      
      [f](x0) = 1,
      
      [+](x0, x1) = x1,
      
      [:](x0, x1) = 0
     orientation:
      :#(:(x,y),z) = z >= z = :#(y,z)
      
      :#(:(x,y),z) = z >= 0 = :#(x,:(y,z))
      
      :#(+(x,y),z) = z >= z = :#(y,z)
      
      :#(+(x,y),z) = z >= z = :#(x,z)
      
      :#(z,+(x,f(y))) = 1 >= 0 = :#(g(z,y),+(x,a()))
      
      :(:(x,y),z) = 0 >= 0 = :(x,:(y,z))
      
      :(+(x,y),z) = 0 >= 0 = +(:(x,z),:(y,z))
      
      :(z,+(x,f(y))) = 0 >= 0 = :(g(z,y),+(x,a()))
     problem:
      DPs:
       :#(:(x,y),z) -> :#(y,z)
       :#(:(x,y),z) -> :#(x,:(y,z))
       :#(+(x,y),z) -> :#(y,z)
       :#(+(x,y),z) -> :#(x,z)
      TRS:
       :(:(x,y),z) -> :(x,:(y,z))
       :(+(x,y),z) -> +(:(x,z),:(y,z))
       :(z,+(x,f(y))) -> :(g(z,y),+(x,a()))
     Open