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

TRS termination of:
[1] a__U11(tt,M,N) -> a__U12(tt,M,N)
[2] a__U12(tt,M,N) -> s(a__plus(mark(N),mark(M)))
[3] a__plus(N,0) -> mark(N)
[4] a__plus(N,s(M)) -> a__U11(tt,M,N)
[5] mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
[6] mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
[7] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
[8] mark(tt) -> tt
[9] mark(s(X)) -> s(mark(X))
[10] mark(0) -> 0
[11] a__U11(X1,X2,X3) -> U11(X1,X2,X3)
[12] a__U12(X1,X2,X3) -> U12(X1,X2,X3)
[13] a__plus(X1,X2) -> plus(X1,X2)


Sub problem: 
guided: 

DP termination of:
<Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)>
<Marked_a__U12(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__U12(tt,M,N) , Marked_mark(N)>
<Marked_a__U12(tt,M,N) , Marked_mark(M)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__U11(tt,M,N)>
<Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
<Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
<Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
<Marked_mark(s(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(s(X)) , Marked_mark(X)> 
      --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__U11(tt,M,N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_mark(N)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)> 
     --> <Marked_a__U12(tt,M,N) , Marked_mark(M)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)> 
     --> <Marked_a__U12(tt,M,N) , Marked_mark(N)>
  <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)> 
     --> <Marked_a__U12(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)> 
     --> <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)>
  <Marked_a__plus(N,s(M)) , Marked_a__U11(tt,M,N)> 
     --> <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_a__U12(tt,M,N) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__U11(tt,M,N)>
  <Marked_a__U12(tt,M,N) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,0) , Marked_mark(N)>
  <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)> 
     --> <Marked_a__U12(tt,M,N) , Marked_mark(M)>
  <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)> 
     --> <Marked_a__U12(tt,M,N) , Marked_mark(N)>
  <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)> 
     --> <Marked_a__U12(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__U12(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U12(X1,X2,X3) >= U12(X1,X2,X3) ;
  a__U11(tt,M,N) >= a__U12(tt,M,N) ;
  a__U11(X1,X2,X3) >= U11(X1,X2,X3) ;
  a__plus(N,s(M)) >= a__U11(tt,M,N) ;
  a__plus(N,0) >= mark(N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ;
  mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  Marked_a__plus(N,s(M)) >= Marked_a__U11(tt,M,N) ;
  Marked_a__plus(N,0) >= Marked_mark(N) ;
  Marked_a__U12(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ;
  Marked_a__U12(tt,M,N) >= Marked_mark(M) ;
  Marked_a__U12(tt,M,N) >= Marked_mark(N) ;
  Marked_a__U11(tt,M,N) >= Marked_a__U12(tt,M,N) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(U11(X1,X2,X3)) >= Marked_a__U11(mark(X1),X2,X3) ;
  Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(U12(X1,X2,X3)) >= Marked_a__U12(mark(X1),X2,X3) ;
  Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ;
 }
 + Disjunctions:{ 
{
  Marked_a__plus(N,s(M)) > Marked_a__U11(tt,M,N) ;
 }
{
  Marked_a__plus(N,0) > Marked_mark(N) ;
 }
{
  Marked_a__U12(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ;
 }
{
  Marked_a__U12(tt,M,N) > Marked_mark(M) ;
 }
{
  Marked_a__U12(tt,M,N) > Marked_mark(N) ;
 }
{
  Marked_a__U11(tt,M,N) > Marked_a__U12(tt,M,N) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(U11(X1,X2,X3)) > Marked_a__U11(mark(X1),X2,X3) ;
