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

TRS termination of:
[1] active(zeros) -> mark(cons(0,zeros))
[2] active(U11(tt)) -> mark(tt)
[3] active(U21(tt)) -> mark(tt)
[4] active(U31(tt)) -> mark(tt)
[5] active(U41(tt,V2)) -> mark(U42(isNatIList(V2)))
[6] active(U42(tt)) -> mark(tt)
[7] active(U51(tt,V2)) -> mark(U52(isNatList(V2)))
[8] active(U52(tt)) -> mark(tt)
[9] active(U61(tt,L,N)) -> mark(U62(isNat(N),L))
[10] active(U62(tt,L)) -> mark(s(length(L)))
[11] active(isNat(0)) -> mark(tt)
[12] active(isNat(length(V1))) -> mark(U11(isNatList(V1)))
[13] active(isNat(s(V1))) -> mark(U21(isNat(V1)))
[14] active(isNatIList(V)) -> mark(U31(isNatList(V)))
[15] active(isNatIList(zeros)) -> mark(tt)
[16] active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2))
[17] active(isNatList(nil)) -> mark(tt)
[18] active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2))
[19] active(length(nil)) -> mark(0)
[20] active(length(cons(N,L))) -> mark(U61(isNatList(L),L,N))
[21] active(cons(X1,X2)) -> cons(active(X1),X2)
[22] active(U11(X)) -> U11(active(X))
[23] active(U21(X)) -> U21(active(X))
[24] active(U31(X)) -> U31(active(X))
[25] active(U41(X1,X2)) -> U41(active(X1),X2)
[26] active(U42(X)) -> U42(active(X))
[27] active(U51(X1,X2)) -> U51(active(X1),X2)
[28] active(U52(X)) -> U52(active(X))
[29] active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
[30] active(U62(X1,X2)) -> U62(active(X1),X2)
[31] active(s(X)) -> s(active(X))
[32] active(length(X)) -> length(active(X))
[33] cons(mark(X1),X2) -> mark(cons(X1,X2))
[34] U11(mark(X)) -> mark(U11(X))
[35] U21(mark(X)) -> mark(U21(X))
[36] U31(mark(X)) -> mark(U31(X))
[37] U41(mark(X1),X2) -> mark(U41(X1,X2))
[38] U42(mark(X)) -> mark(U42(X))
[39] U51(mark(X1),X2) -> mark(U51(X1,X2))
[40] U52(mark(X)) -> mark(U52(X))
[41] U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
[42] U62(mark(X1),X2) -> mark(U62(X1,X2))
[43] s(mark(X)) -> mark(s(X))
[44] length(mark(X)) -> mark(length(X))
[45] proper(zeros) -> ok(zeros)
[46] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[47] proper(0) -> ok(0)
[48] proper(U11(X)) -> U11(proper(X))
[49] proper(tt) -> ok(tt)
[50] proper(U21(X)) -> U21(proper(X))
[51] proper(U31(X)) -> U31(proper(X))
[52] proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
[53] proper(U42(X)) -> U42(proper(X))
[54] proper(isNatIList(X)) -> isNatIList(proper(X))
[55] proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
[56] proper(U52(X)) -> U52(proper(X))
[57] proper(isNatList(X)) -> isNatList(proper(X))
[58] proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
[59] proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
[60] proper(isNat(X)) -> isNat(proper(X))
[61] proper(s(X)) -> s(proper(X))
[62] proper(length(X)) -> length(proper(X))
[63] proper(nil) -> ok(nil)
[64] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[65] U11(ok(X)) -> ok(U11(X))
[66] U21(ok(X)) -> ok(U21(X))
[67] U31(ok(X)) -> ok(U31(X))
[68] U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
[69] U42(ok(X)) -> ok(U42(X))
[70] isNatIList(ok(X)) -> ok(isNatIList(X))
[71] U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
[72] U52(ok(X)) -> ok(U52(X))
[73] isNatList(ok(X)) -> ok(isNatList(X))
[74] U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
[75] U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
[76] isNat(ok(X)) -> ok(isNat(X))
[77] s(ok(X)) -> ok(s(X))
[78] length(ok(X)) -> ok(length(X))
[79] top(mark(X)) -> top(proper(X))
[80] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(zeros) , Marked_cons(0,zeros)>
<Marked_active(U41(tt,V2)) , Marked_U42(isNatIList(V2))>
<Marked_active(U41(tt,V2)) , Marked_isNatIList(V2)>
<Marked_active(U51(tt,V2)) , Marked_U52(isNatList(V2))>
<Marked_active(U51(tt,V2)) , Marked_isNatList(V2)>
<Marked_active(U61(tt,L,N)) , Marked_U62(isNat(N),L)>
<Marked_active(U61(tt,L,N)) , Marked_isNat(N)>
<Marked_active(U62(tt,L)) , Marked_s(length(L))>
<Marked_active(U62(tt,L)) , Marked_length(L)>
<Marked_active(isNat(length(V1))) , Marked_U11(isNatList(V1))>
<Marked_active(isNat(length(V1))) , Marked_isNatList(V1)>
<Marked_active(isNat(s(V1))) , Marked_U21(isNat(V1))>
<Marked_active(isNat(s(V1))) , Marked_isNat(V1)>
<Marked_active(isNatIList(V)) , Marked_U31(isNatList(V))>
<Marked_active(isNatIList(V)) , Marked_isNatList(V)>
<Marked_active(isNatIList(cons(V1,V2))) , Marked_U41(isNat(V1),V2)>
<Marked_active(isNatIList(cons(V1,V2))) , Marked_isNat(V1)>
<Marked_active(isNatList(cons(V1,V2))) , Marked_U51(isNat(V1),V2)>
<Marked_active(isNatList(cons(V1,V2))) , Marked_isNat(V1)>
<Marked_active(length(cons(N,L))) , Marked_U61(isNatList(L),L,N)>
<Marked_active(length(cons(N,L))) , Marked_isNatList(L)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(U11(X)) , Marked_U11(active(X))>
<Marked_active(U11(X)) , Marked_active(X)>
<Marked_active(U21(X)) , Marked_U21(active(X))>
<Marked_active(U21(X)) , Marked_active(X)>
<Marked_active(U31(X)) , Marked_U31(active(X))>
<Marked_active(U31(X)) , Marked_active(X)>
<Marked_active(U41(X1,X2)) , Marked_U41(active(X1),X2)>
<Marked_active(U41(X1,X2)) , Marked_active(X1)>
