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

TRS termination of:
[1] exp(x,0) -> s(0)
[2] exp(x,s(y)) ->  *(x,exp(x,y))
[3]  *(0,y) -> 0
[4]  *(s(x),y) -> +(y, *(x,y))
[5] -(0,y) -> 0
[6] -(x,0) -> x
[7] -(s(x),s(y)) -> -(x,y)


Sub problem: 
guided: 

DP termination of:
<Marked_exp(x,s(y)) , Marked_*(x,exp(x,y))>
<Marked_exp(x,s(y)) , Marked_exp(x,y)>
<Marked_*(s(x),y) , Marked_*(x,y)>
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_exp(x,s(y)) , Marked_exp(x,y)> 
      --> <Marked_exp(x,s(y)) , Marked_exp(x,y)>
}

{  <Marked_*(s(x),y) , Marked_*(x,y)> --> <Marked_*(s(x),y) , Marked_*(x,y)>
}

{  <Marked_-(s(x),s(y)) , Marked_-(x,y)> 
      --> <Marked_-(s(x),s(y)) , Marked_-(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  exp(x,s(y)) >=  *(x,exp(x,y)) ;
  exp(x,0) >= s(0) ;
   *(s(x),y) >= +(y, *(x,y)) ;
   *(0,y) >= 0 ;
  -(s(x),s(y)) >= -(x,y) ;
  -(0,y) >= 0 ;
  -(x,0) >= x ;
  Marked_exp(x,s(y)) >= Marked_exp(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_exp(x,s(y)) > Marked_exp(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: exp(x,s(y)) >=  *(x,exp(x,y))
constraint: exp(x,0) >= s(0)
constraint:  *(s(x),y) >= +(y, *(x,y))
constraint:  *(0,y) >= 0
constraint: -(s(x),s(y)) >= -(x,y)
constraint: -(0,y) >= 0
constraint: -(x,0) >= x
constraint: Marked_exp(x,s(y)) >= Marked_exp(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  exp(x,s(y)) >=  *(x,exp(x,y)) ;
  exp(x,0) >= s(0) ;
   *(s(x),y) >= +(y, *(x,y)) ;
   *(0,y) >= 0 ;
  -(s(x),s(y)) >= -(x,y) ;
  -(0,y) >= 0 ;
  -(x,0) >= x ;
  Marked_*(s(x),y) >= Marked_*(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_*(s(x),y) > Marked_*(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: exp(x,s(y)) >=  *(x,exp(x,y))
constraint: exp(x,0) >= s(0)
constraint:  *(s(x),y) >= +(y, *(x,y))
constraint:  *(0,y) >= 0
constraint: -(s(x),s(y)) >= -(x,y)
constraint: -(0,y) >= 0
constraint: -(x,0) >= x
constraint: Marked_*(s(x),y) >= Marked_*(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  exp(x,s(y)) >=  *(x,exp(x,y)) ;
  exp(x,0) >= s(0) ;
   *(s(x),y) >= +(y, *(x,y)) ;
   *(0,y) >= 0 ;
  -(s(x),s(y)) >= -(x,y) ;
  -(0,y) >= 0 ;
  -(x,0) >= x ;
  Marked_-(s(x),s(y)) >= Marked_-(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_-(s(x),s(y)) > Marked_-(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: exp(x,s(y)) >=  *(x,exp(x,y))
constraint: exp(x,0) >= s(0)
constraint:  *(s(x),y) >= +(y, *(x,y))
constraint:  *(0,y) >= 0
constraint: -(s(x),s(y)) >= -(x,y)
constraint: -(0,y) >= 0
constraint: -(x,0) >= x
constraint: Marked_-(s(x),s(y)) >= Marked_-(x,y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] exp(x,0) -> s(0)
[2] exp(x,s(y)) ->  *(x,exp(x,y))
[3]  *(0,y) -> 0
[4]  *(s(x),y) -> +(y, *(x,y))
[5] -(0,y) -> 0
[6] -(x,0) -> x
[7] -(s(x),s(y)) -> -(x,y)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_exp(x,s(y)) , Marked_*(x,exp(x,y))>
<Marked_exp(x,s(y)) , Marked_exp(x,y)>
<Marked_*(s(x),y) , Marked_*(x,y)>
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_exp(x,s(y)) , Marked_exp(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ s ] (X0) = 2 + 3*X0 + 0; 
 [ Marked_exp ] (X0,X1) = 3*X1 + 0; 
 [ + ] (X0,X1) = 2 + 0; 
 [ exp ] (X0,X1) = 2 + 3*X0 + 2*X1 + 0; 
 [ 0 ] () = 0; 
 [ - ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ * ] (X0,X1) = 2*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_*(s(x),y) , Marked_*(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ s ] (X0) = 2 + 3*X0 + 0; 
 [ + ] (X0,X1) = 2*X1 + 0; 
 [ exp ] (X0,X1) = 2 + 3*X0 + 2*X1 + 0; 
 [ 0 ] () = 0; 
 [ - ] (X0,X1) = 2*X0 + 2*X1 + 0; 
 [ * ] (X0,X1) = 3*X0 + 0; 
 [ Marked_* ] (X0,X1) = 3*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ s ] (X0) = 1 + 1*X0 + 0; 
 [ + ] (X0,X1) = 1*X0 + 0; 
 [ exp ] (X0,X1) = 1 + 3*X0 + 0; 
 [ Marked_- ] (X0,X1) = 1*X0 + 0; 
 [ 0 ] () = 0; 
 [ - ] (X0,X1) = 2*X0 + 3*X1 + 0; 
 [ * ] (X0,X1) = 1*X1 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.067270 seconds (real time)
Cime Exit Status: 0