MAYBE

Problem:
 active(f(f(a()))) -> mark(f(g(f(a()))))
 active(g(X)) -> g(active(X))
 g(mark(X)) -> mark(g(X))
 proper(f(X)) -> f(proper(X))
 proper(a()) -> ok(a())
 proper(g(X)) -> g(proper(X))
 f(ok(X)) -> ok(f(X))
 g(ok(X)) -> ok(g(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(f(f(a()))) -> g#(f(a()))
   active#(f(f(a()))) -> f#(g(f(a())))
   active#(g(X)) -> active#(X)
   active#(g(X)) -> g#(active(X))
   g#(mark(X)) -> g#(X)
   proper#(f(X)) -> proper#(X)
   proper#(f(X)) -> f#(proper(X))
   proper#(g(X)) -> proper#(X)
   proper#(g(X)) -> g#(proper(X))
   f#(ok(X)) -> f#(X)
   g#(ok(X)) -> g#(X)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(f(f(a()))) -> mark(f(g(f(a()))))
   active(g(X)) -> g(active(X))
   g(mark(X)) -> mark(g(X))
   proper(f(X)) -> f(proper(X))
   proper(a()) -> ok(a())
   proper(g(X)) -> g(proper(X))
   f(ok(X)) -> ok(f(X))
   g(ok(X)) -> ok(g(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  EDG Processor:
   DPs:
    active#(f(f(a()))) -> g#(f(a()))
    active#(f(f(a()))) -> f#(g(f(a())))
    active#(g(X)) -> active#(X)
    active#(g(X)) -> g#(active(X))
    g#(mark(X)) -> g#(X)
    proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X))
    f#(ok(X)) -> f#(X)
    g#(ok(X)) -> g#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(f(f(a()))) -> mark(f(g(f(a()))))
    active(g(X)) -> g(active(X))
    g(mark(X)) -> mark(g(X))
    proper(f(X)) -> f(proper(X))
    proper(a()) -> ok(a())
    proper(g(X)) -> g(proper(X))
    f(ok(X)) -> ok(f(X))
    g(ok(X)) -> ok(g(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   graph:
    top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
    top#(ok(X)) -> top#(active(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
    top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a()))
    top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a())))
    top#(ok(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
    top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X))
    top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(g(X)) -> g#(proper(X)) -> g#(mark(X)) -> g#(X)
    proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X)
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X)
    f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
    g#(ok(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    active#(g(X)) -> g#(active(X)) -> g#(mark(X)) -> g#(X)
    active#(g(X)) -> g#(active(X)) -> g#(ok(X)) -> g#(X)
    active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a()))
    active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a())))
    active#(g(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    active#(g(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
   SCC Processor:
    #sccs: 5
    #rules: 8
    #arcs: 38/225
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     proper#(g(X)) -> proper#(X)
     proper#(f(X)) -> proper#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     f#(ok(X)) -> f#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     active#(g(X)) -> active#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     g#(ok(X)) -> g#(X)
     g#(mark(X)) -> g#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open