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

TRS termination of:
[1] le(0,Y) -> true
[2] le(s(X),0) -> false
[3] le(s(X),s(Y)) -> le(X,Y)
[4] minus(0,Y) -> 0
[5] minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y)
[6] ifMinus(true,s(X),Y) -> 0
[7] ifMinus(false,s(X),Y) -> s(minus(X,Y))
[8] quot(0,s(Y)) -> 0
[9] quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))


Sub problem: 
guided: 

DP termination of:
<Marked_le(s(X),s(Y)) , Marked_le(X,Y)>
<Marked_minus(s(X),Y) , Marked_ifMinus(le(s(X),Y),s(X),Y)>
<Marked_minus(s(X),Y) , Marked_le(s(X),Y)>
<Marked_ifMinus(false,s(X),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)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <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_ifMinus(false,s(X),Y) , Marked_minus(X,Y)> 
      --> <Marked_minus(s(X),Y) , Marked_ifMinus(le(s(X),Y),s(X),Y)>
  <Marked_minus(s(X),Y) , Marked_ifMinus(le(s(X),Y),s(X),Y)> 
     --> <Marked_ifMinus(false,s(X),Y) , Marked_minus(X,Y)>
}

{  <Marked_le(s(X),s(Y)) , Marked_le(X,Y)> 
      --> <Marked_le(s(X),s(Y)) , Marked_le(X,Y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  le(0,Y) >= true ;
  le(s(X),0) >= false ;
  le(s(X),s(Y)) >= le(X,Y) ;
  minus(0,Y) >= 0 ;
  minus(s(X),Y) >= ifMinus(le(s(X),Y),s(X),Y) ;
  ifMinus(true,s(X),Y) >= 0 ;
  ifMinus(false,s(X),Y) >= s(minus(X,Y)) ;
  quot(0,s(Y)) >= 0 ;
  quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y))) ;
  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: le(0,Y) >= true
constraint: le(s(X),0) >= false
constraint: le(s(X),s(Y)) >= le(X,Y)
constraint: minus(0,Y) >= 0
constraint: minus(s(X),Y) >= ifMinus(le(s(X),Y),s(X),Y)
constraint: ifMinus(true,s(X),Y) >= 0
constraint: ifMinus(false,s(X),Y) >= s(minus(X,Y))
constraint: quot(0,s(Y)) >= 0
constraint: quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y)))
constraint: Marked_quot(s(X),s(Y)) >= Marked_quot(minus(X,Y),s(Y))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  le(0,Y) >= true ;
  le(s(X),0) >= false ;
  le(s(X),s(Y)) >= le(X,Y) ;
  minus(0,Y) >= 0 ;
  minus(s(X),Y) >= ifMinus(le(s(X),Y),s(X),Y) ;
  ifMinus(true,s(X),Y) >= 0 ;
  ifMinus(false,s(X),Y) >= s(minus(X,Y)) ;
  quot(0,s(Y)) >= 0 ;
  quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y))) ;
  Marked_minus(s(X),Y) >= Marked_ifMinus(le(s(X),Y),s(X),Y) ;
  Marked_ifMinus(false,s(X),Y) >= Marked_minus(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_minus(s(X),Y) > Marked_ifMinus(le(s(X),Y),s(X),Y) ;
 }
{
  Marked_ifMinus(false,s(X),Y) > Marked_minus(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: le(0,Y) >= true
constraint: le(s(X),0) >= false
constraint: le(s(X),s(Y)) >= le(X,Y)
constraint: minus(0,Y) >= 0
constraint: minus(s(X),Y) >= ifMinus(le(s(X),Y),s(X),Y)
constraint: ifMinus(true,s(X),Y) >= 0
constraint: ifMinus(false,s(X),Y) >= s(minus(X,Y))
constraint: quot(0,s(Y)) >= 0
constraint: quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y)))
constraint: Marked_minus(s(X),Y) >= Marked_ifMinus(le(s(X),Y),s(X),Y)
constraint: Marked_ifMinus(false,s(X),Y) >= Marked_minus(X,Y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  le(0,Y) >= true ;
  le(s(X),0) >= false ;
  le(s(X),s(Y)) >= le(X,Y) ;
  minus(0,Y) >= 0 ;
  minus(s(X),Y) >= ifMinus(le(s(X),Y),s(X),Y) ;
  ifMinus(true,s(X),Y) >= 0 ;
  ifMinus(false,s(X),Y) >= s(minus(X,Y)) ;
  quot(0,s(Y)) >= 0 ;
  quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y))) ;
  Marked_le(s(X),s(Y)) >= Marked_le(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_le(s(X),s(Y)) > Marked_le(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: le(0,Y) >= true
constraint: le(s(X),0) >= false
constraint: le(s(X),s(Y)) >= le(X,Y)
constraint: minus(0,Y) >= 0
constraint: minus(s(X),Y) >= ifMinus(le(s(X),Y),s(X),Y)
constraint: ifMinus(true,s(X),Y) >= 0
constraint: ifMinus(false,s(X),Y) >= s(minus(X,Y))
constraint: quot(0,s(Y)) >= 0
constraint: quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y)))
constraint: Marked_le(s(X),s(Y)) >= Marked_le(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] le(0,Y) -> true
[2] le(s(X),0) -> false
[3] le(s(X),s(Y)) -> le(X,Y)
[4] minus(0,Y) -> 0
[5] minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y)
[6] ifMinus(true,s(X),Y) -> 0
[7] ifMinus(false,s(X),Y) -> s(minus(X,Y))
[8] quot(0,s(Y)) -> 0
[9] quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_le(s(X),s(Y)) , Marked_le(X,Y)>
<Marked_minus(s(X),Y) , Marked_ifMinus(le(s(X),Y),s(X),Y)>
<Marked_minus(s(X),Y) , Marked_le(s(X),Y)>
<Marked_ifMinus(false,s(X),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)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_quot(s(X),s(Y)) , Marked_quot(minus(X,Y),s(Y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ true ] () = 0; 
 [ Marked_quot ] (X0,X1) = 3*X0 + 0; 
 [ s ] (X0) = 2 + 2*X0 + 0; 
 [ 0 ] () = 0; 
 [ ifMinus ] (X0,X1,X2) = 1*X1 + 0; 
 [ le ] (X0,X1) = 0; 
 [ minus ] (X0,X1) = 1*X0 + 0; 
 [ false ] () = 0; 
 [ quot ] (X0,X1) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_minus(s(X),Y) , Marked_ifMinus(le(s(X),Y),s(X),Y)>
<Marked_ifMinus(false,s(X),Y) , Marked_minus(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ true ] () = 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ 0 ] () = 0; 
 [ Marked_ifMinus ] (X0,X1,X2) = 2*X1 + 3*X2 + 0; 
 [ ifMinus ] (X0,X1,X2) = 1*X1 + 0; 
 [ le ] (X0,X1) = 0; 
 [ Marked_minus ] (X0,X1) = 1 + 3*X0 + 3*X1 + 0; 
 [ minus ] (X0,X1) = 1*X0 + 0; 
 [ false ] () = 0; 
 [ quot ] (X0,X1) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_le(s(X),s(Y)) , Marked_le(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ true ] () = 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ 0 ] () = 0; 
 [ ifMinus ] (X0,X1,X2) = 1*X1 + 0; 
 [ le ] (X0,X1) = 0; 
 [ minus ] (X0,X1) = 1*X0 + 0; 
 [ false ] () = 0; 
 [ Marked_le ] (X0,X1) = 1*X0 + 0; 
 [ quot ] (X0,X1) = 1*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.169946 seconds (real time)
Cime Exit Status: 0