- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] active(U11(tt,M,N)) -> mark(U12(tt,M,N))
[2] active(U12(tt,M,N)) -> mark(s(plus(N,M)))
[3] active(U21(tt,M,N)) -> mark(U22(tt,M,N))
[4] active(U22(tt,M,N)) -> mark(plus(x(N,M),N))
[5] active(plus(N,0)) -> mark(N)
[6] active(plus(N,s(M))) -> mark(U11(tt,M,N))
[7] active(x(N,0)) -> mark(0)
[8] active(x(N,s(M))) -> mark(U21(tt,M,N))
[9] active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
[10] active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
[11] active(s(X)) -> s(active(X))
[12] active(plus(X1,X2)) -> plus(active(X1),X2)
[13] active(plus(X1,X2)) -> plus(X1,active(X2))
[14] active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
[15] active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
[16] active(x(X1,X2)) -> x(active(X1),X2)
[17] active(x(X1,X2)) -> x(X1,active(X2))
[18] U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
[19] U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
[20] s(mark(X)) -> mark(s(X))
[21] plus(mark(X1),X2) -> mark(plus(X1,X2))
[22] plus(X1,mark(X2)) -> mark(plus(X1,X2))
[23] U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
[24] U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
[25] x(mark(X1),X2) -> mark(x(X1,X2))
[26] x(X1,mark(X2)) -> mark(x(X1,X2))
[27] proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
[28] proper(tt) -> ok(tt)
[29] proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
[30] proper(s(X)) -> s(proper(X))
[31] proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
[32] proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
[33] proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
[34] proper(x(X1,X2)) -> x(proper(X1),proper(X2))
[35] proper(0) -> ok(0)
[36] U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
[37] U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
[38] s(ok(X)) -> ok(s(X))
[39] plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
[40] U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
[41] U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
[42] x(ok(X1),ok(X2)) -> ok(x(X1,X2))
[43] top(mark(X)) -> top(proper(X))
[44] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(U11(tt,M,N)) , Marked_U12(tt,M,N)>
<Marked_active(U12(tt,M,N)) , Marked_s(plus(N,M))>
<Marked_active(U12(tt,M,N)) , Marked_plus(N,M)>
<Marked_active(U21(tt,M,N)) , Marked_U22(tt,M,N)>
<Marked_active(U22(tt,M,N)) , Marked_plus(x(N,M),N)>
<Marked_active(U22(tt,M,N)) , Marked_x(N,M)>
<Marked_active(plus(N,s(M))) , Marked_U11(tt,M,N)>
<Marked_active(x(N,s(M))) , Marked_U21(tt,M,N)>
<Marked_active(U11(X1,X2,X3)) , Marked_U11(active(X1),X2,X3)>
<Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U12(X1,X2,X3)) , Marked_U12(active(X1),X2,X3)>
<Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_active(plus(X1,X2)) , Marked_plus(active(X1),X2)>
<Marked_active(plus(X1,X2)) , Marked_active(X1)>
<Marked_active(plus(X1,X2)) , Marked_plus(X1,active(X2))>
<Marked_active(plus(X1,X2)) , Marked_active(X2)>
<Marked_active(U21(X1,X2,X3)) , Marked_U21(active(X1),X2,X3)>
<Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U22(X1,X2,X3)) , Marked_U22(active(X1),X2,X3)>
<Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(x(X1,X2)) , Marked_x(active(X1),X2)>
<Marked_active(x(X1,X2)) , Marked_active(X1)>
<Marked_active(x(X1,X2)) , Marked_x(X1,active(X2))>
<Marked_active(x(X1,X2)) , Marked_active(X2)>
<Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
<Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
<Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U22(mark(X1),X2,X3) , Marked_U22(X1,X2,X3)>
<Marked_x(mark(X1),X2) , Marked_x(X1,X2)>
<Marked_x(X1,mark(X2)) , Marked_x(X1,X2)>
<Marked_proper(U11(X1,X2,X3)) , Marked_U11(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U12(X1,X2,X3)) , Marked_U12(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_proper(plus(X1,X2)) , Marked_plus(proper(X1),proper(X2))>
<Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
<Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U21(X1,X2,X3)) , Marked_U21(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U22(X1,X2,X3)) , Marked_U22(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(x(X1,X2)) , Marked_x(proper(X1),proper(X2))>
<Marked_proper(x(X1,X2)) , Marked_proper(X1)>
<Marked_proper(x(X1,X2)) , Marked_proper(X2)>
<Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
<Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)>
<Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)>
<Marked_U22(ok(X1),ok(X2),ok(X3)) , Marked_U22(X1,X2,X3)>
<Marked_x(ok(X1),ok(X2)) , Marked_x(X1,X2)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 10 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(ok(X)) , Marked_top(active(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
}