<Marked_active(U42(X)) , Marked_U42(active(X))>
<Marked_active(U42(X)) , Marked_active(X)>
<Marked_active(U51(X1,X2)) , Marked_U51(active(X1),X2)>
<Marked_active(U51(X1,X2)) , Marked_active(X1)>
<Marked_active(U52(X)) , Marked_U52(active(X))>
<Marked_active(U52(X)) , Marked_active(X)>
<Marked_active(U61(X1,X2,X3)) , Marked_U61(active(X1),X2,X3)>
<Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
<Marked_active(U62(X1,X2)) , Marked_U62(active(X1),X2)>
<Marked_active(U62(X1,X2)) , Marked_active(X1)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_active(length(X)) , Marked_length(active(X))>
<Marked_active(length(X)) , Marked_active(X)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_U11(mark(X)) , Marked_U11(X)>
<Marked_U21(mark(X)) , Marked_U21(X)>
<Marked_U31(mark(X)) , Marked_U31(X)>
<Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)>
<Marked_U42(mark(X)) , Marked_U42(X)>
<Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)>
<Marked_U52(mark(X)) , Marked_U52(X)>
<Marked_U61(mark(X1),X2,X3) , Marked_U61(X1,X2,X3)>
<Marked_U62(mark(X1),X2) , Marked_U62(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_length(mark(X)) , Marked_length(X)>
<Marked_proper(cons(X1,X2)) , Marked_cons(proper(X1),proper(X2))>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U11(X)) , Marked_U11(proper(X))>
<Marked_proper(U11(X)) , Marked_proper(X)>
<Marked_proper(U21(X)) , Marked_U21(proper(X))>
<Marked_proper(U21(X)) , Marked_proper(X)>
<Marked_proper(U31(X)) , Marked_U31(proper(X))>
<Marked_proper(U31(X)) , Marked_proper(X)>
<Marked_proper(U41(X1,X2)) , Marked_U41(proper(X1),proper(X2))>
<Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U42(X)) , Marked_U42(proper(X))>
<Marked_proper(U42(X)) , Marked_proper(X)>
<Marked_proper(isNatIList(X)) , Marked_isNatIList(proper(X))>
<Marked_proper(isNatIList(X)) , Marked_proper(X)>
<Marked_proper(U51(X1,X2)) , Marked_U51(proper(X1),proper(X2))>
<Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U52(X)) , Marked_U52(proper(X))>
<Marked_proper(U52(X)) , Marked_proper(X)>
<Marked_proper(isNatList(X)) , Marked_isNatList(proper(X))>
<Marked_proper(isNatList(X)) , Marked_proper(X)>
<Marked_proper(U61(X1,X2,X3)) , Marked_U61(proper(X1),proper(X2),proper(X3))>
<Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
<Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
<Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
<Marked_proper(U62(X1,X2)) , Marked_U62(proper(X1),proper(X2))>
<Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
<Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
<Marked_proper(isNat(X)) , Marked_isNat(proper(X))>
<Marked_proper(isNat(X)) , Marked_proper(X)>
<Marked_proper(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_proper(length(X)) , Marked_length(proper(X))>
<Marked_proper(length(X)) , Marked_proper(X)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_U11(ok(X)) , Marked_U11(X)>
<Marked_U21(ok(X)) , Marked_U21(X)>
<Marked_U31(ok(X)) , Marked_U31(X)>
<Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)>
<Marked_U42(ok(X)) , Marked_U42(X)>
<Marked_isNatIList(ok(X)) , Marked_isNatIList(X)>
<Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)>
<Marked_U52(ok(X)) , Marked_U52(X)>
<Marked_isNatList(ok(X)) , Marked_isNatList(X)>
<Marked_U61(ok(X1),ok(X2),ok(X3)) , Marked_U61(X1,X2,X3)>
<Marked_U62(ok(X1),ok(X2)) , Marked_U62(X1,X2)>
<Marked_isNat(ok(X)) , Marked_isNat(X)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_length(ok(X)) , Marked_length(X)>
<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 18 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(length(X)) , Marked_proper(X)> 
      --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(length(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNat(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U62(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatList(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U52(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U51(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNatIList(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U42(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U41(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U31(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U21(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(length(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNat(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U62(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X3)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U61(X1,X2,X3)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatList(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U52(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U51(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNatIList(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U42(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U41(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U31(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U21(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
}

