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

TRS termination of:
[1] sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
[2] sum(cons(0,x),y) -> sum(x,y)
[3] sum(nil,y) -> y
[4] weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0,x)))
[5] weight(cons(n,nil)) -> n


Sub problem: 
guided: 

DP termination of:
<Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),cons(s(m),y))>
<Marked_sum(cons(0,x),y) , Marked_sum(x,y)>
<Marked_weight(cons(n,cons(m,x))) , Marked_weight(sum(cons(n,cons(m,x)),
                                                   cons(0,x)))>
<Marked_weight(cons(n,cons(m,x))) , Marked_sum(cons(n,cons(m,x)),cons(0,x))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_weight(cons(n,cons(m,x))) , Marked_weight(sum(cons(n,cons(m,x)),
                                                      cons(0,x)))> 
      --> <Marked_weight(cons(n,cons(m,x))) , Marked_weight(sum(cons(
                                                                 n,cons(m,x)),
                                                             cons(0,x)))>
}

{  <Marked_sum(cons(0,x),y) , Marked_sum(x,y)> 
      --> <Marked_sum(cons(0,x),y) , Marked_sum(x,y)>
  <Marked_sum(cons(0,x),y) , Marked_sum(x,y)> 
     --> <Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),
                                                cons(s(m),y))>
  <Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),cons(s(m),y))> 
     --> <Marked_sum(cons(0,x),y) , Marked_sum(x,y)>
  <Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),cons(s(m),y))> 
     --> <Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),
                                                cons(s(m),y))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sum(cons(s(n),x),cons(m,y)) >= sum(cons(n,x),cons(s(m),y)) ;
  sum(cons(0,x),y) >= sum(x,y) ;
  sum(nil,y) >= y ;
  weight(cons(n,cons(m,x))) >= weight(sum(cons(n,cons(m,x)),cons(0,x))) ;
  weight(cons(n,nil)) >= n ;
  Marked_weight(cons(n,cons(m,x))) >= Marked_weight(sum(cons(n,cons(m,x)),
                                                     cons(0,x))) ;
 }
 + Disjunctions:{ 
{
  Marked_weight(cons(n,cons(m,x))) > Marked_weight(sum(cons(n,cons(m,x)),
                                                    cons(0,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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: sum(cons(s(n),x),cons(m,y)) >= sum(cons(n,x),cons(s(m),y))
constraint: sum(cons(0,x),y) >= sum(x,y)
constraint: sum(nil,y) >= y
constraint: weight(cons(n,cons(m,x))) >= weight(sum(cons(n,cons(m,x)),
                                                 cons(0,x)))
constraint: weight(cons(n,nil)) >= n
constraint: Marked_weight(cons(n,cons(m,x))) >= Marked_weight(sum(cons(
                                                                   n,
                                                                   cons(m,x)),
                                                               cons(0,x)))
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sum(cons(s(n),x),cons(m,y)) >= sum(cons(n,x),cons(s(m),y)) ;
  sum(cons(0,x),y) >= sum(x,y) ;
  sum(nil,y) >= y ;
  weight(cons(n,cons(m,x))) >= weight(sum(cons(n,cons(m,x)),cons(0,x))) ;
  weight(cons(n,nil)) >= n ;
  Marked_sum(cons(s(n),x),cons(m,y)) >= Marked_sum(cons(n,x),cons(s(m),y)) ;
  Marked_sum(cons(0,x),y) >= Marked_sum(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_sum(cons(s(n),x),cons(m,y)) > Marked_sum(cons(n,x),cons(s(m),y)) ;
 }
{
  Marked_sum(cons(0,x),y) > Marked_sum(x,y) ;
 }
 } 
=== 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: sum(cons(s(n),x),cons(m,y)) >= sum(cons(n,x),cons(s(m),y))
constraint: sum(cons(0,x),y) >= sum(x,y)
constraint: sum(nil,y) >= y
constraint: weight(cons(n,cons(m,x))) >= weight(sum(cons(n,cons(m,x)),
