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

TRS termination of:
[1] not(x) -> xor(x,true)
[2] or(x,y) -> xor(and(x,y),xor(x,y))
[3] implies(x,y) -> xor(and(x,y),xor(x,true))
[4] and(x,true) -> x
[5] and(x,false) -> false
[6] and(x,x) -> x
[7] xor(x,false) -> x
[8] xor(x,x) -> false
[9] and(xor(x,y),z) -> xor(and(x,z),and(y,z))


Sub problem: 
guided: 

DP termination of:
<Marked_not(x) , Marked_xor(x,true)>
<Marked_or(x,y) , Marked_xor(and(x,y),xor(x,y))>
<Marked_or(x,y) , Marked_and(x,y)>
<Marked_or(x,y) , Marked_xor(x,y)>
<Marked_implies(x,y) , Marked_xor(and(x,y),xor(x,true))>
<Marked_implies(x,y) , Marked_and(x,y)>
<Marked_implies(x,y) , Marked_xor(x,true)>
<Marked_and(xor(x,y),z) , Marked_xor(and(x,z),and(y,z))>
<Marked_and(xor(x,y),z) , Marked_and(x,z)>
<Marked_and(xor(x,y),z) , Marked_and(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_and(xor(x,y),z) , Marked_and(y,z)> 
      --> <Marked_and(xor(x,y),z) , Marked_and(y,z)>
  <Marked_and(xor(x,y),z) , Marked_and(y,z)> 
     --> <Marked_and(xor(x,y),z) , Marked_and(x,z)>
  <Marked_and(xor(x,y),z) , Marked_and(x,z)> 
     --> <Marked_and(xor(x,y),z) , Marked_and(y,z)>
  <Marked_and(xor(x,y),z) , Marked_and(x,z)> 
     --> <Marked_and(xor(x,y),z) , Marked_and(x,z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  xor(x,false) >= x ;
  xor(x,x) >= false ;
  not(x) >= xor(x,true) ;
  and(xor(x,y),z) >= xor(and(x,z),and(y,z)) ;
  and(x,true) >= x ;
  and(x,false) >= false ;
  and(x,x) >= x ;
  or(x,y) >= xor(and(x,y),xor(x,y)) ;
  implies(x,y) >= xor(and(x,y),xor(x,true)) ;
  Marked_and(xor(x,y),z) >= Marked_and(x,z) ;
  Marked_and(xor(x,y),z) >= Marked_and(y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_and(xor(x,y),z) > Marked_and(x,z) ;
 }
{
  Marked_and(xor(x,y),z) > Marked_and(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: xor(x,false) >= x
constraint: xor(x,x) >= false
constraint: not(x) >= xor(x,true)
constraint: and(xor(x,y),z) >= xor(and(x,z),and(y,z))
constraint: and(x,true) >= x
constraint: and(x,false) >= false
constraint: and(x,x) >= x
constraint: or(x,y) >= xor(and(x,y),xor(x,y))
constraint: implies(x,y) >= xor(and(x,y),xor(x,true))
constraint: Marked_and(xor(x,y),z) >= Marked_and(x,z)
constraint: Marked_and(xor(x,y),z) >= Marked_and(y,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] not(x) -> xor(x,true)
[2] or(x,y) -> xor(and(x,y),xor(x,y))
[3] implies(x,y) -> xor(and(x,y),xor(x,true))
[4] and(x,true) -> x
[5] and(x,false) -> false
[6] and(x,x) -> x
[7] xor(x,false) -> x
[8] xor(x,x) -> false
[9] and(xor(x,y),z) -> xor(and(x,z),and(y,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_not(x) , Marked_xor(x,true)>
<Marked_or(x,y) , Marked_xor(and(x,y),xor(x,y))>
<Marked_or(x,y) , Marked_and(x,y)>
<Marked_or(x,y) , Marked_xor(x,y)>
<Marked_implies(x,y) , Marked_xor(and(x,y),xor(x,true))>
<Marked_implies(x,y) , Marked_and(x,y)>
<Marked_implies(x,y) , Marked_xor(x,true)>
<Marked_and(xor(x,y),z) , Marked_xor(and(x,z),and(y,z))>
<Marked_and(xor(x,y),z) , Marked_and(x,z)>
<Marked_and(xor(x,y),z) , Marked_and(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_and(xor(x,y),z) , Marked_and(x,z)>
<Marked_and(xor(x,y),z) , Marked_and(y,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ xor ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; 
 [ or ] (X0,X1) = 3 + 3*X0 + 3*X1 + 0; 
 [ not ] (X0) = 1 + 1*X0 + 0; 
 [ false ] () = 1 + 0; 
 [ true ] () = 0; 
 [ implies ] (X0,X1) = 3 + 3*X0 + 1*X1 + 0; 
 [ and ] (X0,X1) = 1 + 2*X0 + 0; 
 [ Marked_and ] (X0,X1) = 3*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.030549 seconds (real time)
Cime Exit Status: 0