Input TRS:
    1: top(ok(U(x,y))) -> top(check(D(x,y)))
    2: D(x,B()) -> U(x,B())
    3: F(x,U(O(y),z)) -> U(x,F(y,z))
    4: F(x,U(N(y),z)) -> U(x,F(y,z))
    5: D(O(x),F(y,z)) -> F(x,D(y,z))
    6: D(N(x),F(y,z)) -> F(x,D(y,z))
    7: F(x,U(E(),y)) -> U(x,F(E(),y))
    8: D(E(),F(x,y)) -> F(E(),D(x,y))
   e1: U(O(x),y) ->= U(x,y)	[relative]
   e2: U(N(x),y) ->= U(x,y)	[relative]
   e3: D(O(x),y) ->= D(x,y)	[relative]
   e4: D(N(x),y) ->= D(x,y)	[relative]
   e5: E() ->= N(E())	[relative]
   e6: check(O(x)) ->= ok(O(x))	[relative]
   e7: check(U(x,y)) ->= U(check(x),y)	[relative]
   e8: check(U(x,y)) ->= U(x,check(y))	[relative]
   e9: check(D(x,y)) ->= D(check(x),y)	[relative]
   e10: check(D(x,y)) ->= D(x,check(y))	[relative]
   e11: check(F(x,y)) ->= F(check(x),y)	[relative]
   e12: check(F(x,y)) ->= F(x,check(y))	[relative]
   e13: check(O(x)) ->= O(check(x))	[relative]
   e14: check(N(x)) ->= N(check(x))	[relative]
   e15: U(ok(x),y) ->= ok(U(x,y))	[relative]
   e16: U(x,ok(y)) ->= ok(U(x,y))	[relative]
   e17: D(ok(x),y) ->= ok(D(x,y))	[relative]
   e18: D(x,ok(y)) ->= ok(D(x,y))	[relative]
   e19: F(ok(x),y) ->= ok(F(x,y))	[relative]
   e20: F(x,ok(y)) ->= ok(F(x,y))	[relative]
   e21: O(ok(x)) ->= ok(O(x))	[relative]
   e22: N(ok(x)) ->= ok(N(x))	[relative]
Number of Rules: 8
Direct POLO(Sum) ... removes: 3 5 e3 e1
	I(F) = x1 + x2
	I(top) = x1
	I(E) = 0
	I(D) = x1 + x2
	I(O) = x1 + 1
	I(B) = 0
	I(check) = x1
	I(ok) = x1
	I(N) = x1
	I(U) = x1 + x2
Number of Rules: 6
Direct POLO(Sum) ...Direct Mat2b ... failed.
Dependency Pairs:
   #1: # D(N(x),F(y,z)) -> # F(x,D(y,z))
   #2: # D(N(x),F(y,z)) -> # D(y,z)
   #3: # check(F(x,y)) -> # F(check(x),y)	[relative]
   #4: # check(F(x,y)) -> # check(x)	[relative]
   #5: # F(x,ok(y)) -> # F(x,y)	[relative]
   #6: # D(N(x),y) -> # D(x,y)	[relative]
   #7: # check(D(x,y)) -> # D(check(x),y)	[relative]
   #8: # check(D(x,y)) -> # check(x)	[relative]
   #9: # check(D(x,y)) -> # D(x,check(y))	[relative]
   #10: # check(D(x,y)) -> # check(y)	[relative]
   #11: # check(U(x,y)) -> # check(x)	[relative]
   #12: # F(x,U(E(),y)) -> # F(E(),y)
   #13: # check(F(x,y)) -> # F(x,check(y))	[relative]
   #14: # check(F(x,y)) -> # check(y)	[relative]
   #15: # D(x,ok(y)) -> # D(x,y)	[relative]
   #16: # check(U(x,y)) -> # check(y)	[relative]
   #17: # check(O(x)) -> # check(x)	[relative]
   #18: # F(ok(x),y) -> # F(x,y)	[relative]
   #19: # top(ok(U(x,y))) -> # top(check(D(x,y)))
   #20: # top(ok(U(x,y))) -> # check(D(x,y))
   #21: # top(ok(U(x,y))) -> # D(x,y)
   #22: # D(E(),F(x,y)) -> # F(E(),D(x,y))
   #23: # D(E(),F(x,y)) -> # D(x,y)
   #24: # D(ok(x),y) -> # D(x,y)	[relative]
   #25: # F(x,U(N(y),z)) -> # F(y,z)
   #26: # check(N(x)) -> # check(x)	[relative]
Number of SCCs: 4
  SCC { #19 }
    POLO(Sum)... QLPOS... QWPOpS(mSum)... Mat2b... failed.