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

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


Sub problem: 
guided: 

DP termination of:
<Marked_i(+(x,y)) , Marked_+(i(x),i(y))>
<Marked_i(+(x,y)) , Marked_i(x)>
<Marked_i(+(x,y)) , Marked_i(y)>
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_i(+(x,y)) , Marked_i(y)> --> <Marked_i(+(x,y)) , Marked_i(y)>
  <Marked_i(+(x,y)) , Marked_i(y)> --> <Marked_i(+(x,y)) , Marked_i(x)>
  <Marked_i(+(x,y)) , Marked_i(x)> --> <Marked_i(+(x,y)) , Marked_i(y)>
  <Marked_i(+(x,y)) , Marked_i(x)> --> <Marked_i(+(x,y)) , Marked_i(x)>
}

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

ST: Marked_i -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] i(0) -> 0
[2] +(0,y) -> y
[3] +(x,0) -> x
[4] i(i(x)) -> x
[5] +(i(x),x) -> 0
[6] +(x,i(x)) -> 0
[7] i(+(x,y)) -> +(i(x),i(y))
[8] +(x,+(y,z)) -> +(+(x,y),z)
[9] +(+(x,i(y)),y) -> x
[10] +(+(x,y),i(y)) -> x
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_i(+(x,y)) , Marked_+(i(x),i(y))>
<Marked_i(+(x,y)) , Marked_i(x)>
<Marked_i(+(x,y)) , Marked_i(y)>
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_i(+(x,y)) , Marked_i(x)>
<Marked_i(+(x,y)) , Marked_i(y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.008405 seconds (real time)
Cime Exit Status: 0