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

TRS termination of:
[1] times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0))),times(x,s(z)))
[2] times(x,0) -> 0
[3] times(x,s(y)) -> plus(times(x,y),x)
[4] plus(x,0) -> x
[5] plus(x,s(y)) -> s(plus(x,y))


Sub problem: 
guided: 

DP termination of:
<Marked_times(x,plus(y,s(z))) , Marked_plus(times(x,plus(y,times(s(z),0))),
                                 times(x,s(z)))>
<Marked_times(x,plus(y,s(z))) , Marked_times(x,plus(y,times(s(z),0)))>
<Marked_times(x,plus(y,s(z))) , Marked_plus(y,times(s(z),0))>
<Marked_times(x,plus(y,s(z))) , Marked_times(s(z),0)>
<Marked_times(x,plus(y,s(z))) , Marked_times(x,s(z))>
<Marked_times(x,s(y)) , Marked_plus(times(x,y),x)>
<Marked_times(x,s(y)) , Marked_times(x,y)>
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_times(x,s(y)) , Marked_times(x,y)> 
      --> <Marked_times(x,s(y)) , Marked_times(x,y)>
  <Marked_times(x,s(y)) , Marked_times(x,y)> 
     --> <Marked_times(x,plus(y,s(z))) , Marked_times(x,s(z))>
  <Marked_times(x,s(y)) , Marked_times(x,y)> 
     --> <Marked_times(x,plus(y,s(z))) , Marked_times(x,plus(y,times(s(z),0)))>
  <Marked_times(x,plus(y,s(z))) , Marked_times(x,s(z))> 
     --> <Marked_times(x,s(y)) , Marked_times(x,y)>
  <Marked_times(x,plus(y,s(z))) , Marked_times(x,plus(y,times(s(z),0)))> 
     --> <Marked_times(x,s(y)) , Marked_times(x,y)>
  <Marked_times(x,plus(y,s(z))) , Marked_times(x,plus(y,times(s(z),0)))> 
     --> <Marked_times(x,plus(y,s(z))) , Marked_times(x,s(z))>
  <Marked_times(x,plus(y,s(z))) , Marked_times(x,plus(y,times(s(z),0)))> 
     --> <Marked_times(x,plus(y,s(z))) , Marked_times(x,plus(y,times(s(z),0)))>
}

{  <Marked_plus(x,s(y)) , Marked_plus(x,y)> 
      --> <Marked_plus(x,s(y)) , Marked_plus(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  plus(x,s(y)) >= s(plus(x,y)) ;
  plus(x,0) >= x ;
  times(x,plus(y,s(z))) >= plus(times(x,plus(y,times(s(z),0))),times(x,s(z))) ;
  times(x,s(y)) >= plus(times(x,y),x) ;
  times(x,0) >= 0 ;
  Marked_times(x,plus(y,s(z))) >= Marked_times(x,plus(y,times(s(z),0))) ;
  Marked_times(x,plus(y,s(z))) >= Marked_times(x,s(z)) ;
  Marked_times(x,s(y)) >= Marked_times(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_times(x,plus(y,s(z))) > Marked_times(x,plus(y,times(s(z),0))) ;
 }
{
  Marked_times(x,plus(y,s(z))) > Marked_times(x,s(z)) ;
 }
{
  Marked_times(x,s(y)) > Marked_times(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
=== 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 : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: plus(x,s(y)) >= s(plus(x,y))
constraint: plus(x,0) >= x
constraint: times(x,plus(y,s(z))) >= plus(times(x,plus(y,times(s(z),0))),
                                      times(x,s(z)))
constraint: times(x,s(y)) >= plus(times(x,y),x)
constraint: times(x,0) >= 0
constraint: Marked_times(x,plus(y,s(z))) >= Marked_times(x,
                                             plus(y,times(s(z),0)))
constraint: Marked_times(x,plus(y,s(z))) >= Marked_times(x,s(z))
constraint: Marked_times(x,s(y)) >= Marked_times(x,y)
APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0))),times(x,s(z)))
[2] times(x,0) -> 0
[3] times(x,s(y)) -> plus(times(x,y),x)
[4] plus(x,0) -> x
[5] plus(x,s(y)) -> s(plus(x,y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_times(x,plus(y,s(z))) , Marked_plus(times(x,plus(y,times(s(z),0))),
                                      times(x,s(z)))>
<Marked_times(x,plus(y,s(z))) , Marked_times(x,plus(y,times(s(z),0)))>
<Marked_times(x,plus(y,s(z))) , Marked_plus(y,times(s(z),0))>
<Marked_times(x,plus(y,s(z))) , Marked_times(s(z),0)>
<Marked_times(x,plus(y,s(z))) , Marked_times(x,s(z))>
<Marked_times(x,s(y)) , Marked_plus(times(x,y),x)>
<Marked_times(x,s(y)) , Marked_times(x,y)>
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_times(x,plus(y,s(z))) , Marked_times(x,plus(y,times(s(z),0)))>
<Marked_times(x,plus(y,s(z))) , Marked_times(x,s(z))>
<Marked_times(x,s(y)) , Marked_times(x,y)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ plus ] (X0,X1) = 1*X1 + 1*X0; 
 [ s ] (X0) = 1*X0 + 2; 
 [ times ] (X0,X1) = 1*X1*X0; 
 [ Marked_times ] (X0,X1) = 2*X1; 
 [ 0 ] () = 0; 
 removing <Marked_times(x,plus(y,s(z))),Marked_times(x,plus(y,times(s(z),0)))><
Marked_times(x,s(y)),Marked_times(x,y)>
 [ {
      
     DP termination of:
     <Marked_times(x,plus(y,s(z))) , Marked_times(x,s(z))>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
{
 
DP termination of:
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 1.069001 seconds (real time)
Cime Exit Status: 0