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

TRS termination of:
[1] U11(tt,V2) -> U12(isNat(activate(V2)))
[2] U12(tt) -> tt
[3] U21(tt) -> tt
[4] U31(tt,N) -> activate(N)
[5] U41(tt,M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
[6] U42(tt,M,N) -> s(plus(activate(N),activate(M)))
[7] isNat(n__0) -> tt
[8] isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
[9] isNat(n__s(V1)) -> U21(isNat(activate(V1)))
[10] plus(N,0) -> U31(isNat(N),N)
[11] plus(N,s(M)) -> U41(isNat(M),M,N)
[12] 0 -> n__0
[13] plus(X1,X2) -> n__plus(X1,X2)
[14] s(X) -> n__s(X)
[15] activate(n__0) -> 0
[16] activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
[17] activate(n__s(X)) -> s(activate(X))
[18] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_U11(tt,V2) , Marked_U12(isNat(activate(V2)))>
<Marked_U11(tt,V2) , Marked_isNat(activate(V2))>
<Marked_U11(tt,V2) , Marked_activate(V2)>
<Marked_U31(tt,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_U42(isNat(activate(N)),activate(M),activate(N))>
<Marked_U41(tt,M,N) , Marked_isNat(activate(N))>
<Marked_U41(tt,M,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_activate(M)>
<Marked_U41(tt,M,N) , Marked_activate(N)>
<Marked_U42(tt,M,N) , Marked_s(plus(activate(N),activate(M)))>
<Marked_U42(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U42(tt,M,N) , Marked_activate(N)>
<Marked_U42(tt,M,N) , Marked_activate(M)>
<Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),activate(V2))>
<Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
<Marked_isNat(n__s(V1)) , Marked_U21(isNat(activate(V1)))>
<Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
<Marked_isNat(n__s(V1)) , Marked_activate(V1)>
<Marked_plus(N,0) , Marked_U31(isNat(N),N)>
<Marked_plus(N,0) , Marked_isNat(N)>
<Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)>
<Marked_plus(N,s(M)) , Marked_isNat(M)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))>
<Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
<Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
<Marked_activate(n__s(X)) , Marked_s(activate(X))>
<Marked_activate(n__s(X)) , Marked_activate(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__s(X)) , Marked_activate(X)> 
      --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,s(M)) , Marked_isNat(M)>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,0) , Marked_isNat(N)>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,0) , Marked_U31(isNat(N),N)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),
                                          activate(V2))>
  <Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)> 
     --> <Marked_U41(tt,M,N) , Marked_activate(N)>
  <Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)> 
     --> <Marked_U41(tt,M,N) , Marked_activate(M)>
  <Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)> 
     --> <Marked_U41(tt,M,N) , Marked_activate(N)>
  <Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)> 
     --> <Marked_U41(tt,M,N) , Marked_isNat(activate(N))>
  <Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)> 
     --> <Marked_U41(tt,M,N) , Marked_U42(isNat(activate(N)),activate(M),
                                activate(N))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),
                                          activate(V2))>
  <Marked_plus(N,0) , Marked_U31(isNat(N),N)> 
     --> <Marked_U31(tt,N) , Marked_activate(N)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
  <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
  <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),
                                          activate(V2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),
                                          activate(V2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),activate(V2))> 
     --> <Marked_U11(tt,V2) , Marked_activate(V2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),activate(V2))> 
     --> <Marked_U11(tt,V2) , Marked_isNat(activate(V2))>
  <Marked_U42(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U42(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U42(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U42(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U42(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U42(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U42(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U42(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U42(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_isNat(M)>
