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

TRS termination of:
[1] sum(0) -> 0
[2] sum(s(x)) -> +(sum(x),s(x))
[3] sum1(0) -> 0
[4] sum1(s(x)) -> s(+(sum1(x),+(x,x)))


Sub problem: 
guided: 

DP termination of:
<Marked_sum(s(x)) , Marked_sum(x)>
<Marked_sum1(s(x)) , Marked_sum1(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_sum(s(x)) , Marked_sum(x)> --> <Marked_sum(s(x)) , Marked_sum(x)>
}

{  <Marked_sum1(s(x)) , Marked_sum1(x)> 
      --> <Marked_sum1(s(x)) , Marked_sum1(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sum(0) >= 0 ;
  sum(s(x)) >= +(sum(x),s(x)) ;
  sum1(0) >= 0 ;
  sum1(s(x)) >= s(+(sum1(x),+(x,x))) ;
  Marked_sum(s(x)) >= Marked_sum(x) ;
 }
 + Disjunctions:{ 
{
  Marked_sum(s(x)) > Marked_sum(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(0) >= 0
constraint: sum(s(x)) >= +(sum(x),s(x))
constraint: sum1(0) >= 0
constraint: sum1(s(x)) >= s(+(sum1(x),+(x,x)))
constraint: Marked_sum(s(x)) >= Marked_sum(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sum(0) >= 0 ;
  sum(s(x)) >= +(sum(x),s(x)) ;
  sum1(0) >= 0 ;
  sum1(s(x)) >= s(+(sum1(x),+(x,x))) ;
  Marked_sum1(s(x)) >= Marked_sum1(x) ;
 }
 + Disjunctions:{ 
{
  Marked_sum1(s(x)) > Marked_sum1(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(0) >= 0
constraint: sum(s(x)) >= +(sum(x),s(x))
constraint: sum1(0) >= 0
constraint: sum1(s(x)) >= s(+(sum1(x),+(x,x)))
constraint: Marked_sum1(s(x)) >= Marked_sum1(x)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] sum(0) -> 0
[2] sum(s(x)) -> +(sum(x),s(x))
[3] sum1(0) -> 0
[4] sum1(s(x)) -> s(+(sum1(x),+(x,x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_sum(s(x)) , Marked_sum(x)>
<Marked_sum1(s(x)) , Marked_sum1(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sum(s(x)) , Marked_sum(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ sum1 ] (X0) = 2 + 0; 
 [ + ] (X0,X1) = 0; 
 [ Marked_sum ] (X0) = 3*X0 + 0; 
 [ sum ] (X0) = 2 + 2*X0 + 0; 
 [ s ] (X0) = 2 + 3*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_sum1(s(x)) , Marked_sum1(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ sum1 ] (X0) = 2 + 0; 
 [ + ] (X0,X1) = 0; 
 [ sum ] (X0) = 2 + 2*X0 + 0; 
 [ Marked_sum1 ] (X0) = 3*X0 + 0; 
 [ s ] (X0) = 2 + 3*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.056871 seconds (real time)
Cime Exit Status: 0