                                                 cons(0,x)))
constraint: weight(cons(n,nil)) >= n
constraint: Marked_sum(cons(s(n),x),cons(m,y)) >= Marked_sum(cons(n,x),
                                                   cons(s(m),y))
constraint: Marked_sum(cons(0,x),y) >= Marked_sum(x,y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),cons(s(m),y))> 
      --> <Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),
                                                 cons(s(m),y))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sum(cons(s(n),x),cons(m,y)) >= sum(cons(n,x),cons(s(m),y)) ;
  sum(cons(0,x),y) >= sum(x,y) ;
  sum(nil,y) >= y ;
  weight(cons(n,cons(m,x))) >= weight(sum(cons(n,cons(m,x)),cons(0,x))) ;
  weight(cons(n,nil)) >= n ;
  Marked_sum(cons(s(n),x),cons(m,y)) >= Marked_sum(cons(n,x),cons(s(m),y)) ;
 }
 + Disjunctions:{ 
{
  Marked_sum(cons(s(n),x),cons(m,y)) > Marked_sum(cons(n,x),cons(s(m),y)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: sum(cons(s(n),x),cons(m,y)) >= sum(cons(n,x),cons(s(m),y))
constraint: sum(cons(0,x),y) >= sum(x,y)
constraint: sum(nil,y) >= y
constraint: weight(cons(n,cons(m,x))) >= weight(sum(cons(n,cons(m,x)),
                                                 cons(0,x)))
constraint: weight(cons(n,nil)) >= n
constraint: Marked_sum(cons(s(n),x),cons(m,y)) >= Marked_sum(cons(n,x),
                                                   cons(s(m),y))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
[2] sum(cons(0,x),y) -> sum(x,y)
[3] sum(nil,y) -> y
[4] weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0,x)))
[5] weight(cons(n,nil)) -> n
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),cons(s(m),y))>
<Marked_sum(cons(0,x),y) , Marked_sum(x,y)>
<Marked_weight(cons(n,cons(m,x))) , Marked_weight(sum(cons(n,cons(m,x)),
                                                   cons(0,x)))>
<Marked_weight(cons(n,cons(m,x))) , Marked_sum(cons(n,cons(m,x)),cons(0,x))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_weight(cons(n,cons(m,x))) , Marked_weight(sum(cons(n,cons(m,x)),
                                                        cons(0,x)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ sum ] (X0,X1) = 1 + 2*X1 + 0; 
 [ nil ] () = 2 + 0; 
 [ s ] (X0) = 0; 
 [ Marked_weight ] (X0) = 3*X0 + 0; 
 [ cons ] (X0,X1) = 2 + 1*X0 + 2*X1 + 0; 
 [ weight ] (X0) = 3 + 1*X0 + 0; 
 [ 0 ] () = 0; 
 ]} 
{
 
DP termination of:
<Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),cons(s(m),y))>
<Marked_sum(cons(0,x),y) , Marked_sum(x,y)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ sum ] (X0,X1) = 1*X1; 
 [ nil ] () = 3; 
 [ s ] (X0) = 1*X0; 
 [ cons ] (X0,X1) = 2*X1 + 2*X0 + 2; 
 [ weight ] (X0) = 1*X0 + 2; 
 [ 0 ] () = 0; 
 [ Marked_sum ] (X0,X1) = 1*X0; 
 removing <Marked_sum(cons(0,x),y),Marked_sum(x,y)>
 [ {
      
     DP termination of:
     <Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),cons(s(m),y))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sum(cons(s(n),x),cons(m,y)) , Marked_sum(cons(n,x),cons(s(m),y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
      [ sum ] (X0,X1) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X1 + 
     [ [ 0 , 1 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ nil ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ s ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ cons ] (X0,X1) = [ [ 1 , 1 , 1 ] [ 0 , 1 , 0 ] [ 1 , 0 , 1 ] ]*X1 + 
[ [ 1 , 1 , 1 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ weight ] (X0) = [ [ 1 , 0 , 1 ] [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_sum ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + 
[ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 1.482970 seconds (real time)
Cime Exit Status: 0