  <Marked_U42(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)>
  <Marked_U42(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_isNat(N)>
  <Marked_U42(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_U31(isNat(N),N)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U41(tt,M,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U41(tt,M,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
  <Marked_U41(tt,M,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U41(tt,M,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U41(tt,M,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
  <Marked_U41(tt,M,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),
                                          activate(V2))>
  <Marked_U41(tt,M,N) , Marked_U42(isNat(activate(N)),activate(M),activate(N))> 
     --> <Marked_U42(tt,M,N) , Marked_activate(M)>
  <Marked_U41(tt,M,N) , Marked_U42(isNat(activate(N)),activate(M),activate(N))> 
     --> <Marked_U42(tt,M,N) , Marked_activate(N)>
  <Marked_U41(tt,M,N) , Marked_U42(isNat(activate(N)),activate(M),activate(N))> 
     --> <Marked_U42(tt,M,N) , Marked_plus(activate(N),activate(M))>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U11(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U11(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U11(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U11(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U11(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U11(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
  <Marked_U11(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U11(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U11(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
  <Marked_U11(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),
                                          activate(V2))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  U12(tt) >= tt ;
  isNat(n__0) >= tt ;
  isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) ;
  isNat(n__s(V1)) >= U21(isNat(activate(V1))) ;
  activate(n__0) >= 0 ;
  activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) ;
  activate(n__s(X)) >= s(activate(X)) ;
  activate(X) >= X ;
  U11(tt,V2) >= U12(isNat(activate(V2))) ;
  U21(tt) >= tt ;
  U31(tt,N) >= activate(N) ;
  U42(tt,M,N) >= s(plus(activate(N),activate(M))) ;
  U41(tt,M,N) >= U42(isNat(activate(N)),activate(M),activate(N)) ;
  s(X) >= n__s(X) ;
  plus(N,s(M)) >= U41(isNat(M),M,N) ;
  plus(N,0) >= U31(isNat(N),N) ;
  plus(X1,X2) >= n__plus(X1,X2) ;
  0 >= n__0 ;
  Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1) ;
  Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2) ;
  Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1),activate(X2)) ;
  Marked_activate(n__s(X)) >= Marked_activate(X) ;
  Marked_plus(N,s(M)) >= Marked_U41(isNat(M),M,N) ;
  Marked_plus(N,s(M)) >= Marked_isNat(M) ;
  Marked_plus(N,0) >= Marked_isNat(N) ;
  Marked_plus(N,0) >= Marked_U31(isNat(N),N) ;
  Marked_U41(tt,M,N) >= Marked_activate(N) ;
  Marked_U41(tt,M,N) >= Marked_activate(M) ;
  Marked_U41(tt,M,N) >= Marked_isNat(activate(N)) ;
  Marked_U41(tt,M,N) >= Marked_U42(isNat(activate(N)),activate(M),activate(N)) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)),activate(V2)) ;
  Marked_isNat(n__s(V1)) >= Marked_activate(V1) ;
  Marked_isNat(n__s(V1)) >= Marked_isNat(activate(V1)) ;
  Marked_U31(tt,N) >= Marked_activate(N) ;
  Marked_U11(tt,V2) >= Marked_activate(V2) ;
  Marked_U11(tt,V2) >= Marked_isNat(activate(V2)) ;
  Marked_U42(tt,M,N) >= Marked_activate(N) ;
  Marked_U42(tt,M,N) >= Marked_activate(M) ;
  Marked_U42(tt,M,N) >= Marked_plus(activate(N),activate(M)) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__plus(X1,X2)) > Marked_activate(X1) ;
 }
{
  Marked_activate(n__plus(X1,X2)) > Marked_activate(X2) ;
 }
{
  Marked_activate(n__plus(X1,X2)) > Marked_plus(activate(X1),activate(X2)) ;
 }
{
  Marked_activate(n__s(X)) > Marked_activate(X) ;
 }
{
  Marked_plus(N,s(M)) > Marked_U41(isNat(M),M,N) ;
 }
{
  Marked_plus(N,s(M)) > Marked_isNat(M) ;
 }
{
  Marked_plus(N,0) > Marked_isNat(N) ;
 }
{
  Marked_plus(N,0) > Marked_U31(isNat(N),N) ;
 }
{
  Marked_U41(tt,M,N) > Marked_activate(N) ;
 }
{
  Marked_U41(tt,M,N) > Marked_activate(M) ;
 }
{
  Marked_U41(tt,M,N) > Marked_isNat(activate(N)) ;
 }
{
