- : unit = ()
- : 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 (Subterm criterion)

ST: Marked_and -> 1

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: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.005533 seconds (real time)
Cime Exit Status: 0