{  <Marked_active(length(X)) , Marked_active(X)> 
      --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(length(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U62(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U52(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U51(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U42(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U41(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U31(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U21(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(length(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U62(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U61(X1,X2,X3)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U52(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U51(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U42(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U41(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U31(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U21(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
}

{  <Marked_isNatIList(ok(X)) , Marked_isNatIList(X)> 
      --> <Marked_isNatIList(ok(X)) , Marked_isNatIList(X)>
}

{  <Marked_isNat(ok(X)) , Marked_isNat(X)> 
      --> <Marked_isNat(ok(X)) , Marked_isNat(X)>
}

{  <Marked_isNatList(ok(X)) , Marked_isNatList(X)> 
      --> <Marked_isNatList(ok(X)) , Marked_isNatList(X)>
}

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

{  <Marked_U11(ok(X)) , Marked_U11(X)> --> <Marked_U11(ok(X)) , Marked_U11(X)>
  <Marked_U11(ok(X)) , Marked_U11(X)> --> <Marked_U11(mark(X)) , Marked_U11(X)>
  <Marked_U11(mark(X)) , Marked_U11(X)> --> <Marked_U11(ok(X)) , Marked_U11(X)>
  <Marked_U11(mark(X)) , Marked_U11(X)> 
     --> <Marked_U11(mark(X)) , Marked_U11(X)>
}

{  <Marked_U21(ok(X)) , Marked_U21(X)> --> <Marked_U21(ok(X)) , Marked_U21(X)>
  <Marked_U21(ok(X)) , Marked_U21(X)> --> <Marked_U21(mark(X)) , Marked_U21(X)>
  <Marked_U21(mark(X)) , Marked_U21(X)> --> <Marked_U21(ok(X)) , Marked_U21(X)>
  <Marked_U21(mark(X)) , Marked_U21(X)> 
     --> <Marked_U21(mark(X)) , Marked_U21(X)>
}