  Marked_U41(tt,M,N) > Marked_U42(isNat(activate(N)),activate(M),activate(N)) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_activate(V2) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_activate(V1) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_isNat(activate(V1)) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_U11(isNat(activate(V1)),activate(V2)) ;
 }
{
  Marked_isNat(n__s(V1)) > Marked_activate(V1) ;
 }
{
  Marked_isNat(n__s(V1)) > Marked_isNat(activate(V1)) ;
 }
{
  Marked_U31(tt,N) > Marked_activate(N) ;
 }
{
  Marked_U11(tt,V2) > Marked_activate(V2) ;
 }
{
  Marked_U11(tt,V2) > Marked_isNat(activate(V2)) ;
 }
{
  Marked_U42(tt,M,N) > Marked_activate(N) ;
 }
{
  Marked_U42(tt,M,N) > Marked_activate(M) ;
 }
{
  Marked_U42(tt,M,N) > Marked_plus(activate(N),activate(M)) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: U12(tt) >= tt
constraint: isNat(n__0) >= tt
constraint: isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2))
constraint: isNat(n__s(V1)) >= U21(isNat(activate(V1)))
constraint: activate(n__0) >= 0
constraint: activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2))
constraint: activate(n__s(X)) >= s(activate(X))
constraint: activate(X) >= X
constraint: U11(tt,V2) >= U12(isNat(activate(V2)))
constraint: U21(tt) >= tt
constraint: U31(tt,N) >= activate(N)
constraint: U42(tt,M,N) >= s(plus(activate(N),activate(M)))
constraint: U41(tt,M,N) >= U42(isNat(activate(N)),activate(M),activate(N))
constraint: s(X) >= n__s(X)
constraint: plus(N,s(M)) >= U41(isNat(M),M,N)
constraint: plus(N,0) >= U31(isNat(N),N)
constraint: plus(X1,X2) >= n__plus(X1,X2)
constraint: 0 >= n__0
constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1)
constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2)
constraint: Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1),
                                                activate(X2))
constraint: Marked_activate(n__s(X)) >= Marked_activate(X)
constraint: Marked_plus(N,s(M)) >= Marked_U41(isNat(M),M,N)
constraint: Marked_plus(N,s(M)) >= Marked_isNat(M)
constraint: Marked_plus(N,0) >= Marked_isNat(N)
constraint: Marked_plus(N,0) >= Marked_U31(isNat(N),N)
constraint: Marked_U41(tt,M,N) >= Marked_activate(N)
constraint: Marked_U41(tt,M,N) >= Marked_activate(M)
constraint: Marked_U41(tt,M,N) >= Marked_isNat(activate(N))
constraint: Marked_U41(tt,M,N) >= Marked_U42(isNat(activate(N)),activate(M),
                                   activate(N))
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2)
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1)
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1))
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)),
                                             activate(V2))
constraint: Marked_isNat(n__s(V1)) >= Marked_activate(V1)
constraint: Marked_isNat(n__s(V1)) >= Marked_isNat(activate(V1))
constraint: Marked_U31(tt,N) >= Marked_activate(N)
constraint: Marked_U11(tt,V2) >= Marked_activate(V2)
constraint: Marked_U11(tt,V2) >= Marked_isNat(activate(V2))
constraint: Marked_U42(tt,M,N) >= Marked_activate(N)
constraint: Marked_U42(tt,M,N) >= Marked_activate(M)
constraint: Marked_U42(tt,M,N) >= Marked_plus(activate(N),activate(M))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] U11(tt,V2) -> U12(isNat(activate(V2)))
[2] U12(tt) -> tt
[3] U21(tt) -> tt
[4] U31(tt,N) -> activate(N)
[5] U41(tt,M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
[6] U42(tt,M,N) -> s(plus(activate(N),activate(M)))
[7] isNat(n__0) -> tt
[8] isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
[9] isNat(n__s(V1)) -> U21(isNat(activate(V1)))
[10] plus(N,0) -> U31(isNat(N),N)
[11] plus(N,s(M)) -> U41(isNat(M),M,N)
[12] 0 -> n__0
[13] plus(X1,X2) -> n__plus(X1,X2)
[14] s(X) -> n__s(X)
[15] activate(n__0) -> 0
[16] activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
[17] activate(n__s(X)) -> s(activate(X))
[18] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_U11(tt,V2) , Marked_U12(isNat(activate(V2)))>
<Marked_U11(tt,V2) , Marked_isNat(activate(V2))>
<Marked_U11(tt,V2) , Marked_activate(V2)>
<Marked_U31(tt,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_U42(isNat(activate(N)),activate(M),activate(N))>
<Marked_U41(tt,M,N) , Marked_isNat(activate(N))>
<Marked_U41(tt,M,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_activate(M)>
<Marked_U41(tt,M,N) , Marked_activate(N)>
<Marked_U42(tt,M,N) , Marked_s(plus(activate(N),activate(M)))>
<Marked_U42(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U42(tt,M,N) , Marked_activate(N)>
<Marked_U42(tt,M,N) , Marked_activate(M)>
<Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),activate(V2))>
<Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
<Marked_isNat(n__s(V1)) , Marked_U21(isNat(activate(V1)))>
<Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
<Marked_isNat(n__s(V1)) , Marked_activate(V1)>
<Marked_plus(N,0) , Marked_U31(isNat(N),N)>
<Marked_plus(N,0) , Marked_isNat(N)>
<Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)>
<Marked_plus(N,s(M)) , Marked_isNat(M)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))>
<Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
<Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
<Marked_activate(n__s(X)) , Marked_s(activate(X))>
<Marked_activate(n__s(X)) , Marked_activate(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_U11(tt,V2) , Marked_isNat(activate(V2))>
<Marked_U11(tt,V2) , Marked_activate(V2)>
<Marked_U31(tt,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_U42(isNat(activate(N)),activate(M),activate(N))>
<Marked_U41(tt,M,N) , Marked_isNat(activate(N))>
<Marked_U41(tt,M,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_activate(M)>
<Marked_U41(tt,M,N) , Marked_activate(N)>
<Marked_U42(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U42(tt,M,N) , Marked_activate(N)>
<Marked_U42(tt,M,N) , Marked_activate(M)>
<Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),activate(V2))>
<Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
<Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
<Marked_isNat(n__s(V1)) , Marked_activate(V1)>
<Marked_plus(N,0) , Marked_U31(isNat(N),N)>
<Marked_plus(N,0) , Marked_isNat(N)>
<Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)>
<Marked_plus(N,s(M)) , Marked_isNat(M)>
<Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))>
<Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
<Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
<Marked_activate(n__s(X)) , Marked_activate(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ U12 ] (X0) = 3; 
 [ U41 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0 + 2; 
 [ Marked_U42 ] (X0,X1,X2) = 2*X2 + 3*X1 + 1*X0 + 3; 
 [ tt ] () = 3; 
 [ Marked_isNat ] (X0) = 2*X0; 
 [ n__plus ] (X0,X1) = 2*X1 + 2*X0 + 3; 
 [ activate ] (X0) = 1*X0; 
 [ plus ] (X0,X1) = 2*X1 + 2*X0 + 3; 
 [ U31 ] (X0,X1) = 1*X1 + 2; 
 [ 0 ] () = 3; 
 [ isNat ] (X0) = 3; 
 [ Marked_plus ] (X0,X1) = 3*X1 + 2*X0 + 1; 
 [ s ] (X0) = 1*X0 + 3; 
 [ U21 ] (X0) = 3; 
 [ Marked_U31 ] (X0,X1) = 2*X1 + 3*X0 + 1; 
 [ n__s ] (X0) = 1*X0 + 3; 
 [ U11 ] (X0,X1) = 3; 
 [ Marked_U41 ] (X0,X1,X2) = 2*X2 + 3*X1 + 3*X0 + 1; 
 [ n__0 ] () = 3; 
 [ U42 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; 
 [ Marked_U11 ] (X0,X1) = 2*X1 + 2*X0; 
 [ Marked_activate ] (X0) = 2*X0; 
 removing <Marked_U11(tt,V2),Marked_isNat(activate(V2))><Marked_U11(tt,V2),
Marked_activate(V2)><Marked_U31(tt,N),Marked_activate(N)><Marked_U41(tt,M,N),
Marked_U42(isNat(activate(N)),activate(M),activate(N))><Marked_U41(tt,M,N),
Marked_isNat(activate(N))><Marked_U41(tt,M,N),Marked_activate(N)><Marked_U41(
                                                                   tt,
                                                                   M,
                                                                   N),
Marked_activate(M)><Marked_U41(tt,M,N),Marked_activate(N)><Marked_U42(tt,M,N),
Marked_plus(activate(N),activate(M))><Marked_U42(tt,M,N),Marked_activate(N)><
Marked_U42(tt,M,N),Marked_activate(M)><Marked_isNat(n__plus(V1,V2)),Marked_isNat(
                                                                    activate(
                                                                    V1))><
Marked_isNat(n__plus(V1,V2)),Marked_activate(V1)><Marked_isNat(n__plus(V1,V2)),
Marked_activate(V2)><Marked_isNat(n__s(V1)),Marked_isNat(activate(V1))><
Marked_isNat(n__s(V1)),Marked_activate(V1)><Marked_plus(N,0),Marked_isNat(N)><
Marked_plus(N,s(M)),Marked_isNat(M)><Marked_activate(n__plus(X1,X2)),
Marked_plus(activate(X1),activate(X2))><Marked_activate(n__plus(X1,X2)),
Marked_activate(X1)><Marked_activate(n__plus(X1,X2)),Marked_activate(X2)><
Marked_activate(n__s(X)),Marked_activate(X)>
 [ {
      
     DP termination of:
     <Marked_isNat(n__plus(V1,V2)) , Marked_U11(isNat(activate(V1)),
                                      activate(V2))>
<Marked_plus(N,0) , Marked_U31(isNat(N),N)>
<Marked_plus(N,s(M)) , Marked_U41(isNat(M),M,N)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.181648 seconds (real time)
Cime Exit Status: 0