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

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


Sub problem: 
guided: 

DP termination of:
<Marked_+(s(x),y) , Marked_s(+(x,y))>
<Marked_+(s(x),y) , Marked_+(x,y)>
<Marked_+(p(x),y) , Marked_p(+(x,y))>
<Marked_+(p(x),y) , Marked_+(x,y)>
<Marked_minus(s(x)) , Marked_p(minus(x))>
<Marked_minus(s(x)) , Marked_minus(x)>
<Marked_minus(p(x)) , Marked_s(minus(x))>
<Marked_minus(p(x)) , Marked_minus(x)>
<Marked_*(s(x),y) , Marked_+( *(x,y),y)>
<Marked_*(s(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_+( *(x,y),minus(y))>
<Marked_*(p(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_minus(y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

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

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

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

ST: Marked_* -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_minus -> 1

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] p(s(x)) -> x
[2] s(p(x)) -> x
[3] +(0,y) -> y
[4] +(s(x),y) -> s(+(x,y))
[5] +(p(x),y) -> p(+(x,y))
[6] minus(0) -> 0
[7] minus(s(x)) -> p(minus(x))
[8] minus(p(x)) -> s(minus(x))
[9]  *(0,y) -> 0
[10]  *(s(x),y) -> +( *(x,y),y)
[11]  *(p(x),y) -> +( *(x,y),minus(y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_+(s(x),y) , Marked_s(+(x,y))>
<Marked_+(s(x),y) , Marked_+(x,y)>
<Marked_+(p(x),y) , Marked_p(+(x,y))>
<Marked_+(p(x),y) , Marked_+(x,y)>
<Marked_minus(s(x)) , Marked_p(minus(x))>
<Marked_minus(s(x)) , Marked_minus(x)>
<Marked_minus(p(x)) , Marked_s(minus(x))>
<Marked_minus(p(x)) , Marked_minus(x)>
<Marked_*(s(x),y) , Marked_+( *(x,y),y)>
<Marked_*(s(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_+( *(x,y),minus(y))>
<Marked_*(p(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_minus(y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(s(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_*(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_+(s(x),y) , Marked_+(x,y)>
<Marked_+(p(x),y) , Marked_+(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_minus(s(x)) , Marked_minus(x)>
<Marked_minus(p(x)) , Marked_minus(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.012568 seconds (real time)
Cime Exit Status: 0