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

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


Sub problem: 
guided: 

DP termination of:
<Marked_U11(tt,N) , Marked_activate(N)>
<Marked_U21(tt,M,N) , Marked_s(plus(activate(N),activate(M)))>
<Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U21(tt,M,N) , Marked_activate(N)>
<Marked_U21(tt,M,N) , Marked_activate(M)>
<Marked_and(tt,X) , Marked_activate(X)>
<Marked_isNat(n__plus(V1,V2)) , Marked_and(isNat(activate(V1)),
                                 n__isNat(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_U11(isNat(N),N)>
<Marked_plus(N,0) , Marked_isNat(N)>
<Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)>
<Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNat(N))>
<Marked_plus(N,s(M)) , Marked_isNat(M)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)>
<Marked_activate(n__isNat(X)) , Marked_isNat(X)>
<Marked_activate(n__s(X)) , Marked_s(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
      --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNat(activate(V1))>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNat(activate(V1)),
                                          n__isNat(activate(V2)))>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(N,s(M)) , Marked_isNat(M)>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNat(N))>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(N,0) , Marked_isNat(N)>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(N,0) , Marked_U11(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_and(isNat(activate(V1)),
                                          n__isNat(activate(V2)))>
  <Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNat(N))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)> 
     --> <Marked_U21(tt,M,N) , Marked_activate(M)>
  <Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)> 
     --> <Marked_U21(tt,M,N) , Marked_activate(N)>
  <Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)> 
     --> <Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))>
  <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_and(isNat(activate(V1)),
                                          n__isNat(activate(V2)))>
  <Marked_plus(N,0) , Marked_U11(isNat(N),N)> 
     --> <Marked_U11(tt,N) , Marked_activate(N)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,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_and(isNat(activate(V1)),
                                          n__isNat(activate(V2)))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,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_and(isNat(activate(V1)),
                                          n__isNat(activate(V2)))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNat(activate(V1)),
                                   n__isNat(activate(V2)))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)>
  <Marked_U21(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U21(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)>
  <Marked_U21(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U21(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)>
  <Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_isNat(M)>
  <Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNat(N))>
  <Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)>
  <Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_isNat(N)>
  <Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_U11(isNat(N),N)>
