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

TRS termination of:
[1] a(h,h,h,x) -> s(x)
[2] a(l,x,s(y),h) -> a(l,x,y,s(h))
[3] a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
[4] a(l,s(x),h,z) -> a(l,x,z,z)
[5] a(s(l),h,h,z) -> a(l,z,h,z)
[6] +(x,h) -> x
[7] +(h,x) -> x
[8] +(s(x),s(y)) -> s(s(+(x,y)))
[9] +(+(x,y),z) -> +(x,+(y,z))
[10] s(h) -> 1
[11]  *(h,x) -> h
[12]  *(x,h) -> h
[13]  *(s(x),s(y)) -> s(+(+( *(x,y),x),y))


Sub problem: 
guided: 

DP termination of:
<Marked_a(h,h,h,x) , Marked_s(x)>
<Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
<Marked_a(l,x,s(y),h) , Marked_s(h)>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
<Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
<Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
<Marked_+(s(x),s(y)) , Marked_s(s(+(x,y)))>
<Marked_+(s(x),s(y)) , Marked_s(+(x,y))>
<Marked_+(s(x),s(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_*(s(x),s(y)) , Marked_s(+(+( *(x,y),x),y))>
<Marked_*(s(x),s(y)) , Marked_+(+( *(x,y),x),y)>
<Marked_*(s(x),s(y)) , Marked_+( *(x,y),x)>
<Marked_*(s(x),s(y)) , Marked_*(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)> 
      --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
}

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

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

ST: Marked_a -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_* -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
      --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_a -> 2

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
      --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_a -> 3

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
      --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_a -> 4

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] a(h,h,h,x) -> s(x)
[2] a(l,x,s(y),h) -> a(l,x,y,s(h))
[3] a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
[4] a(l,s(x),h,z) -> a(l,x,z,z)
[5] a(s(l),h,h,z) -> a(l,z,h,z)
[6] +(x,h) -> x
[7] +(h,x) -> x
[8] +(s(x),s(y)) -> s(s(+(x,y)))
[9] +(+(x,y),z) -> +(x,+(y,z))
[10] s(h) -> 1
[11]  *(h,x) -> h
[12]  *(x,h) -> h
[13]  *(s(x),s(y)) -> s(+(+( *(x,y),x),y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a(h,h,h,x) , Marked_s(x)>
<Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
<Marked_a(l,x,s(y),h) , Marked_s(h)>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
<Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
<Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
<Marked_+(s(x),s(y)) , Marked_s(s(+(x,y)))>
<Marked_+(s(x),s(y)) , Marked_s(+(x,y))>
<Marked_+(s(x),s(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_*(s(x),s(y)) , Marked_s(+(+( *(x,y),x),y))>
<Marked_*(s(x),s(y)) , Marked_+(+( *(x,y),x),y)>
<Marked_*(s(x),s(y)) , Marked_+( *(x,y),x)>
<Marked_*(s(x),s(y)) , Marked_*(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
<Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
<Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_*(s(x),s(y)) , Marked_*(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_+(s(x),s(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.031256 seconds (real time)
Cime Exit Status: 0