{  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
      --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(x(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(x(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U22(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X1,X2,X3)) , Marked_proper(X1)>
}

{  <Marked_active(x(X1,X2)) , Marked_active(X2)> 
      --> <Marked_active(x(X1,X2)) , Marked_active(X2)>
  <Marked_active(x(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(x(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(x(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X2)>
  <Marked_active(x(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(x(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(x(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(x(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X2)>
  <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X2)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X2)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X2)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(x(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U22(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U12(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X1,X2,X3)) , Marked_active(X1)>
}

{  <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)> 
      --> <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
  <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)> 
     --> <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
  <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)> 
     --> <Marked_U11(ok(X1),ok(X2),ok(X3)) , Marked_U11(X1,X2,X3)>
  <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)> 
     --> <Marked_U11(mark(X1),X2,X3) , Marked_U11(X1,X2,X3)>
}

{  <Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)> 
      --> <Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)>
  <Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)> 
     --> <Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)>
  <Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)> 
     --> <Marked_U12(ok(X1),ok(X2),ok(X3)) , Marked_U12(X1,X2,X3)>
  <Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)> 
     --> <Marked_U12(mark(X1),X2,X3) , Marked_U12(X1,X2,X3)>
}

{  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
}

{  <Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)> 
      --> <Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
}

{  <Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)> 
      --> <Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(ok(X1),ok(X2),ok(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
}

{  <Marked_U22(ok(X1),ok(X2),ok(X3)) , Marked_U22(X1,X2,X3)> 
      --> <Marked_U22(ok(X1),ok(X2),ok(X3)) , Marked_U22(X1,X2,X3)>
  <Marked_U22(ok(X1),ok(X2),ok(X3)) , Marked_U22(X1,X2,X3)> 
     --> <Marked_U22(mark(X1),X2,X3) , Marked_U22(X1,X2,X3)>
  <Marked_U22(mark(X1),X2,X3) , Marked_U22(X1,X2,X3)> 
     --> <Marked_U22(ok(X1),ok(X2),ok(X3)) , Marked_U22(X1,X2,X3)>
  <Marked_U22(mark(X1),X2,X3) , Marked_U22(X1,X2,X3)> 
     --> <Marked_U22(mark(X1),X2,X3) , Marked_U22(X1,X2,X3)>
}

