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

TRS termination of:
[1] min(x,0) -> 0
[2] min(0,y) -> 0
[3] min(s(x),s(y)) -> s(min(x,y))
[4] max(x,0) -> x
[5] max(0,y) -> y
[6] max(s(x),s(y)) -> s(max(x,y))
[7] -(x,0) -> x
[8] -(s(x),s(y)) -> -(x,y)
[9] gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)
[10] gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))
[11] gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))
[12] gcd(x,0,0) -> x
[13] gcd(0,y,0) -> y
[14] gcd(0,0,z) -> z


Sub problem: 
guided: 

DP termination of:
<Marked_min(s(x),s(y)) , Marked_min(x,y)>
<Marked_max(s(x),s(y)) , Marked_max(x,y)>
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
<Marked_gcd(s(x),s(y),z) , Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)>
<Marked_gcd(s(x),s(y),z) , Marked_-(max(x,y),min(x,y))>
<Marked_gcd(s(x),s(y),z) , Marked_max(x,y)>
<Marked_gcd(s(x),s(y),z) , Marked_min(x,y)>
<Marked_gcd(s(x),s(y),z) , Marked_min(x,y)>
<Marked_gcd(x,s(y),s(z)) , Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))>
<Marked_gcd(x,s(y),s(z)) , Marked_-(max(y,z),min(y,z))>
<Marked_gcd(x,s(y),s(z)) , Marked_max(y,z)>
<Marked_gcd(x,s(y),s(z)) , Marked_min(y,z)>
<Marked_gcd(x,s(y),s(z)) , Marked_min(y,z)>
<Marked_gcd(s(x),y,s(z)) , Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))>
<Marked_gcd(s(x),y,s(z)) , Marked_-(max(x,z),min(x,z))>
<Marked_gcd(s(x),y,s(z)) , Marked_max(x,z)>
<Marked_gcd(s(x),y,s(z)) , Marked_min(x,z)>
<Marked_gcd(s(x),y,s(z)) , Marked_min(x,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_gcd(s(x),y,s(z)) , Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))> 
      --> <Marked_gcd(s(x),y,s(z)) , Marked_gcd(-(max(x,z),min(x,z)),
                                      y,s(min(x,z)))>
  <Marked_gcd(s(x),y,s(z)) , Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))> 
     --> <Marked_gcd(x,s(y),s(z)) , Marked_gcd(x,-(max(y,z),min(y,z)),
                                     s(min(y,z)))>
  <Marked_gcd(s(x),y,s(z)) , Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))> 
     --> <Marked_gcd(s(x),s(y),z) , Marked_gcd(-(max(x,y),min(x,y)),
                                     s(min(x,y)),z)>
  <Marked_gcd(x,s(y),s(z)) , Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))> 
     --> <Marked_gcd(s(x),y,s(z)) , Marked_gcd(-(max(x,z),min(x,z)),y,
                                     s(min(x,z)))>
  <Marked_gcd(x,s(y),s(z)) , Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))> 
     --> <Marked_gcd(x,s(y),s(z)) , Marked_gcd(x,-(max(y,z),min(y,z)),
                                     s(min(y,z)))>
  <Marked_gcd(x,s(y),s(z)) , Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))> 
     --> <Marked_gcd(s(x),s(y),z) , Marked_gcd(-(max(x,y),min(x,y)),
                                     s(min(x,y)),z)>
  <Marked_gcd(s(x),s(y),z) , Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)> 
     --> <Marked_gcd(s(x),y,s(z)) , Marked_gcd(-(max(x,z),min(x,z)),y,
                                     s(min(x,z)))>
  <Marked_gcd(s(x),s(y),z) , Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)> 
     --> <Marked_gcd(x,s(y),s(z)) , Marked_gcd(x,-(max(y,z),min(y,z)),
                                     s(min(y,z)))>
  <Marked_gcd(s(x),s(y),z) , Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)> 
     --> <Marked_gcd(s(x),s(y),z) , Marked_gcd(-(max(x,y),min(x,y)),
                                     s(min(x,y)),z)>
}