  <Marked_U11(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U11(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  activate(n__0) >= 0 ;
  activate(n__isNat(X)) >= isNat(X) ;
  activate(n__plus(X1,X2)) >= plus(X1,X2) ;
  activate(n__s(X)) >= s(X) ;
  activate(X) >= X ;
  U11(tt,N) >= activate(N) ;
  s(X) >= n__s(X) ;
  plus(N,s(M)) >= U21(and(isNat(M),n__isNat(N)),M,N) ;
  plus(N,0) >= U11(isNat(N),N) ;
  plus(X1,X2) >= n__plus(X1,X2) ;
  U21(tt,M,N) >= s(plus(activate(N),activate(M))) ;
  and(tt,X) >= activate(X) ;
  isNat(n__0) >= tt ;
  isNat(n__plus(V1,V2)) >= and(isNat(activate(V1)),n__isNat(activate(V2))) ;
  isNat(n__s(V1)) >= isNat(activate(V1)) ;
  isNat(X) >= n__isNat(X) ;
  0 >= n__0 ;
  Marked_activate(n__isNat(X)) >= Marked_isNat(X) ;
  Marked_activate(n__plus(X1,X2)) >= Marked_plus(X1,X2) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_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_and(isNat(activate(V1)),
                                   n__isNat(activate(V2))) ;
  Marked_isNat(n__s(V1)) >= Marked_activate(V1) ;
  Marked_isNat(n__s(V1)) >= Marked_isNat(activate(V1)) ;
  Marked_plus(N,s(M)) >= Marked_isNat(M) ;
  Marked_plus(N,s(M)) >= Marked_U21(and(isNat(M),n__isNat(N)),M,N) ;
  Marked_plus(N,s(M)) >= Marked_and(isNat(M),n__isNat(N)) ;
  Marked_plus(N,0) >= Marked_isNat(N) ;
  Marked_plus(N,0) >= Marked_U11(isNat(N),N) ;
  Marked_U21(tt,M,N) >= Marked_activate(N) ;
  Marked_U21(tt,M,N) >= Marked_activate(M) ;
  Marked_U21(tt,M,N) >= Marked_plus(activate(N),activate(M)) ;
  Marked_and(tt,X) >= Marked_activate(X) ;
  Marked_U11(tt,N) >= Marked_activate(N) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__isNat(X)) > Marked_isNat(X) ;
 }
{
  Marked_activate(n__plus(X1,X2)) > Marked_plus(X1,X2) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_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_and(isNat(activate(V1)),
                                  n__isNat(activate(V2))) ;
 }
{
  Marked_isNat(n__s(V1)) > Marked_activate(V1) ;
 }
{
  Marked_isNat(n__s(V1)) > Marked_isNat(activate(V1)) ;
 }
{
  Marked_plus(N,s(M)) > Marked_isNat(M) ;
 }
{
  Marked_plus(N,s(M)) > Marked_U21(and(isNat(M),n__isNat(N)),M,N) ;
 }
{
  Marked_plus(N,s(M)) > Marked_and(isNat(M),n__isNat(N)) ;
 }
{
  Marked_plus(N,0) > Marked_isNat(N) ;
 }
{
  Marked_plus(N,0) > Marked_U11(isNat(N),N) ;
 }
{
  Marked_U21(tt,M,N) > Marked_activate(N) ;
 }
{
  Marked_U21(tt,M,N) > Marked_activate(M) ;
 }
{
  Marked_U21(tt,M,N) > Marked_plus(activate(N),activate(M)) ;
 }
{
  Marked_and(tt,X) > Marked_activate(X) ;
 }
{
  Marked_U11(tt,N) > Marked_activate(N) ;
 }
 } 
=== 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: activate(n__0) >= 0
constraint: activate(n__isNat(X)) >= isNat(X)
constraint: activate(n__plus(X1,X2)) >= plus(X1,X2)
constraint: activate(n__s(X)) >= s(X)
constraint: activate(X) >= X
constraint: U11(tt,N) >= activate(N)
constraint: s(X) >= n__s(X)
constraint: plus(N,s(M)) >= U21(and(isNat(M),n__isNat(N)),M,N)
constraint: plus(N,0) >= U11(isNat(N),N)
constraint: plus(X1,X2) >= n__plus(X1,X2)
constraint: U21(tt,M,N) >= s(plus(activate(N),activate(M)))
constraint: and(tt,X) >= activate(X)
constraint: isNat(n__0) >= tt
constraint: isNat(n__plus(V1,V2)) >= and(isNat(activate(V1)),
                                      n__isNat(activate(V2)))
constraint: isNat(n__s(V1)) >= isNat(activate(V1))
constraint: isNat(X) >= n__isNat(X)
constraint: 0 >= n__0
constraint: Marked_activate(n__isNat(X)) >= Marked_isNat(X)
constraint: Marked_activate(n__plus(X1,X2)) >= Marked_plus(X1,X2)
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1)
