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

TRS termination of:
[1] minus(0,y) -> 0
[2] minus(s(x),0) -> s(x)
[3] minus(s(x),s(y)) -> minus(x,y)
[4] le(0,y) -> true
[5] le(s(x),0) -> false
[6] le(s(x),s(y)) -> le(x,y)
[7] if(true,x,y) -> x
[8] if(false,x,y) -> y
[9] perfectp(0) -> false
[10] perfectp(s(x)) -> f(x,s(0),s(x),s(x))
[11] f(0,y,0,u) -> true
[12] f(0,y,s(z),u) -> false
[13] f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
[14] f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))


Sub problem: 
guided: 

DP termination of:
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_le(s(x),s(y)) , Marked_le(x,y)>
<Marked_perfectp(s(x)) , Marked_f(x,s(0),s(x),s(x))>
<Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
<Marked_f(s(x),0,z,u) , Marked_minus(z,s(x))>
<Marked_f(s(x),s(y),z,u) , Marked_if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))>
<Marked_f(s(x),s(y),z,u) , Marked_le(x,y)>
<Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
<Marked_f(s(x),s(y),z,u) , Marked_minus(y,x)>
<Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)> 
      --> <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
  <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)> 
     --> <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
  <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)> 
     --> <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
  <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)> 
     --> <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
  <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)> 
     --> <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
  <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)> 
     --> <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
  <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)> 
     --> <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
  <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)> 
     --> <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
  <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)> 
     --> <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
}

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

{  <Marked_minus(s(x),s(y)) , Marked_minus(x,y)> 
      --> <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_le -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_minus -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)> 
      --> <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(0,y) >= 0 ;
  minus(s(x),0) >= s(x) ;
  minus(s(x),s(y)) >= minus(x,y) ;
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  if(true,x,y) >= x ;
  if(false,x,y) >= y ;
  perfectp(0) >= false ;
  perfectp(s(x)) >= f(x,s(0),s(x),s(x)) ;
  f(0,y,0,u) >= true ;
  f(0,y,s(z),u) >= false ;
  f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u) ;
  f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u)) ;
  Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),minus(y,x),z,u) ;
 }
 + Disjunctions:{ 
{
  Marked_f(s(x),s(y),z,u) > Marked_f(s(x),minus(y,x),z,u) ;
 }
 } 
=== 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: minus(0,y) >= 0
constraint: minus(s(x),0) >= s(x)
constraint: minus(s(x),s(y)) >= minus(x,y)
constraint: le(0,y) >= true
constraint: le(s(x),0) >= false
constraint: le(s(x),s(y)) >= le(x,y)
constraint: if(true,x,y) >= x
constraint: if(false,x,y) >= y
constraint: perfectp(0) >= false
constraint: perfectp(s(x)) >= f(x,s(0),s(x),s(x))
constraint: f(0,y,0,u) >= true
constraint: f(0,y,s(z),u) >= false
constraint: f(s(x),0,z,u) >= f(x,u,minus(z,s(x)),u)
constraint: f(s(x),s(y),z,u) >= if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
constraint: Marked_f(s(x),s(y),z,u) >= Marked_f(s(x),minus(y,x),z,u)
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(0,y) -> 0
[2] minus(s(x),0) -> s(x)
[3] minus(s(x),s(y)) -> minus(x,y)
[4] le(0,y) -> true
[5] le(s(x),0) -> false
[6] le(s(x),s(y)) -> le(x,y)
[7] if(true,x,y) -> x
[8] if(false,x,y) -> y
[9] perfectp(0) -> false
[10] perfectp(s(x)) -> f(x,s(0),s(x),s(x))
[11] f(0,y,0,u) -> true
[12] f(0,y,s(z),u) -> false
[13] f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
[14] f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_le(s(x),s(y)) , Marked_le(x,y)>
<Marked_perfectp(s(x)) , Marked_f(x,s(0),s(x),s(x))>
<Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
<Marked_f(s(x),0,z,u) , Marked_minus(z,s(x))>
<Marked_f(s(x),s(y),z,u) , Marked_if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))>
<Marked_f(s(x),s(y),z,u) , Marked_le(x,y)>
<Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
<Marked_f(s(x),s(y),z,u) , Marked_minus(y,x)>
<Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
<Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
<Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ f ] (X0,X1,X2,X3) = 0; 
 [ le ] (X0,X1) = 3*X1 + 0; 
 [ s ] (X0) = 2 + 2*X0 + 0; 
 [ if ] (X0,X1,X2) = 2*X1 + 1*X2 + 0; 
 [ minus ] (X0,X1) = 2*X0 + 0; 
 [ Marked_f ] (X0,X1,X2,X3) = 2*X1 + 0; 
 [ false ] () = 0; 
 [ true ] () = 0; 
 [ perfectp ] (X0) = 2 + 2*X0 + 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(s(x),s(y)) , Marked_minus(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.092624 seconds (real time)
Cime Exit Status: 0