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

TRS termination of:
[1] fac(0) -> 1
[2] fac(s(x)) ->  *(s(x),fac(x))
[3] floop(0,y) -> y
[4] floop(s(x),y) -> floop(x, *(s(x),y))
[5]  *(x,0) -> 0
[6]  *(x,s(y)) -> +( *(x,y),x)
[7] +(x,0) -> x
[8] +(x,s(y)) -> s(+(x,y))
[9] 1 -> s(0)
[10] fac(0) -> s(0)


Sub problem: 
guided: 

DP termination of:
<Marked_fac(0) , Marked_1>
<Marked_fac(s(x)) , Marked_*(s(x),fac(x))>
<Marked_fac(s(x)) , Marked_fac(x)>
<Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))>
<Marked_floop(s(x),y) , Marked_*(s(x),y)>
<Marked_*(x,s(y)) , Marked_+( *(x,y),x)>
<Marked_*(x,s(y)) , Marked_*(x,y)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_fac(s(x)) , Marked_fac(x)> --> <Marked_fac(s(x)) , Marked_fac(x)>
}

{  <Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))> 
      --> <Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))>
}

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

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

ST: Marked_fac -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_floop -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_* -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 2

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] fac(0) -> 1
[2] fac(s(x)) ->  *(s(x),fac(x))
[3] floop(0,y) -> y
[4] floop(s(x),y) -> floop(x, *(s(x),y))
[5]  *(x,0) -> 0
[6]  *(x,s(y)) -> +( *(x,y),x)
[7] +(x,0) -> x
[8] +(x,s(y)) -> s(+(x,y))
[9] 1 -> s(0)
[10] fac(0) -> s(0)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_fac(0) , Marked_1>
<Marked_fac(s(x)) , Marked_*(s(x),fac(x))>
<Marked_fac(s(x)) , Marked_fac(x)>
<Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))>
<Marked_floop(s(x),y) , Marked_*(s(x),y)>
<Marked_*(x,s(y)) , Marked_+( *(x,y),x)>
<Marked_*(x,s(y)) , Marked_*(x,y)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_fac(s(x)) , Marked_fac(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_floop(s(x),y) , Marked_floop(x, *(s(x),y))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_*(x,s(y)) , Marked_*(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_+(x,s(y)) , Marked_+(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.012023 seconds (real time)
Cime Exit Status: 0