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

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

{  <Marked_min(s(x),s(y)) , Marked_min(x,y)> 
      --> <Marked_min(s(x),s(y)) , Marked_min(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  min(0,y) >= 0 ;
  min(s(x),s(y)) >= s(min(x,y)) ;
  min(x,0) >= 0 ;
  max(0,y) >= y ;
  max(s(x),s(y)) >= s(max(x,y)) ;
  max(x,0) >= x ;
  -(s(x),s(y)) >= -(x,y) ;
  -(x,0) >= x ;
  gcd(0,0,z) >= z ;
  gcd(0,y,0) >= y ;
  gcd(s(x),s(y),z) >= gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) ;
  gcd(s(x),y,s(z)) >= gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) ;
  gcd(x,0,0) >= x ;
  gcd(x,s(y),s(z)) >= gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) ;
  Marked_gcd(s(x),s(y),z) >= Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) ;
  Marked_gcd(s(x),y,s(z)) >= Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) ;
  Marked_gcd(x,s(y),s(z)) >= Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) ;
 }
 + Disjunctions:{ 
{
  Marked_gcd(s(x),s(y),z) > Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) ;
 }
{
  Marked_gcd(s(x),y,s(z)) > Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) ;
 }
{
  Marked_gcd(x,s(y),s(z)) > Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) ;
 }
 } 
=== 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: min(0,y) >= 0
constraint: min(s(x),s(y)) >= s(min(x,y))
constraint: min(x,0) >= 0
constraint: max(0,y) >= y
constraint: max(s(x),s(y)) >= s(max(x,y))
constraint: max(x,0) >= x
constraint: -(s(x),s(y)) >= -(x,y)
constraint: -(x,0) >= x
constraint: gcd(0,0,z) >= z
constraint: gcd(0,y,0) >= y
constraint: gcd(s(x),s(y),z) >= gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)
constraint: gcd(s(x),y,s(z)) >= gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))
constraint: gcd(x,0,0) >= x
constraint: gcd(x,s(y),s(z)) >= gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))
constraint: Marked_gcd(s(x),s(y),z) >= Marked_gcd(-(max(x,y),min(x,y)),
                                        s(min(x,y)),z)
constraint: Marked_gcd(s(x),y,s(z)) >= Marked_gcd(-(max(x,z),min(x,z)),
                                        y,s(min(x,z)))
constraint: Marked_gcd(x,s(y),s(z)) >= Marked_gcd(x,-(max(y,z),min(y,z)),
                                        s(min(y,z)))
APPLY CRITERIA (Subterm criterion)

ST: Marked_- -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_max -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_min -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
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] min(x,0) -> 0
[2] min(0,y) -> 0
[3] min(s(x),s(y)) -> s(min(x,y))
[4] max(x,0) -> x
[5] max(0,y) -> y
[6] max(s(x),s(y)) -> s(max(x,y))
[7] -(x,0) -> x
[8] -(s(x),s(y)) -> -(x,y)
[9] gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)
[10] gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))
[11] gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))
[12] gcd(x,0,0) -> x
[13] gcd(0,y,0) -> y
[14] gcd(0,0,z) -> z
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_min(s(x),s(y)) , Marked_min(x,y)>
<Marked_max(s(x),s(y)) , Marked_max(x,y)>
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
<Marked_gcd(s(x),s(y),z) , Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)>
<Marked_gcd(s(x),s(y),z) , Marked_-(max(x,y),min(x,y))>
<Marked_gcd(s(x),s(y),z) , Marked_max(x,y)>
<Marked_gcd(s(x),s(y),z) , Marked_min(x,y)>
<Marked_gcd(s(x),s(y),z) , Marked_min(x,y)>
<Marked_gcd(x,s(y),s(z)) , Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))>
<Marked_gcd(x,s(y),s(z)) , Marked_-(max(y,z),min(y,z))>
<Marked_gcd(x,s(y),s(z)) , Marked_max(y,z)>
<Marked_gcd(x,s(y),s(z)) , Marked_min(y,z)>
<Marked_gcd(x,s(y),s(z)) , Marked_min(y,z)>
<Marked_gcd(s(x),y,s(z)) , Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))>
<Marked_gcd(s(x),y,s(z)) , Marked_-(max(x,z),min(x,z))>
<Marked_gcd(s(x),y,s(z)) , Marked_max(x,z)>
<Marked_gcd(s(x),y,s(z)) , Marked_min(x,z)>
<Marked_gcd(s(x),y,s(z)) , Marked_min(x,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_gcd(s(x),s(y),z) , Marked_gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)>
<Marked_gcd(x,s(y),s(z)) , Marked_gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))>
<Marked_gcd(s(x),y,s(z)) , Marked_gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ - ] (X0,X1) = 1*X0 + 0; 
 [ s ] (X0) = 2 + 3*X0 + 0; 
 [ Marked_gcd ] (X0,X1,X2) = 3*X0 + 2*X1 + 1*X2 + 0; 
 [ min ] (X0,X1) = 1*X0 + 0; 
 [ gcd ] (X0,X1,X2) = 3 + 3*X0 + 2*X1 + 1*X2 + 0; 
 [ max ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_max(s(x),s(y)) , Marked_max(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_min(s(x),s(y)) , Marked_min(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.149381 seconds (real time)
Cime Exit Status: 0