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

TRS termination of:
[1] pred(s(x)) -> x
[2] minus(x,0) -> x
[3] minus(x,s(y)) -> pred(minus(x,y))
[4] quot(0,s(y)) -> 0
[5] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
[6] log(s(0)) -> 0
[7] log(s(s(x))) -> s(log(s(quot(x,s(s(0))))))


Sub problem: 
guided: 

DP termination of:
<Marked_minus(x,s(y)) , Marked_pred(minus(x,y))>
<Marked_minus(x,s(y)) , Marked_minus(x,y)>
<Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))>
<Marked_quot(s(x),s(y)) , Marked_minus(x,y)>
<Marked_log(s(s(x))) , Marked_log(s(quot(x,s(s(0)))))>
<Marked_log(s(s(x))) , Marked_quot(x,s(s(0)))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_log(s(s(x))) , Marked_log(s(quot(x,s(s(0)))))> 
      --> <Marked_log(s(s(x))) , Marked_log(s(quot(x,s(s(0)))))>
}

{  <Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))> 
      --> <Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))>
}

{  <Marked_minus(x,s(y)) , Marked_minus(x,y)> 
      --> <Marked_minus(x,s(y)) , Marked_minus(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  pred(s(x)) >= x ;
  minus(x,s(y)) >= pred(minus(x,y)) ;
  minus(x,0) >= x ;
  quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ;
  quot(0,s(y)) >= 0 ;
  log(s(s(x))) >= s(log(s(quot(x,s(s(0)))))) ;
  log(s(0)) >= 0 ;
  Marked_log(s(s(x))) >= Marked_log(s(quot(x,s(s(0))))) ;
 }
 + Disjunctions:{ 
{
  Marked_log(s(s(x))) > Marked_log(s(quot(x,s(s(0))))) ;
 }
 } 
=== 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: pred(s(x)) >= x
constraint: minus(x,s(y)) >= pred(minus(x,y))
constraint: minus(x,0) >= x
constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y)))
constraint: quot(0,s(y)) >= 0
constraint: log(s(s(x))) >= s(log(s(quot(x,s(s(0))))))
constraint: log(s(0)) >= 0
constraint: Marked_log(s(s(x))) >= Marked_log(s(quot(x,s(s(0)))))
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  pred(s(x)) >= x ;
  minus(x,s(y)) >= pred(minus(x,y)) ;
  minus(x,0) >= x ;
  quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ;
  quot(0,s(y)) >= 0 ;
  log(s(s(x))) >= s(log(s(quot(x,s(s(0)))))) ;
  log(s(0)) >= 0 ;
  Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y)) ;
 }
 + Disjunctions:{ 
{
  Marked_quot(s(x),s(y)) > Marked_quot(minus(x,y),s(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: pred(s(x)) >= x
constraint: minus(x,s(y)) >= pred(minus(x,y))
constraint: minus(x,0) >= x
constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y)))
constraint: quot(0,s(y)) >= 0
constraint: log(s(s(x))) >= s(log(s(quot(x,s(s(0))))))
constraint: log(s(0)) >= 0
constraint: Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y))
APPLY CRITERIA (Subterm criterion)

ST: Marked_minus -> 2

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] pred(s(x)) -> x
[2] minus(x,0) -> x
[3] minus(x,s(y)) -> pred(minus(x,y))
[4] quot(0,s(y)) -> 0
[5] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
[6] log(s(0)) -> 0
[7] log(s(s(x))) -> s(log(s(quot(x,s(s(0))))))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(x,s(y)) , Marked_pred(minus(x,y))>
<Marked_minus(x,s(y)) , Marked_minus(x,y)>
<Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))>
<Marked_quot(s(x),s(y)) , Marked_minus(x,y)>
<Marked_log(s(s(x))) , Marked_log(s(quot(x,s(s(0)))))>
<Marked_log(s(s(x))) , Marked_quot(x,s(s(0)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_log(s(s(x))) , Marked_log(s(quot(x,s(s(0)))))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ pred ] (X0) = 1*X0 + 0; 
 [ quot ] (X0,X1) = 1*X0 + 0; 
 [ minus ] (X0,X1) = 1*X0 + 0; 
 [ Marked_log ] (X0) = 2*X0 + 0; 
 [ s ] (X0) = 2 + 2*X0 + 0; 
 [ log ] (X0) = 1*X0 + 0; 
 [ 0 ] () = 0; 
 ]} 
{
 
DP termination of:
<Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ pred ] (X0) = 1*X0 + 0; 
 [ quot ] (X0,X1) = 1*X0 + 0; 
 [ minus ] (X0,X1) = 1*X0 + 0; 
 [ s ] (X0) = 3 + 2*X0 + 0; 
 [ log ] (X0) = 2*X0 + 0; 
 [ 0 ] () = 0; 
 [ Marked_quot ] (X0,X1) = 2*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_minus(x,s(y)) , Marked_minus(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.193255 seconds (real time)
Cime Exit Status: 0