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2)
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1))
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_and(isNat(activate(V1)),
                                             n__isNat(activate(V2)))
constraint: Marked_isNat(n__s(V1)) >= Marked_activate(V1)
constraint: Marked_isNat(n__s(V1)) >= Marked_isNat(activate(V1))
constraint: Marked_plus(N,s(M)) >= Marked_isNat(M)
constraint: Marked_plus(N,s(M)) >= Marked_U21(and(isNat(M),n__isNat(N)),M,N)
constraint: Marked_plus(N,s(M)) >= Marked_and(isNat(M),n__isNat(N))
constraint: Marked_plus(N,0) >= Marked_isNat(N)
constraint: Marked_plus(N,0) >= Marked_U11(isNat(N),N)
constraint: Marked_U21(tt,M,N) >= Marked_activate(N)
constraint: Marked_U21(tt,M,N) >= Marked_activate(M)
constraint: Marked_U21(tt,M,N) >= Marked_plus(activate(N),activate(M))
constraint: Marked_and(tt,X) >= Marked_activate(X)
constraint: Marked_U11(tt,N) >= Marked_activate(N)
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)> 
      --> <Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))>
  <Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)>
}

{  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
      --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <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))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  activate(n__0) >= 0 ;
  activate(n__isNat(X)) >= isNat(X) ;
  activate(n__plus(X1,X2)) >= plus(X1,X2) ;
  activate(n__s(X)) >= s(X) ;
  activate(X) >= X ;
  U11(tt,N) >= activate(N) ;
  s(X) >= n__s(X) ;
  plus(N,s(M)) >= U21(and(isNat(M),n__isNat(N)),M,N) ;
  plus(N,0) >= U11(isNat(N),N) ;
  plus(X1,X2) >= n__plus(X1,X2) ;
  U21(tt,M,N) >= s(plus(activate(N),activate(M))) ;
  and(tt,X) >= activate(X) ;
  isNat(n__0) >= tt ;
  isNat(n__plus(V1,V2)) >= and(isNat(activate(V1)),n__isNat(activate(V2))) ;
  isNat(n__s(V1)) >= isNat(activate(V1)) ;
  isNat(X) >= n__isNat(X) ;
  0 >= n__0 ;
  Marked_plus(N,s(M)) >= Marked_U21(and(isNat(M),n__isNat(N)),M,N) ;
  Marked_U21(tt,M,N) >= Marked_plus(activate(N),activate(M)) ;
 }
 + Disjunctions:{ 
{
  Marked_plus(N,s(M)) > Marked_U21(and(isNat(M),n__isNat(N)),M,N) ;
 }
{
  Marked_U21(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: activate(n__0) >= 0
constraint: activate(n__isNat(X)) >= isNat(X)
constraint: activate(n__plus(X1,X2)) >= plus(X1,X2)
constraint: activate(n__s(X)) >= s(X)
constraint: activate(X) >= X
constraint: U11(tt,N) >= activate(N)
constraint: s(X) >= n__s(X)
constraint: plus(N,s(M)) >= U21(and(isNat(M),n__isNat(N)),M,N)
constraint: plus(N,0) >= U11(isNat(N),N)
constraint: plus(X1,X2) >= n__plus(X1,X2)
constraint: U21(tt,M,N) >= s(plus(activate(N),activate(M)))
constraint: and(tt,X) >= activate(X)
constraint: isNat(n__0) >= tt
constraint: isNat(n__plus(V1,V2)) >= and(isNat(activate(V1)),
                                      n__isNat(activate(V2)))
constraint: isNat(n__s(V1)) >= isNat(activate(V1))
constraint: isNat(X) >= n__isNat(X)
constraint: 0 >= n__0
constraint: Marked_plus(N,s(M)) >= Marked_U21(and(isNat(M),n__isNat(N)),M,N)
constraint: Marked_U21(tt,M,N) >= Marked_plus(activate(N),activate(M))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  activate(n__0) >= 0 ;
  activate(n__isNat(X)) >= isNat(X) ;
  activate(n__plus(X1,X2)) >= plus(X1,X2) ;
  activate(n__s(X)) >= s(X) ;
  activate(X) >= X ;
  U11(tt,N) >= activate(N) ;
  s(X) >= n__s(X) ;
  plus(N,s(M)) >= U21(and(isNat(M),n__isNat(N)),M,N) ;
  plus(N,0) >= U11(isNat(N),N) ;
  plus(X1,X2) >= n__plus(X1,X2) ;