{  <Marked_U31(ok(X)) , Marked_U31(X)> --> <Marked_U31(ok(X)) , Marked_U31(X)>
  <Marked_U31(ok(X)) , Marked_U31(X)> --> <Marked_U31(mark(X)) , Marked_U31(X)>
  <Marked_U31(mark(X)) , Marked_U31(X)> --> <Marked_U31(ok(X)) , Marked_U31(X)>
  <Marked_U31(mark(X)) , Marked_U31(X)> 
     --> <Marked_U31(mark(X)) , Marked_U31(X)>
}

{  <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)> 
      --> <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)>
  <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)> 
     --> <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)>
  <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)> 
     --> <Marked_U41(ok(X1),ok(X2)) , Marked_U41(X1,X2)>
  <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)> 
     --> <Marked_U41(mark(X1),X2) , Marked_U41(X1,X2)>
}

{  <Marked_U42(ok(X)) , Marked_U42(X)> --> <Marked_U42(ok(X)) , Marked_U42(X)>
  <Marked_U42(ok(X)) , Marked_U42(X)> --> <Marked_U42(mark(X)) , Marked_U42(X)>
  <Marked_U42(mark(X)) , Marked_U42(X)> --> <Marked_U42(ok(X)) , Marked_U42(X)>
  <Marked_U42(mark(X)) , Marked_U42(X)> 
     --> <Marked_U42(mark(X)) , Marked_U42(X)>
}

{  <Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)> 
      --> <Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)>
  <Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)> 
     --> <Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)>
  <Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)> 
     --> <Marked_U51(ok(X1),ok(X2)) , Marked_U51(X1,X2)>
  <Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)> 
     --> <Marked_U51(mark(X1),X2) , Marked_U51(X1,X2)>
}

{  <Marked_U52(ok(X)) , Marked_U52(X)> --> <Marked_U52(ok(X)) , Marked_U52(X)>
  <Marked_U52(ok(X)) , Marked_U52(X)> --> <Marked_U52(mark(X)) , Marked_U52(X)>
  <Marked_U52(mark(X)) , Marked_U52(X)> --> <Marked_U52(ok(X)) , Marked_U52(X)>
  <Marked_U52(mark(X)) , Marked_U52(X)> 
     --> <Marked_U52(mark(X)) , Marked_U52(X)>
}

{  <Marked_U61(ok(X1),ok(X2),ok(X3)) , Marked_U61(X1,X2,X3)> 
      --> <Marked_U61(ok(X1),ok(X2),ok(X3)) , Marked_U61(X1,X2,X3)>
  <Marked_U61(ok(X1),ok(X2),ok(X3)) , Marked_U61(X1,X2,X3)> 
     --> <Marked_U61(mark(X1),X2,X3) , Marked_U61(X1,X2,X3)>
  <Marked_U61(mark(X1),X2,X3) , Marked_U61(X1,X2,X3)> 
     --> <Marked_U61(ok(X1),ok(X2),ok(X3)) , Marked_U61(X1,X2,X3)>
  <Marked_U61(mark(X1),X2,X3) , Marked_U61(X1,X2,X3)> 
     --> <Marked_U61(mark(X1),X2,X3) , Marked_U61(X1,X2,X3)>
}

{  <Marked_U62(ok(X1),ok(X2)) , Marked_U62(X1,X2)> 
      --> <Marked_U62(ok(X1),ok(X2)) , Marked_U62(X1,X2)>
  <Marked_U62(ok(X1),ok(X2)) , Marked_U62(X1,X2)> 
     --> <Marked_U62(mark(X1),X2) , Marked_U62(X1,X2)>
  <Marked_U62(mark(X1),X2) , Marked_U62(X1,X2)> 
     --> <Marked_U62(ok(X1),ok(X2)) , Marked_U62(X1,X2)>
  <Marked_U62(mark(X1),X2) , Marked_U62(X1,X2)> 
     --> <Marked_U62(mark(X1),X2) , Marked_U62(X1,X2)>
}

