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

TRS termination of:
[1] f(x,nil) -> g(nil,x)
[2] f(x,g(y,z)) -> g(f(x,y),z)
[3] ++(x,nil) -> x
[4] ++(x,g(y,z)) -> g(++(x,y),z)
[5] null(nil) -> true
[6] null(g(x,y)) -> false
[7] mem(nil,y) -> false
[8] mem(g(x,y),z) -> or(=(y,z),mem(x,z))
[9] mem(x,max(x)) -> not(null(x))
[10] max(g(g(nil,x),y)) -> max'(x,y)
[11] max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)


Sub problem: 
guided: 

DP termination of:
<Marked_f(x,g(y,z)) , Marked_f(x,y)>
<Marked_++(x,g(y,z)) , Marked_++(x,y)>
<Marked_mem(g(x,y),z) , Marked_mem(x,z)>
<Marked_mem(x,max(x)) , Marked_null(x)>
<Marked_max(g(g(g(x,y),z),u)) , Marked_max(g(g(x,y),z))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

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

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

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

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

ST: Marked_f -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_++ -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_mem -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_max -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
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] f(x,nil) -> g(nil,x)
[2] f(x,g(y,z)) -> g(f(x,y),z)
[3] ++(x,nil) -> x
[4] ++(x,g(y,z)) -> g(++(x,y),z)
[5] null(nil) -> true
[6] null(g(x,y)) -> false
[7] mem(nil,y) -> false
[8] mem(g(x,y),z) -> or(=(y,z),mem(x,z))
[9] mem(x,max(x)) -> not(null(x))
[10] max(g(g(nil,x),y)) -> max'(x,y)
[11] max(g(g(g(x,y),z),u)) -> max'(max(g(g(x,y),z)),u)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(x,g(y,z)) , Marked_f(x,y)>
<Marked_++(x,g(y,z)) , Marked_++(x,y)>
<Marked_mem(g(x,y),z) , Marked_mem(x,z)>
<Marked_mem(x,max(x)) , Marked_null(x)>
<Marked_max(g(g(g(x,y),z),u)) , Marked_max(g(g(x,y),z))>
 ,
 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_++(x,g(y,z)) , Marked_++(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_mem(g(x,y),z) , Marked_mem(x,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_max(g(g(g(x,y),z),u)) , Marked_max(g(g(x,y),z))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.016361 seconds (real time)
Cime Exit Status: 0