MAYBE

Problem:
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 +(0(),y) -> y
 +(s(x),y) -> s(+(x,y))
 +(x,+(y,z)) -> +(+(x,y),z)
 f(g(f(x))) -> f(h(s(0()),x))
 f(g(h(x,y))) -> f(h(s(x),y))
 f(h(x,h(y,z))) -> f(h(+(x,y),z))

Proof:
 DP Processor:
  DPs:
   +#(x,s(y)) -> +#(x,y)
   +#(s(x),y) -> +#(x,y)
   +#(x,+(y,z)) -> +#(x,y)
   +#(x,+(y,z)) -> +#(+(x,y),z)
   f#(g(f(x))) -> f#(h(s(0()),x))
   f#(g(h(x,y))) -> f#(h(s(x),y))
   f#(h(x,h(y,z))) -> +#(x,y)
   f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
  TRS:
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   +(0(),y) -> y
   +(s(x),y) -> s(+(x,y))
   +(x,+(y,z)) -> +(+(x,y),z)
   f(g(f(x))) -> f(h(s(0()),x))
   f(g(h(x,y))) -> f(h(s(x),y))
   f(h(x,h(y,z))) -> f(h(+(x,y),z))
  Usable Rule Processor:
   DPs:
    +#(x,s(y)) -> +#(x,y)
    +#(s(x),y) -> +#(x,y)
    +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(+(x,y),z)
    f#(g(f(x))) -> f#(h(s(0()),x))
    f#(g(h(x,y))) -> f#(h(s(x),y))
    f#(h(x,h(y,z))) -> +#(x,y)
    f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
   TRS:
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    +(0(),y) -> y
    +(s(x),y) -> s(+(x,y))
    +(x,+(y,z)) -> +(+(x,y),z)
   EDG Processor:
    DPs:
     +#(x,s(y)) -> +#(x,y)
     +#(s(x),y) -> +#(x,y)
     +#(x,+(y,z)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(+(x,y),z)
     f#(g(f(x))) -> f#(h(s(0()),x))
     f#(g(h(x,y))) -> f#(h(s(x),y))
     f#(h(x,h(y,z))) -> +#(x,y)
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
    TRS:
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     +(0(),y) -> y
     +(s(x),y) -> s(+(x,y))
     +(x,+(y,z)) -> +(+(x,y),z)
    graph:
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z)) ->
     f#(h(x,h(y,z))) -> +#(x,y)
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z)) ->
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
     f#(h(x,h(y,z))) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
     f#(h(x,h(y,z))) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
     f#(h(x,h(y,z))) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
     f#(h(x,h(y,z))) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
     f#(g(h(x,y))) -> f#(h(s(x),y)) -> f#(h(x,h(y,z))) -> +#(x,y)
     f#(g(h(x,y))) -> f#(h(s(x),y)) ->
     f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
     f#(g(f(x))) -> f#(h(s(0()),x)) -> f#(h(x,h(y,z))) -> +#(x,y)
     f#(g(f(x))) -> f#(h(s(0()),x)) -> f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
     +#(s(x),y) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
     +#(s(x),y) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
     +#(s(x),y) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
     +#(s(x),y) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
     +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
     +#(x,s(y)) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
     +#(x,s(y)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
     +#(x,s(y)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
     +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,s(y)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(s(x),y) -> +#(x,y)
     +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z)
     +#(x,+(y,z)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
     +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
     +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    Restore Modifier:
     DPs:
      +#(x,s(y)) -> +#(x,y)
      +#(s(x),y) -> +#(x,y)
      +#(x,+(y,z)) -> +#(x,y)
      +#(x,+(y,z)) -> +#(+(x,y),z)
      f#(g(f(x))) -> f#(h(s(0()),x))
      f#(g(h(x,y))) -> f#(h(s(x),y))
      f#(h(x,h(y,z))) -> +#(x,y)
      f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
     TRS:
      +(x,0()) -> x
      +(x,s(y)) -> s(+(x,y))
      +(0(),y) -> y
      +(s(x),y) -> s(+(x,y))
      +(x,+(y,z)) -> +(+(x,y),z)
      f(g(f(x))) -> f(h(s(0()),x))
      f(g(h(x,y))) -> f(h(s(x),y))
      f(h(x,h(y,z))) -> f(h(+(x,y),z))
     SCC Processor:
      #sccs: 2
      #rules: 5
      #arcs: 26/64
      DPs:
       f#(h(x,h(y,z))) -> f#(h(+(x,y),z))
      TRS:
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       +(x,+(y,z)) -> +(+(x,y),z)
       f(g(f(x))) -> f(h(s(0()),x))
       f(g(h(x,y))) -> f(h(s(x),y))
       f(h(x,h(y,z))) -> f(h(+(x,y),z))
      Open
      
      DPs:
       +#(x,+(y,z)) -> +#(+(x,y),z)
       +#(x,+(y,z)) -> +#(x,y)
       +#(s(x),y) -> +#(x,y)
       +#(x,s(y)) -> +#(x,y)
      TRS:
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       +(x,+(y,z)) -> +(+(x,y),z)
       f(g(f(x))) -> f(h(s(0()),x))
       f(g(h(x,y))) -> f(h(s(x),y))
       f(h(x,h(y,z))) -> f(h(+(x,y),z))
      Open