- : 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 (Choosing graph)
Trying to solve the following constraints:
{
  f(x,g(y,z)) >= g(f(x,y),z) ;
  f(x,nil) >= g(nil,x) ;
  ++(x,g(y,z)) >= g(++(x,y),z) ;
  ++(x,nil) >= x ;
  null(g(x,y)) >= false ;
  null(nil) >= true ;
  mem(g(x,y),z) >= or(=(y,z),mem(x,z)) ;
  mem(nil,y) >= false ;
  mem(x,max(x)) >= not(null(x)) ;
  max(g(g(g(x,y),z),u)) >= max'(max(g(g(x,y),z)),u) ;
  max(g(g(nil,x),y)) >= max'(x,y) ;
  Marked_f(x,g(y,z)) >= Marked_f(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_f(x,g(y,z)) > Marked_f(x,y) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(x,g(y,z)) >= g(f(x,y),z)
constraint: f(x,nil) >= g(nil,x)
constraint: ++(x,g(y,z)) >= g(++(x,y),z)
constraint: ++(x,nil) >= x
constraint: null(g(x,y)) >= false
constraint: null(nil) >= true
constraint: mem(g(x,y),z) >= or(=(y,z),mem(x,z))
constraint: mem(nil,y) >= false
constraint: mem(x,max(x)) >= not(null(x))
constraint: max(g(g(g(x,y),z),u)) >= max'(max(g(g(x,y),z)),u)
constraint: max(g(g(nil,x),y)) >= max'(x,y)
constraint: Marked_f(x,g(y,z)) >= Marked_f(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(x,g(y,z)) >= g(f(x,y),z) ;
  f(x,nil) >= g(nil,x) ;
  ++(x,g(y,z)) >= g(++(x,y),z) ;
  ++(x,nil) >= x ;
  null(g(x,y)) >= false ;
  null(nil) >= true ;
  mem(g(x,y),z) >= or(=(y,z),mem(x,z)) ;
  mem(nil,y) >= false ;
  mem(x,max(x)) >= not(null(x)) ;
  max(g(g(g(x,y),z),u)) >= max'(max(g(g(x,y),z)),u) ;
  max(g(g(nil,x),y)) >= max'(x,y) ;
  Marked_++(x,g(y,z)) >= Marked_++(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_++(x,g(y,z)) > Marked_++(x,y) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(x,g(y,z)) >= g(f(x,y),z)
constraint: f(x,nil) >= g(nil,x)
constraint: ++(x,g(y,z)) >= g(++(x,y),z)
constraint: ++(x,nil) >= x
constraint: null(g(x,y)) >= false
constraint: null(nil) >= true
constraint: mem(g(x,y),z) >= or(=(y,z),mem(x,z))
constraint: mem(nil,y) >= false
constraint: mem(x,max(x)) >= not(null(x))
constraint: max(g(g(g(x,y),z),u)) >= max'(max(g(g(x,y),z)),u)
constraint: max(g(g(nil,x),y)) >= max'(x,y)
constraint: Marked_++(x,g(y,z)) >= Marked_++(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(x,g(y,z)) >= g(f(x,y),z) ;
  f(x,nil) >= g(nil,x) ;
  ++(x,g(y,z)) >= g(++(x,y),z) ;
  ++(x,nil) >= x ;
  null(g(x,y)) >= false ;
  null(nil) >= true ;
  mem(g(x,y),z) >= or(=(y,z),mem(x,z)) ;
  mem(nil,y) >= false ;
  mem(x,max(x)) >= not(null(x)) ;
  max(g(g(g(x,y),z),u)) >= max'(max(g(g(x,y),z)),u) ;
  max(g(g(nil,x),y)) >= max'(x,y) ;
  Marked_mem(g(x,y),z) >= Marked_mem(x,z) ;
 }
 + Disjunctions:{ 
{
  Marked_mem(g(x,y),z) > Marked_mem(x,z) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(x,g(y,z)) >= g(f(x,y),z)
constraint: f(x,nil) >= g(nil,x)
constraint: ++(x,g(y,z)) >= g(++(x,y),z)
constraint: ++(x,nil) >= x
constraint: null(g(x,y)) >= false
constraint: null(nil) >= true
constraint: mem(g(x,y),z) >= or(=(y,z),mem(x,z))
constraint: mem(nil,y) >= false
constraint: mem(x,max(x)) >= not(null(x))
constraint: max(g(g(g(x,y),z),u)) >= max'(max(g(g(x,y),z)),u)
constraint: max(g(g(nil,x),y)) >= max'(x,y)
constraint: Marked_mem(g(x,y),z) >= Marked_mem(x,z)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(x,g(y,z)) >= g(f(x,y),z) ;
  f(x,nil) >= g(nil,x) ;
