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

TRS termination of:
[1] norm(nil) -> 0
[2] norm(g(x,y)) -> s(norm(x))
[3] f(x,nil) -> g(nil,x)
[4] f(x,g(y,z)) -> g(f(x,y),z)
[5] rem(nil,y) -> nil
[6] rem(g(x,y),0) -> g(x,y)
[7] rem(g(x,y),s(z)) -> rem(x,z)


Sub problem: 
guided: 

DP termination of:
<Marked_norm(g(x,y)) , Marked_norm(x)>
<Marked_f(x,g(y,z)) , Marked_f(x,y)>
<Marked_rem(g(x,y),s(z)) , Marked_rem(x,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_norm(g(x,y)) , Marked_norm(x)> 
      --> <Marked_norm(g(x,y)) , Marked_norm(x)>
}

{  <Marked_f(x,g(y,z)) , Marked_f(x,y)> 
      --> <Marked_f(x,g(y,z)) , Marked_f(x,y)>
}

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

ST: Marked_norm -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_rem -> 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] norm(nil) -> 0
[2] norm(g(x,y)) -> s(norm(x))
[3] f(x,nil) -> g(nil,x)
[4] f(x,g(y,z)) -> g(f(x,y),z)
[5] rem(nil,y) -> nil
[6] rem(g(x,y),0) -> g(x,y)
[7] rem(g(x,y),s(z)) -> rem(x,z)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_norm(g(x,y)) , Marked_norm(x)>
<Marked_f(x,g(y,z)) , Marked_f(x,y)>
<Marked_rem(g(x,y),s(z)) , Marked_rem(x,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_norm(g(x,y)) , Marked_norm(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_f(x,g(y,z)) , Marked_f(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_rem(g(x,y),s(z)) , Marked_rem(x,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.007641 seconds (real time)
Cime Exit Status: 0