{  <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_length(ok(X)) , Marked_length(X)> 
      --> <Marked_length(ok(X)) , Marked_length(X)>
  <Marked_length(ok(X)) , Marked_length(X)> 
     --> <Marked_length(mark(X)) , Marked_length(X)>
  <Marked_length(mark(X)) , Marked_length(X)> 
     --> <Marked_length(ok(X)) , Marked_length(X)>
  <Marked_length(mark(X)) , Marked_length(X)> 
     --> <Marked_length(mark(X)) , Marked_length(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(U11(tt)) >= mark(tt) ;
  active(U11(X)) >= U11(active(X)) ;
  active(U21(tt)) >= mark(tt) ;
  active(U21(X)) >= U21(active(X)) ;
  active(U31(tt)) >= mark(tt) ;
  active(U31(X)) >= U31(active(X)) ;
  active(U42(tt)) >= mark(tt) ;
  active(U42(X)) >= U42(active(X)) ;
  active(isNatIList(cons(V1,V2))) >= mark(U41(isNat(V1),V2)) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(V)) >= mark(U31(isNatList(V))) ;
  active(U41(tt,V2)) >= mark(U42(isNatIList(V2))) ;
  active(U41(X1,X2)) >= U41(active(X1),X2) ;
  active(U52(tt)) >= mark(tt) ;
  active(U52(X)) >= U52(active(X)) ;
  active(isNatList(cons(V1,V2))) >= mark(U51(isNat(V1),V2)) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(U51(tt,V2)) >= mark(U52(isNatList(V2))) ;
  active(U51(X1,X2)) >= U51(active(X1),X2) ;
  active(U62(tt,L)) >= mark(s(length(L))) ;
  active(U62(X1,X2)) >= U62(active(X1),X2) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(V1))) >= mark(U21(isNat(V1))) ;
  active(isNat(length(V1))) >= mark(U11(isNatList(V1))) ;
  active(U61(tt,L,N)) >= mark(U62(isNat(N),L)) ;
  active(U61(X1,X2,X3)) >= U61(active(X1),X2,X3) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U61(isNatList(L),L,N)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  U11(mark(X)) >= mark(U11(X)) ;
  U11(ok(X)) >= ok(U11(X)) ;
  U21(mark(X)) >= mark(U21(X)) ;
  U21(ok(X)) >= ok(U21(X)) ;
  U31(mark(X)) >= mark(U31(X)) ;
  U31(ok(X)) >= ok(U31(X)) ;
  U42(mark(X)) >= mark(U42(X)) ;
  U42(ok(X)) >= ok(U42(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  U41(mark(X1),X2) >= mark(U41(X1,X2)) ;
  U41(ok(X1),ok(X2)) >= ok(U41(X1,X2)) ;
  U52(mark(X)) >= mark(U52(X)) ;
  U52(ok(X)) >= ok(U52(X)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  U51(mark(X1),X2) >= mark(U51(X1,X2)) ;
  U51(ok(X1),ok(X2)) >= ok(U51(X1,X2)) ;
  U62(mark(X1),X2) >= mark(U62(X1,X2)) ;
  U62(ok(X1),ok(X2)) >= ok(U62(X1,X2)) ;
  isNat(ok(X)) >= ok(isNat(X)) ;
  U61(mark(X1),X2,X3) >= mark(U61(X1,X2,X3)) ;
  U61(ok(X1),ok(X2),ok(X3)) >= ok(U61(X1,X2,X3)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tt) >= ok(tt) ;
  proper(U11(X)) >= U11(proper(X)) ;
  proper(U21(X)) >= U21(proper(X)) ;
  proper(U31(X)) >= U31(proper(X)) ;
  proper(U42(X)) >= U42(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  proper(U41(X1,X2)) >= U41(proper(X1),proper(X2)) ;
  proper(U52(X)) >= U52(proper(X)) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(U51(X1,X2)) >= U51(proper(X1),proper(X2)) ;
  proper(U62(X1,X2)) >= U62(proper(X1),proper(X2)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(U61(X1,X2,X3)) >= U61(proper(X1),proper(X2),proper(X3)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(nil) >= ok(nil) ;