  U21(tt,M,N) >= s(plus(activate(N),activate(M))) ;
  and(tt,X) >= activate(X) ;
  isNat(n__0) >= tt ;
  isNat(n__plus(V1,V2)) >= and(isNat(activate(V1)),n__isNat(activate(V2))) ;
  isNat(n__s(V1)) >= isNat(activate(V1)) ;
  isNat(X) >= n__isNat(X) ;
  0 >= n__0 ;
  Marked_activate(n__isNat(X)) >= Marked_isNat(X) ;
  Marked_isNat(n__s(V1)) >= Marked_activate(V1) ;
  Marked_isNat(n__s(V1)) >= Marked_isNat(activate(V1)) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__isNat(X)) > Marked_isNat(X) ;
 }
{
  Marked_isNat(n__s(V1)) > Marked_activate(V1) ;
 }
{
  Marked_isNat(n__s(V1)) > Marked_isNat(activate(V1)) ;
 }
 } 
=== 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: activate(n__0) >= 0
constraint: activate(n__isNat(X)) >= isNat(X)
constraint: activate(n__plus(X1,X2)) >= plus(X1,X2)
constraint: activate(n__s(X)) >= s(X)
constraint: activate(X) >= X
constraint: U11(tt,N) >= activate(N)
constraint: s(X) >= n__s(X)
constraint: plus(N,s(M)) >= U21(and(isNat(M),n__isNat(N)),M,N)
constraint: plus(N,0) >= U11(isNat(N),N)
constraint: plus(X1,X2) >= n__plus(X1,X2)
constraint: U21(tt,M,N) >= s(plus(activate(N),activate(M)))
constraint: and(tt,X) >= activate(X)
constraint: isNat(n__0) >= tt
constraint: isNat(n__plus(V1,V2)) >= and(isNat(activate(V1)),
                                      n__isNat(activate(V2)))
constraint: isNat(n__s(V1)) >= isNat(activate(V1))
constraint: isNat(X) >= n__isNat(X)
constraint: 0 >= n__0
constraint: Marked_activate(n__isNat(X)) >= Marked_isNat(X)
constraint: Marked_isNat(n__s(V1)) >= Marked_activate(V1)
constraint: Marked_isNat(n__s(V1)) >= Marked_isNat(activate(V1))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] U11(tt,N) -> activate(N)
[2] U21(tt,M,N) -> s(plus(activate(N),activate(M)))
[3] and(tt,X) -> activate(X)
[4] isNat(n__0) -> tt
[5] isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
[6] isNat(n__s(V1)) -> isNat(activate(V1))
[7] plus(N,0) -> U11(isNat(N),N)
[8] plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
[9] 0 -> n__0
[10] plus(X1,X2) -> n__plus(X1,X2)
[11] isNat(X) -> n__isNat(X)
[12] s(X) -> n__s(X)
[13] activate(n__0) -> 0
[14] activate(n__plus(X1,X2)) -> plus(X1,X2)
[15] activate(n__isNat(X)) -> isNat(X)
[16] activate(n__s(X)) -> s(X)
[17] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_U11(tt,N) , Marked_activate(N)>
<Marked_U21(tt,M,N) , Marked_s(plus(activate(N),activate(M)))>
<Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U21(tt,M,N) , Marked_activate(N)>
<Marked_U21(tt,M,N) , Marked_activate(M)>
<Marked_and(tt,X) , Marked_activate(X)>
<Marked_isNat(n__plus(V1,V2)) , Marked_and(isNat(activate(V1)),
                                 n__isNat(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_U11(isNat(N),N)>
<Marked_plus(N,0) , Marked_isNat(N)>
<Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)>
<Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNat(N))>
<Marked_plus(N,s(M)) , Marked_isNat(M)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)>
<Marked_activate(n__isNat(X)) , Marked_isNat(X)>
<Marked_activate(n__s(X)) , Marked_s(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_U11(tt,N) , Marked_activate(N)>
<Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U21(tt,M,N) , Marked_activate(N)>
<Marked_U21(tt,M,N) , Marked_activate(M)>
<Marked_and(tt,X) , Marked_activate(X)>
<Marked_isNat(n__plus(V1,V2)) , Marked_and(isNat(activate(V1)),
                                 n__isNat(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_U11(isNat(N),N)>