 }
{
  Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U12(X1,X2,X3)) > Marked_a__U12(mark(X1),X2,X3) ;
 }
{
  Marked_mark(U12(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X2) ;
 }
 } 
=== 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: a__U12(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U12(X1,X2,X3) >= U12(X1,X2,X3)
constraint: a__U11(tt,M,N) >= a__U12(tt,M,N)
constraint: a__U11(X1,X2,X3) >= U11(X1,X2,X3)
constraint: a__plus(N,s(M)) >= a__U11(tt,M,N)
constraint: a__plus(N,0) >= mark(N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3)
constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: Marked_a__plus(N,s(M)) >= Marked_a__U11(tt,M,N)
constraint: Marked_a__plus(N,0) >= Marked_mark(N)
constraint: Marked_a__U12(tt,M,N) >= Marked_a__plus(mark(N),mark(M))
constraint: Marked_a__U12(tt,M,N) >= Marked_mark(M)
constraint: Marked_a__U12(tt,M,N) >= Marked_mark(N)
constraint: Marked_a__U11(tt,M,N) >= Marked_a__U12(tt,M,N)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_a__U11(mark(X1),X2,X3)
constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_a__U12(mark(X1),X2,X3)
constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2))
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
      --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)> 
     --> <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U12(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U12(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
  <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)> 
     --> <Marked_a__U12(tt,M,N) , Marked_mark(M)>
  <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)> 
     --> <Marked_a__U12(tt,M,N) , Marked_mark(N)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__U12(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U12(X1,X2,X3) >= U12(X1,X2,X3) ;
  a__U11(tt,M,N) >= a__U12(tt,M,N) ;
  a__U11(X1,X2,X3) >= U11(X1,X2,X3) ;
  a__plus(N,s(M)) >= a__U11(tt,M,N) ;
  a__plus(N,0) >= mark(N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ;
  mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  Marked_a__U12(tt,M,N) >= Marked_mark(M) ;
  Marked_a__U12(tt,M,N) >= Marked_mark(N) ;
  Marked_a__U11(tt,M,N) >= Marked_a__U12(tt,M,N) ;
  Marked_mark(U11(X1,X2,X3)) >= Marked_a__U11(mark(X1),X2,X3) ;
  Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__U12(tt,M,N) > Marked_mark(M) ;
 }
{
  Marked_a__U12(tt,M,N) > Marked_mark(N) ;
 }
{
  Marked_a__U11(tt,M,N) > Marked_a__U12(tt,M,N) ;
 }
{
  Marked_mark(U11(X1,X2,X3)) > Marked_a__U11(mark(X1),X2,X3) ;
 }
{
  Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ;
 }
 } 
=== 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: a__U12(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U12(X1,X2,X3) >= U12(X1,X2,X3)
constraint: a__U11(tt,M,N) >= a__U12(tt,M,N)
constraint: a__U11(X1,X2,X3) >= U11(X1,X2,X3)
constraint: a__plus(N,s(M)) >= a__U11(tt,M,N)
constraint: a__plus(N,0) >= mark(N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3)
constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: Marked_a__U12(tt,M,N) >= Marked_mark(M)
constraint: Marked_a__U12(tt,M,N) >= Marked_mark(N)
constraint: Marked_a__U11(tt,M,N) >= Marked_a__U12(tt,M,N)
constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_a__U11(mark(X1),X2,X3)
constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__U11(tt,M,N) -> a__U12(tt,M,N)
[2] a__U12(tt,M,N) -> s(a__plus(mark(N),mark(M)))
[3] a__plus(N,0) -> mark(N)
[4] a__plus(N,s(M)) -> a__U11(tt,M,N)
[5] mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
[6] mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
[7] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