  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 ===
Time out for these parameters.
=== 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 timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(U11(tt)) >= mark(tt) ;
  active(U11(X)) >= U11(active(X)) ;
  active(U21(tt)) >= mark(tt) ;
  active(U21(X)) >= U21(active(X)) ;
  active(U31(tt)) >= mark(tt) ;
  active(U31(X)) >= U31(active(X)) ;
  active(U42(tt)) >= mark(tt) ;
  active(U42(X)) >= U42(active(X)) ;
  active(isNatIList(cons(V1,V2))) >= mark(U41(isNat(V1),V2)) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(V)) >= mark(U31(isNatList(V))) ;
  active(U41(tt,V2)) >= mark(U42(isNatIList(V2))) ;
  active(U41(X1,X2)) >= U41(active(X1),X2) ;
  active(U52(tt)) >= mark(tt) ;
  active(U52(X)) >= U52(active(X)) ;
  active(isNatList(cons(V1,V2))) >= mark(U51(isNat(V1),V2)) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(U51(tt,V2)) >= mark(U52(isNatList(V2))) ;
  active(U51(X1,X2)) >= U51(active(X1),X2) ;
  active(U62(tt,L)) >= mark(s(length(L))) ;
  active(U62(X1,X2)) >= U62(active(X1),X2) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(V1))) >= mark(U21(isNat(V1))) ;
  active(isNat(length(V1))) >= mark(U11(isNatList(V1))) ;
  active(U61(tt,L,N)) >= mark(U62(isNat(N),L)) ;
  active(U61(X1,X2,X3)) >= U61(active(X1),X2,X3) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U61(isNatList(L),L,N)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  U11(mark(X)) >= mark(U11(X)) ;
  U11(ok(X)) >= ok(U11(X)) ;
  U21(mark(X)) >= mark(U21(X)) ;
  U21(ok(X)) >= ok(U21(X)) ;
  U31(mark(X)) >= mark(U31(X)) ;
  U31(ok(X)) >= ok(U31(X)) ;
  U42(mark(X)) >= mark(U42(X)) ;
  U42(ok(X)) >= ok(U42(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  U41(mark(X1),X2) >= mark(U41(X1,X2)) ;
  U41(ok(X1),ok(X2)) >= ok(U41(X1,X2)) ;
  U52(mark(X)) >= mark(U52(X)) ;
  U52(ok(X)) >= ok(U52(X)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  U51(mark(X1),X2) >= mark(U51(X1,X2)) ;
  U51(ok(X1),ok(X2)) >= ok(U51(X1,X2)) ;
  U62(mark(X1),X2) >= mark(U62(X1,X2)) ;
  U62(ok(X1),ok(X2)) >= ok(U62(X1,X2)) ;
  isNat(ok(X)) >= ok(isNat(X)) ;
  U61(mark(X1),X2,X3) >= mark(U61(X1,X2,X3)) ;
  U61(ok(X1),ok(X2),ok(X3)) >= ok(U61(X1,X2,X3)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tt) >= ok(tt) ;
  proper(U11(X)) >= U11(proper(X)) ;
  proper(U21(X)) >= U21(proper(X)) ;
  proper(U31(X)) >= U31(proper(X)) ;
  proper(U42(X)) >= U42(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  proper(U41(X1,X2)) >= U41(proper(X1),proper(X2)) ;
  proper(U52(X)) >= U52(proper(X)) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(U51(X1,X2)) >= U51(proper(X1),proper(X2)) ;
  proper(U62(X1,X2)) >= U62(proper(X1),proper(X2)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(U61(X1,X2,X3)) >= U61(proper(X1),proper(X2),proper(X3)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(nil) >= ok(nil) ;
  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)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(U11(tt)) >= mark(tt) ;
  active(U11(X)) >= U11(active(X)) ;
  active(U21(tt)) >= mark(tt) ;
