MAYBE

Problem:
 f(s(x),y,b()) -> f(g(h(x)),y,i(y))
 g(h(x)) -> g(x)
 g(s(x)) -> s(x)
 g(0()) -> s(0())
 h(0()) -> a()
 i(0()) -> b()
 i(s(y)) -> i(y)

Proof:
 DP Processor:
  DPs:
   f#(s(x),y,b()) -> i#(y)
   f#(s(x),y,b()) -> h#(x)
   f#(s(x),y,b()) -> g#(h(x))
   f#(s(x),y,b()) -> f#(g(h(x)),y,i(y))
   g#(h(x)) -> g#(x)
   i#(s(y)) -> i#(y)
  TRS:
   f(s(x),y,b()) -> f(g(h(x)),y,i(y))
   g(h(x)) -> g(x)
   g(s(x)) -> s(x)
   g(0()) -> s(0())
   h(0()) -> a()
   i(0()) -> b()
   i(s(y)) -> i(y)
  CDG Processor:
   DPs:
    f#(s(x),y,b()) -> i#(y)
    f#(s(x),y,b()) -> h#(x)
    f#(s(x),y,b()) -> g#(h(x))
    f#(s(x),y,b()) -> f#(g(h(x)),y,i(y))
    g#(h(x)) -> g#(x)
    i#(s(y)) -> i#(y)
   TRS:
    f(s(x),y,b()) -> f(g(h(x)),y,i(y))
    g(h(x)) -> g(x)
    g(s(x)) -> s(x)
    g(0()) -> s(0())
    h(0()) -> a()
    i(0()) -> b()
    i(s(y)) -> i(y)
   graph:
    g#(h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
    i#(s(y)) -> i#(y) -> i#(s(y)) -> i#(y)
    f#(s(x),y,b()) -> g#(h(x)) -> g#(h(x)) -> g#(x)
    f#(s(x),y,b()) -> i#(y) -> i#(s(y)) -> i#(y)
    f#(s(x),y,b()) -> f#(g(h(x)),y,i(y)) ->
    f#(s(x),y,b()) -> i#(y)
    f#(s(x),y,b()) -> f#(g(h(x)),y,i(y)) ->
    f#(s(x),y,b()) -> h#(x)
    f#(s(x),y,b()) -> f#(g(h(x)),y,i(y)) ->
    f#(s(x),y,b()) -> g#(h(x))
    f#(s(x),y,b()) -> f#(g(h(x)),y,i(y)) -> f#(s(x),y,b()) -> f#(g(h(x)),y,i(y))
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 8/36
    DPs:
     f#(s(x),y,b()) -> f#(g(h(x)),y,i(y))
    TRS:
     f(s(x),y,b()) -> f(g(h(x)),y,i(y))
     g(h(x)) -> g(x)
     g(s(x)) -> s(x)
     g(0()) -> s(0())
     h(0()) -> a()
     i(0()) -> b()
     i(s(y)) -> i(y)
    Open
    
    DPs:
     i#(s(y)) -> i#(y)
    TRS:
     f(s(x),y,b()) -> f(g(h(x)),y,i(y))
     g(h(x)) -> g(x)
     g(s(x)) -> s(x)
     g(0()) -> s(0())
     h(0()) -> a()
     i(0()) -> b()
     i(s(y)) -> i(y)
    Open
    
    DPs:
     g#(h(x)) -> g#(x)
    TRS:
     f(s(x),y,b()) -> f(g(h(x)),y,i(y))
     g(h(x)) -> g(x)
     g(s(x)) -> s(x)
     g(0()) -> s(0())
     h(0()) -> a()
     i(0()) -> b()
     i(s(y)) -> i(y)
    Open