[8] mark(tt) -> tt
[9] mark(s(X)) -> s(mark(X))
[10] mark(0) -> 0
[11] a__U11(X1,X2,X3) -> U11(X1,X2,X3)
[12] a__U12(X1,X2,X3) -> U12(X1,X2,X3)
[13] a__plus(X1,X2) -> plus(X1,X2)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)>
<Marked_a__U12(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__U12(tt,M,N) , Marked_mark(N)>
<Marked_a__U12(tt,M,N) , Marked_mark(M)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__U11(tt,M,N)>
<Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
<Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
<Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)>
<Marked_a__U12(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__U12(tt,M,N) , Marked_mark(N)>
<Marked_a__U12(tt,M,N) , Marked_mark(M)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__U11(tt,M,N)>
<Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
<Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(U12(X1,X2,X3)) , Marked_a__U12(mark(X1),X2,X3)>
<Marked_mark(U12(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ a__U12 ] (X0,X1,X2) = 1*X2 + 3*X1 + 2*X0 + 3; 
 [ U12 ] (X0,X1,X2) = 1*X2 + 3*X1 + 2*X0 + 3; 
 [ a__plus ] (X0,X1) = 3*X1 + 1*X0 + 3; 
 [ Marked_a__U11 ] (X0,X1,X2) = 1*X2 + 2*X1 + 3; 
 [ a__U11 ] (X0,X1,X2) = 1*X2 + 3*X1 + 3*X0; 
 [ Marked_a__plus ] (X0,X1) = 2*X1 + 1*X0; 
 [ 0 ] () = 2; 
 [ tt ] () = 3; 
 [ plus ] (X0,X1) = 3*X1 + 1*X0 + 3; 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 1*X0 + 3; 
 [ s ] (X0) = 1*X0 + 2; 
 [ Marked_a__U12 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1*X0; 
 [ U11 ] (X0,X1,X2) = 1*X2 + 3*X1 + 3*X0; 
 removing <Marked_a__U12(tt,M,N),Marked_a__plus(mark(N),mark(M))><Marked_a__plus(
                                                                   N,
                                                                   0),
Marked_mark(N)><Marked_a__plus(N,s(M)),Marked_a__U11(tt,M,N)><Marked_mark(
                                                               U12(X1,
                                                                X2,X3)),
Marked_a__U12(mark(X1),X2,X3)><Marked_mark(U12(X1,X2,X3)),Marked_mark(X1)><
Marked_mark(plus(X1,X2)),Marked_a__plus(mark(X1),mark(X2))><Marked_mark(
                                                             plus(X1,
                                                              X2)),Marked_mark(
                                                                    X1)><
Marked_mark(plus(X1,X2)),Marked_mark(X2)><Marked_mark(s(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)>
<Marked_a__U12(tt,M,N) , Marked_mark(N)>
<Marked_a__U12(tt,M,N) , Marked_mark(M)>
<Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
<Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__U11(tt,M,N) , Marked_a__U12(tt,M,N)>
<Marked_a__U12(tt,M,N) , Marked_mark(N)>
<Marked_a__U12(tt,M,N) , Marked_mark(M)>
<Marked_mark(U11(X1,X2,X3)) , Marked_a__U11(mark(X1),X2,X3)>
<Marked_mark(U11(X1,X2,X3)) , Marked_mark(X1)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ a__U12 ] (X0,X1,X2) = 1*X0 + 2*X1 + 1*X2 + 0; 
 [ U12 ] (X0,X1,X2) = 1*X0 + 2*X1 + 1*X2 + 0; 
 [ a__plus ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ Marked_a__U11 ] (X0,X1,X2) = 3 + 3*X0 + 3*X1 + 3*X2 + 0; 
 [ a__U11 ] (X0,X1,X2) = 2 + 1*X0 + 2*X1 + 1*X2 + 0; 
 [ 0 ] () = 0; 
 [ tt ] () = 2 + 0; 
 [ plus ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ mark ] (X0) = 1*X0 + 0; 
 [ Marked_mark ] (X0) = 2 + 3*X0 + 0; 
 [ s ] (X0) = 2 + 1*X0 + 0; 
 [ Marked_a__U12 ] (X0,X1,X2) = 3 + 1*X0 + 3*X1 + 3*X2 + 0; 
 [ U11 ] (X0,X1,X2) = 2 + 1*X0 + 2*X1 + 1*X2 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.154133 seconds (real time)
Cime Exit Status: 0