  active(U21(X)) >= U21(active(X)) ;
  active(U31(tt)) >= mark(tt) ;
  active(U31(X)) >= U31(active(X)) ;
  active(U42(tt)) >= mark(tt) ;
  active(U42(X)) >= U42(active(X)) ;
  active(isNatIList(cons(V1,V2))) >= mark(U41(isNat(V1),V2)) ;
  active(isNatIList(zeros)) >= mark(tt) ;
  active(isNatIList(V)) >= mark(U31(isNatList(V))) ;
  active(U41(tt,V2)) >= mark(U42(isNatIList(V2))) ;
  active(U41(X1,X2)) >= U41(active(X1),X2) ;
  active(U52(tt)) >= mark(tt) ;
  active(U52(X)) >= U52(active(X)) ;
  active(isNatList(cons(V1,V2))) >= mark(U51(isNat(V1),V2)) ;
  active(isNatList(nil)) >= mark(tt) ;
  active(U51(tt,V2)) >= mark(U52(isNatList(V2))) ;
  active(U51(X1,X2)) >= U51(active(X1),X2) ;
  active(U62(tt,L)) >= mark(s(length(L))) ;
  active(U62(X1,X2)) >= U62(active(X1),X2) ;
  active(isNat(0)) >= mark(tt) ;
  active(isNat(s(V1))) >= mark(U21(isNat(V1))) ;
  active(isNat(length(V1))) >= mark(U11(isNatList(V1))) ;
  active(U61(tt,L,N)) >= mark(U62(isNat(N),L)) ;
  active(U61(X1,X2,X3)) >= U61(active(X1),X2,X3) ;
  active(s(X)) >= s(active(X)) ;
  active(length(cons(N,L))) >= mark(U61(isNatList(L),L,N)) ;
  active(length(nil)) >= mark(0) ;
  active(length(X)) >= length(active(X)) ;
  U11(mark(X)) >= mark(U11(X)) ;
  U11(ok(X)) >= ok(U11(X)) ;
  U21(mark(X)) >= mark(U21(X)) ;
  U21(ok(X)) >= ok(U21(X)) ;
  U31(mark(X)) >= mark(U31(X)) ;
  U31(ok(X)) >= ok(U31(X)) ;
  U42(mark(X)) >= mark(U42(X)) ;
  U42(ok(X)) >= ok(U42(X)) ;
  isNatIList(ok(X)) >= ok(isNatIList(X)) ;
  U41(mark(X1),X2) >= mark(U41(X1,X2)) ;
  U41(ok(X1),ok(X2)) >= ok(U41(X1,X2)) ;
  U52(mark(X)) >= mark(U52(X)) ;
  U52(ok(X)) >= ok(U52(X)) ;
  isNatList(ok(X)) >= ok(isNatList(X)) ;
  U51(mark(X1),X2) >= mark(U51(X1,X2)) ;
  U51(ok(X1),ok(X2)) >= ok(U51(X1,X2)) ;
  U62(mark(X1),X2) >= mark(U62(X1,X2)) ;
  U62(ok(X1),ok(X2)) >= ok(U62(X1,X2)) ;
  isNat(ok(X)) >= ok(isNat(X)) ;
  U61(mark(X1),X2,X3) >= mark(U61(X1,X2,X3)) ;
  U61(ok(X1),ok(X2),ok(X3)) >= ok(U61(X1,X2,X3)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  length(mark(X)) >= mark(length(X)) ;
  length(ok(X)) >= ok(length(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tt) >= ok(tt) ;
  proper(U11(X)) >= U11(proper(X)) ;
  proper(U21(X)) >= U21(proper(X)) ;
  proper(U31(X)) >= U31(proper(X)) ;
  proper(U42(X)) >= U42(proper(X)) ;
  proper(isNatIList(X)) >= isNatIList(proper(X)) ;
  proper(U41(X1,X2)) >= U41(proper(X1),proper(X2)) ;
  proper(U52(X)) >= U52(proper(X)) ;
  proper(isNatList(X)) >= isNatList(proper(X)) ;
  proper(U51(X1,X2)) >= U51(proper(X1),proper(X2)) ;
  proper(U62(X1,X2)) >= U62(proper(X1),proper(X2)) ;
  proper(isNat(X)) >= isNat(proper(X)) ;
  proper(U61(X1,X2,X3)) >= U61(proper(X1),proper(X2),proper(X3)) ;
  proper(s(X)) >= s(proper(X)) ;
  proper(length(X)) >= length(proper(X)) ;
  proper(nil) >= ok(nil) ;
  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:{ 
 } 
=== 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 ===
Time out for these parameters.
=== 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 timeout reached
=== 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 156.305272 seconds (real time)
Cime Exit Status: 0