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

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


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_le(s(X),s(Y)) , Marked_le(X,Y)>
<Marked_gcd(s(X),s(Y)) , Marked_if(le(Y,X),s(X),s(Y))>
<Marked_gcd(s(X),s(Y)) , Marked_le(Y,X)>
<Marked_if(true,s(X),s(Y)) , Marked_gcd(minus(X,Y),s(Y))>
<Marked_if(true,s(X),s(Y)) , Marked_minus(X,Y)>
<Marked_if(false,s(X),s(Y)) , Marked_gcd(minus(Y,X),s(X))>
<Marked_if(false,s(X),s(Y)) , Marked_minus(Y,X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_if(false,s(X),s(Y)) , Marked_gcd(minus(Y,X),s(X))> 
      --> <Marked_gcd(s(X),s(Y)) , Marked_if(le(Y,X),s(X),s(Y))>
  <Marked_if(true,s(X),s(Y)) , Marked_gcd(minus(X,Y),s(Y))> 
     --> <Marked_gcd(s(X),s(Y)) , Marked_if(le(Y,X),s(X),s(Y))>
  <Marked_gcd(s(X),s(Y)) , Marked_if(le(Y,X),s(X),s(Y))> 
     --> <Marked_if(false,s(X),s(Y)) , Marked_gcd(minus(Y,X),s(X))>
  <Marked_gcd(s(X),s(Y)) , Marked_if(le(Y,X),s(X),s(Y))> 
     --> <Marked_if(true,s(X),s(Y)) , Marked_gcd(minus(X,Y),s(Y))>
}

{  <Marked_le(s(X),s(Y)) , Marked_le(X,Y)> 
      --> <Marked_le(s(X),s(Y)) , Marked_le(X,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 ;
  le(s(X),s(Y)) >= le(X,Y) ;
  le(s(X),0) >= false ;
  le(0,Y) >= true ;
  gcd(s(X),s(Y)) >= if(le(Y,X),s(X),s(Y)) ;
  gcd(s(X),0) >= s(X) ;
  gcd(0,Y) >= 0 ;
  if(false,s(X),s(Y)) >= gcd(minus(Y,X),s(X)) ;
  if(true,s(X),s(Y)) >= gcd(minus(X,Y),s(Y)) ;
  Marked_if(false,s(X),s(Y)) >= Marked_gcd(minus(Y,X),s(X)) ;
  Marked_if(true,s(X),s(Y)) >= Marked_gcd(minus(X,Y),s(Y)) ;
  Marked_gcd(s(X),s(Y)) >= Marked_if(le(Y,X),s(X),s(Y)) ;
 }
 + Disjunctions:{ 
{
  Marked_if(false,s(X),s(Y)) > Marked_gcd(minus(Y,X),s(X)) ;
 }
{
  Marked_if(true,s(X),s(Y)) > Marked_gcd(minus(X,Y),s(Y)) ;
 }
{
  Marked_gcd(s(X),s(Y)) > Marked_if(le(Y,X),s(X),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: le(s(X),s(Y)) >= le(X,Y)
constraint: le(s(X),0) >= false
constraint: le(0,Y) >= true
constraint: gcd(s(X),s(Y)) >= if(le(Y,X),s(X),s(Y))
constraint: gcd(s(X),0) >= s(X)
constraint: gcd(0,Y) >= 0
constraint: if(false,s(X),s(Y)) >= gcd(minus(Y,X),s(X))
constraint: if(true,s(X),s(Y)) >= gcd(minus(X,Y),s(Y))
constraint: Marked_if(false,s(X),s(Y)) >= Marked_gcd(minus(Y,X),s(X))
constraint: Marked_if(true,s(X),s(Y)) >= Marked_gcd(minus(X,Y),s(Y))
constraint: Marked_gcd(s(X),s(Y)) >= Marked_if(le(Y,X),s(X),s(Y))
APPLY CRITERIA (Subterm criterion)

ST: Marked_le -> 1

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] minus(X,s(Y)) -> pred(minus(X,Y))
[2] minus(X,0) -> X
[3] pred(s(X)) -> X
[4] le(s(X),s(Y)) -> le(X,Y)
[5] le(s(X),0) -> false
[6] le(0,Y) -> true
[7] gcd(0,Y) -> 0
[8] gcd(s(X),0) -> s(X)
[9] gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
[10] if(true,s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
[11] if(false,s(X),s(Y)) -> gcd(minus(Y,X),s(X))
 ,
 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_le(s(X),s(Y)) , Marked_le(X,Y)>
<Marked_gcd(s(X),s(Y)) , Marked_if(le(Y,X),s(X),s(Y))>
<Marked_gcd(s(X),s(Y)) , Marked_le(Y,X)>
<Marked_if(true,s(X),s(Y)) , Marked_gcd(minus(X,Y),s(Y))>
<Marked_if(true,s(X),s(Y)) , Marked_minus(X,Y)>
<Marked_if(false,s(X),s(Y)) , Marked_gcd(minus(Y,X),s(X))>
<Marked_if(false,s(X),s(Y)) , Marked_minus(Y,X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_gcd(s(X),s(Y)) , Marked_if(le(Y,X),s(X),s(Y))>
<Marked_if(true,s(X),s(Y)) , Marked_gcd(minus(X,Y),s(Y))>
<Marked_if(false,s(X),s(Y)) , Marked_gcd(minus(Y,X),s(X))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ pred ] (X0) = 1*X0 + 0; 
 [ if ] (X0,X1,X2) = 2*X1 + 1*X2 + 0; 
 [ le ] (X0,X1) = 0; 
 [ s ] (X0) = 3 + 2*X0 + 0; 
 [ Marked_gcd ] (X0,X1) = 1 + 3*X0 + 2*X1 + 0; 
 [ true ] () = 0; 
 [ minus ] (X0,X1) = 1*X0 + 0; 
 [ Marked_if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; 
 [ false ] () = 0; 
 [ 0 ] () = 0; 
 [ gcd ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_le(s(X),s(Y)) , Marked_le(X,Y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_minus(X,s(Y)) , Marked_minus(X,Y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.084591 seconds (real time)
Cime Exit Status: 0