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

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


Sub problem: 
guided: 

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

{  <Marked_i(.(x,y)) , Marked_i(x)> --> <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(y)> --> <Marked_i(.(x,y)) , Marked_i(x)>
  <Marked_i(.(x,y)) , Marked_i(y)> --> <Marked_i(.(x,y)) , Marked_i(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_.(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))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_i -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_. -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] .(1,x) -> x
[2] .(x,1) -> x
[3] .(i(x),x) -> 1
[4] .(x,i(x)) -> 1
[5] i(1) -> 1
[6] i(i(x)) -> x
[7] .(i(y),.(y,z)) -> z
[8] .(y,.(i(y),z)) -> z
[9] .(.(x,y),z) -> .(x,.(y,z))
[10] i(.(x,y)) -> .(i(y),i(x))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_.(.(x,y),z) , Marked_.(x,.(y,z))>
<Marked_.(.(x,y),z) , Marked_.(y,z)>
<Marked_i(.(x,y)) , Marked_.(i(y),i(x))>
<Marked_i(.(x,y)) , Marked_i(y)>
<Marked_i(.(x,y)) , Marked_i(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_i(.(x,y)) , Marked_i(y)>
<Marked_i(.(x,y)) , Marked_i(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<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 0.007337 seconds (real time)
Cime Exit Status: 0