{  <Marked_x(ok(X1),ok(X2)) , Marked_x(X1,X2)> 
      --> <Marked_x(ok(X1),ok(X2)) , Marked_x(X1,X2)>
  <Marked_x(ok(X1),ok(X2)) , Marked_x(X1,X2)> 
     --> <Marked_x(X1,mark(X2)) , Marked_x(X1,X2)>
  <Marked_x(ok(X1),ok(X2)) , Marked_x(X1,X2)> 
     --> <Marked_x(mark(X1),X2) , Marked_x(X1,X2)>
  <Marked_x(X1,mark(X2)) , Marked_x(X1,X2)> 
     --> <Marked_x(ok(X1),ok(X2)) , Marked_x(X1,X2)>
  <Marked_x(X1,mark(X2)) , Marked_x(X1,X2)> 
     --> <Marked_x(X1,mark(X2)) , Marked_x(X1,X2)>
  <Marked_x(X1,mark(X2)) , Marked_x(X1,X2)> 
     --> <Marked_x(mark(X1),X2) , Marked_x(X1,X2)>
  <Marked_x(mark(X1),X2) , Marked_x(X1,X2)> 
     --> <Marked_x(ok(X1),ok(X2)) , Marked_x(X1,X2)>
  <Marked_x(mark(X1),X2) , Marked_x(X1,X2)> 
     --> <Marked_x(X1,mark(X2)) , Marked_x(X1,X2)>
  <Marked_x(mark(X1),X2) , Marked_x(X1,X2)> 
     --> <Marked_x(mark(X1),X2) , Marked_x(X1,X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  U12(mark(X1),X2,X3) >= mark(U12(X1,X2,X3)) ;
  U12(ok(X1),ok(X2),ok(X3)) >= ok(U12(X1,X2,X3)) ;
  active(U12(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(U12(X1,X2,X3)) >= U12(active(X1),X2,X3) ;
  active(U11(tt,M,N)) >= mark(U12(tt,M,N)) ;
  active(U11(X1,X2,X3)) >= U11(active(X1),X2,X3) ;
  active(s(X)) >= s(active(X)) ;
  active(plus(N,s(M))) >= mark(U11(tt,M,N)) ;
  active(plus(N,0)) >= mark(N) ;
  active(plus(X1,X2)) >= plus(active(X1),X2) ;
  active(plus(X1,X2)) >= plus(X1,active(X2)) ;
  active(U22(tt,M,N)) >= mark(plus(x(N,M),N)) ;
  active(U22(X1,X2,X3)) >= U22(active(X1),X2,X3) ;
  active(U21(tt,M,N)) >= mark(U22(tt,M,N)) ;
  active(U21(X1,X2,X3)) >= U21(active(X1),X2,X3) ;
  active(x(N,s(M))) >= mark(U21(tt,M,N)) ;
  active(x(N,0)) >= mark(0) ;
  active(x(X1,X2)) >= x(active(X1),X2) ;
  active(x(X1,X2)) >= x(X1,active(X2)) ;
  U11(mark(X1),X2,X3) >= mark(U11(X1,X2,X3)) ;
  U11(ok(X1),ok(X2),ok(X3)) >= ok(U11(X1,X2,X3)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  plus(mark(X1),X2) >= mark(plus(X1,X2)) ;
  plus(ok(X1),ok(X2)) >= ok(plus(X1,X2)) ;
  plus(X1,mark(X2)) >= mark(plus(X1,X2)) ;
  U22(mark(X1),X2,X3) >= mark(U22(X1,X2,X3)) ;
  U22(ok(X1),ok(X2),ok(X3)) >= ok(U22(X1,X2,X3)) ;
  U21(mark(X1),X2,X3) >= mark(U21(X1,X2,X3)) ;
  U21(ok(X1),ok(X2),ok(X3)) >= ok(U21(X1,X2,X3)) ;
  x(mark(X1),X2) >= mark(x(X1,X2)) ;
  x(ok(X1),ok(X2)) >= ok(x(X1,X2)) ;
  x(X1,mark(X2)) >= mark(x(X1,X2)) ;
  proper(U12(X1,X2,X3)) >= U12(proper(X1),proper(X2),proper(X3)) ;
  proper(tt) >= ok(tt) ;
  proper(U11(X1,X2,X3)) >= U11(proper(X1),proper(X2),proper(X3)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(plus(X1,X2)) >= plus(proper(X1),proper(X2)) ;
  proper(U22(X1,X2,X3)) >= U22(proper(X1),proper(X2),proper(X3)) ;
  proper(U21(X1,X2,X3)) >= U21(proper(X1),proper(X2),proper(X3)) ;
  proper(x(X1,X2)) >= x(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 48.865734 seconds (real time)
Cime Exit Status: 0