<Marked_plus(N,0) , Marked_isNat(N)>
<Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)>
<Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNat(N))>
<Marked_plus(N,s(M)) , Marked_isNat(M)>
<Marked_activate(n__plus(X1,X2)) , Marked_plus(X1,X2)>
<Marked_activate(n__isNat(X)) , Marked_isNat(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ activate ] (X0) = 1*X0; 
 [ Marked_plus ] (X0,X1) = 2*X1 + 2*X0; 
 [ n__0 ] () = 0; 
 [ plus ] (X0,X1) = 2*X1 + 1*X0 + 1; 
 [ Marked_U11 ] (X0,X1) = 2*X1; 
 [ 0 ] () = 0; 
 [ tt ] () = 0; 
 [ Marked_U21 ] (X0,X1,X2) = 2*X2 + 2*X1; 
 [ n__plus ] (X0,X1) = 2*X1 + 1*X0 + 1; 
 [ and ] (X0,X1) = 2*X1 + 1; 
 [ U11 ] (X0,X1) = 1*X1; 
 [ n__isNat ] (X0) = 1*X0; 
 [ U21 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1; 
 [ Marked_activate ] (X0) = 2*X0; 
 [ s ] (X0) = 1*X0; 
 [ Marked_and ] (X0,X1) = 2*X1; 
 [ n__s ] (X0) = 1*X0; 
 [ isNat ] (X0) = 1*X0; 
 [ Marked_isNat ] (X0) = 2*X0; 
 removing <Marked_isNat(n__plus(V1,V2)),Marked_and(isNat(activate(V1)),
                                         n__isNat(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_activate(n__plus(
                                                                   X1,
                                                                   X2)),
Marked_plus(X1,X2)>
 [ {
      
     DP termination of:
     <Marked_U11(tt,N) , Marked_activate(N)>
<Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U21(tt,M,N) , Marked_activate(N)>
<Marked_U21(tt,M,N) , Marked_activate(M)>
<Marked_and(tt,X) , Marked_activate(X)>
<Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
<Marked_isNat(n__s(V1)) , Marked_activate(V1)>
<Marked_plus(N,0) , Marked_U11(isNat(N),N)>
<Marked_plus(N,0) , Marked_isNat(N)>
<Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)>
<Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNat(N))>
<Marked_plus(N,s(M)) , Marked_isNat(M)>
<Marked_activate(n__isNat(X)) , Marked_isNat(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_U21(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ activate ] (X0) = 1*X0; 
 [ Marked_plus ] (X0,X1) = 1*X1; 
 [ n__0 ] () = 0; 
 [ plus ] (X0,X1) = 2*X1 + 1*X0; 
 [ 0 ] () = 0; 
 [ tt ] () = 0; 
 [ Marked_U21 ] (X0,X1,X2) = 1*X1 + 1; 
 [ n__plus ] (X0,X1) = 2*X1 + 1*X0; 
 [ and ] (X0,X1) = 1*X1; 
 [ U11 ] (X0,X1) = 1*X1; 
 [ n__isNat ] (X0) = 0; 
 [ U21 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1; 
 [ s ] (X0) = 1*X0 + 1; 
 [ n__s ] (X0) = 1*X0 + 1; 
 [ isNat ] (X0) = 0; 
 removing <Marked_U21(tt,M,N),Marked_plus(activate(N),activate(M))>
 [ {
      
     DP termination of:
     <Marked_plus(N,s(M)) , Marked_U21(and(isNat(M),n__isNat(N)),M,N)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
{
 
DP termination of:
<Marked_isNat(n__s(V1)) , Marked_isNat(activate(V1))>
<Marked_isNat(n__s(V1)) , Marked_activate(V1)>
<Marked_activate(n__isNat(X)) , Marked_isNat(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ activate ] (X0) = 1*X0 + 0; 
 [ n__0 ] () = 0; 
 [ plus ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ 0 ] () = 0; 
 [ tt ] () = 0; 
 [ n__plus ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ and ] (X0,X1) = 1*X1 + 0; 
 [ U11 ] (X0,X1) = 1*X1 + 0; 
 [ n__isNat ] (X0) = 1 + 2*X0 + 0; 
 [ U21 ] (X0,X1,X2) = 3 + 2*X1 + 1*X2 + 0; 
 [ Marked_activate ] (X0) = 3 + 1*X0 + 0; 
 [ s ] (X0) = 3 + 1*X0 + 0; 
 [ n__s ] (X0) = 3 + 1*X0 + 0; 
 [ isNat ] (X0) = 1 + 2*X0 + 0; 
 [ Marked_isNat ] (X0) = 2 + 2*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.310932 seconds (real time)
Cime Exit Status: 0