  ++(x,g(y,z)) >= g(++(x,y),z) ;
  ++(x,nil) >= x ;
  null(g(x,y)) >= false ;
  null(nil) >= true ;
  mem(g(x,y),z) >= or(=(y,z),mem(x,z)) ;
  mem(nil,y) >= false ;
  mem(x,max(x)) >= not(null(x)) ;
  max(g(g(g(x,y),z),u)) >= max'(max(g(g(x,y),z)),u) ;
  max(g(g(nil,x),y)) >= max'(x,y) ;
  Marked_max(g(g(g(x,y),z),u)) >= Marked_max(g(g(x,y),z)) ;
 }
 + Disjunctions:{ 
{
  Marked_max(g(g(g(x,y),z),u)) > Marked_max(g(g(x,y),z)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(x,g(y,z)) >= g(f(x,y),z)
constraint: f(x,nil) >= g(nil,x)
constraint: ++(x,g(y,z)) >= g(++(x,y),z)
constraint: ++(x,nil) >= x
constraint: null(g(x,y)) >= false
constraint: null(nil) >= true
constraint: mem(g(x,y),z) >= or(=(y,z),mem(x,z))
constraint: mem(nil,y) >= false
constraint: mem(x,max(x)) >= not(null(x))
constraint: max(g(g(g(x,y),z),u)) >= max'(max(g(g(x,y),z)),u)
constraint: max(g(g(nil,x),y)) >= max'(x,y)
constraint: Marked_max(g(g(g(x,y),z),u)) >= Marked_max(g(g(x,y),z))
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: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ g ] (X0,X1) = 1 + 1*X0 + 3*X1 + 0; 
 [ or ] (X0,X1) = 2 + 0; 
 [ true ] () = 0; 
 [ max' ] (X0,X1) = 3*X1 + 0; 
 [ f ] (X0,X1) = 2 + 3*X0 + 1*X1 + 0; 
 [ Marked_f ] (X0,X1) = 3*X1 + 0; 
 [ not ] (X0) = 0; 
 [ false ] () = 0; 
 [ nil ] () = 2 + 0; 
 [ = ] (X0,X1) = 0; 
 [ null ] (X0) = 0; 
 [ u ] () = 3 + 0; 
 [ ++ ] (X0,X1) = 3*X0 + 2*X1 + 0; 
 [ max ] (X0) = 2 + 2*X0 + 0; 
 [ mem ] (X0,X1) = 2 + 2*X0 + 2*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_++(x,g(y,z)) , Marked_++(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ g ] (X0,X1) = 2 + 1*X0 + 3*X1 + 0; 
 [ or ] (X0,X1) = 0; 
 [ true ] () = 2 + 0; 
 [ max' ] (X0,X1) = 2 + 3*X1 + 0; 
 [ f ] (X0,X1) = 3*X0 + 2*X1 + 0; 
 [ not ] (X0) = 2 + 2*X0 + 0; 
 [ false ] () = 2 + 0; 
 [ nil ] () = 2 + 0; 
 [ Marked_++ ] (X0,X1) = 3*X1 + 0; 
 [ = ] (X0,X1) = 0; 
 [ null ] (X0) = 2 + 0; 
 [ u ] () = 3 + 0; 
 [ ++ ] (X0,X1) = 3*X0 + 2*X1 + 0; 
 [ max ] (X0) = 3 + 2*X0 + 0; 
 [ mem ] (X0,X1) = 2 + 2*X0 + 2*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_mem(g(x,y),z) , Marked_mem(x,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ g ] (X0,X1) = 2 + 1*X0 + 3*X1 + 0; 
 [ or ] (X0,X1) = 0; 
 [ true ] () = 2 + 0; 
 [ max' ] (X0,X1) = 1*X0 + 0; 
 [ f ] (X0,X1) = 3*X0 + 2*X1 + 0; 
 [ not ] (X0) = 2 + 2*X0 + 0; 
 [ false ] () = 2 + 0; 
 [ nil ] () = 2 + 0; 
 [ = ] (X0,X1) = 0; 
 [ null ] (X0) = 2 + 0; 
 [ u ] () = 0; 
 [ ++ ] (X0,X1) = 3*X0 + 1*X1 + 0; 
 [ max ] (X0) = 3 + 2*X0 + 0; 
 [ mem ] (X0,X1) = 2 + 2*X0 + 2*X1 + 0; 
 [ Marked_mem ] (X0,X1) = 3*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_max(g(g(g(x,y),z),u)) , Marked_max(g(g(x,y),z))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ g ] (X0,X1) = 2 + 1*X0 + 3*X1 + 0; 
 [ or ] (X0,X1) = 0; 
 [ true ] () = 0; 
 [ max' ] (X0,X1) = 0; 
 [ f ] (X0,X1) = 2 + 3*X0 + 1*X1 + 0; 
 [ not ] (X0) = 0; 
 [ false ] () = 0; 
 [ Marked_max ] (X0) = 1*X0 + 0; 
 [ nil ] () = 0; 
 [ = ] (X0,X1) = 0; 
 [ null ] (X0) = 0; 
 [ u ] () = 0; 
 [ ++ ] (X0,X1) = 3*X0 + 2*X1 + 0; 
 [ max ] (X0) = 2 + 2*X0 + 0; 
 [ mem ] (X0,X1) = 2 + 2*X0 + 2*X1 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.298916 seconds (real time)
Cime Exit Status: 0