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

TRS termination of:
[1] minus(x,0) -> x
[2] minus(s(x),s(y)) -> minus(x,y)
[3] quot(0,s(y)) -> 0
[4] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
[5] app(nil,y) -> y
[6] app(add(n,x),y) -> add(n,app(x,y))
[7] reverse(nil) -> nil
[8] reverse(add(n,x)) -> app(reverse(x),add(n,nil))
[9] shuffle(nil) -> nil
[10] shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
[11] concat(leaf,y) -> y
[12] concat(cons(u,v),y) -> cons(u,concat(v,y))
[13] less_leaves(x,leaf) -> false
[14] less_leaves(leaf,cons(w,z)) -> true
[15] less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))


Sub problem: 
guided: 

DP termination of:
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))>
<Marked_quot(s(x),s(y)) , Marked_minus(x,y)>
<Marked_app(add(n,x),y) , Marked_app(x,y)>
<Marked_reverse(add(n,x)) , Marked_app(reverse(x),add(n,nil))>
<Marked_reverse(add(n,x)) , Marked_reverse(x)>
<Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))>
<Marked_shuffle(add(n,x)) , Marked_reverse(x)>
<Marked_concat(cons(u,v),y) , Marked_concat(v,y)>
<Marked_less_leaves(cons(u,v),cons(w,z)) , Marked_less_leaves(concat(u,v),
                                            concat(w,z))>
<Marked_less_leaves(cons(u,v),cons(w,z)) , Marked_concat(u,v)>
<Marked_less_leaves(cons(u,v),cons(w,z)) , Marked_concat(w,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 7 components:

{  <Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))> 
      --> <Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))>
}

{  <Marked_minus(s(x),s(y)) , Marked_minus(x,y)> 
      --> <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
}

{  <Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))> 
      --> <Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))>
}

{  <Marked_reverse(add(n,x)) , Marked_reverse(x)> 
      --> <Marked_reverse(add(n,x)) , Marked_reverse(x)>
}

{  <Marked_app(add(n,x),y) , Marked_app(x,y)> 
      --> <Marked_app(add(n,x),y) , Marked_app(x,y)>
}

{  <Marked_less_leaves(cons(u,v),cons(w,z)) , Marked_less_leaves(concat(u,v),
                                               concat(w,z))> 
      --> <Marked_less_leaves(cons(u,v),cons(w,z)) , Marked_less_leaves(
                                                      concat(u,v),concat(w,z))>
}

{  <Marked_concat(cons(u,v),y) , Marked_concat(v,y)> 
      --> <Marked_concat(cons(u,v),y) , Marked_concat(v,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  quot(0,s(y)) >= 0 ;
  quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuffle(nil) >= nil ;
  shuffle(add(n,x)) >= add(n,shuffle(reverse(x))) ;
  concat(leaf,y) >= y ;
  concat(cons(u,v),y) >= cons(u,concat(v,y)) ;
  less_leaves(leaf,cons(w,z)) >= true ;
  less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),concat(w,z)) ;
  less_leaves(x,leaf) >= false ;
  Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y)) ;
 }
 + Disjunctions:{ 
{
  Marked_quot(s(x),s(y)) > Marked_quot(minus(x,y),s(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: minus(s(x),s(y)) >= minus(x,y)
constraint: minus(x,0) >= x
constraint: quot(0,s(y)) >= 0
constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y)))
constraint: app(nil,y) >= y
constraint: app(add(n,x),y) >= add(n,app(x,y))
constraint: reverse(nil) >= nil
constraint: reverse(add(n,x)) >= app(reverse(x),add(n,nil))
constraint: shuffle(nil) >= nil
constraint: shuffle(add(n,x)) >= add(n,shuffle(reverse(x)))
constraint: concat(leaf,y) >= y
constraint: concat(cons(u,v),y) >= cons(u,concat(v,y))
constraint: less_leaves(leaf,cons(w,z)) >= true
constraint: less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),
                                                 concat(w,z))
constraint: less_leaves(x,leaf) >= false
constraint: Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  quot(0,s(y)) >= 0 ;
  quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuffle(nil) >= nil ;
  shuffle(add(n,x)) >= add(n,shuffle(reverse(x))) ;
  concat(leaf,y) >= y ;
  concat(cons(u,v),y) >= cons(u,concat(v,y)) ;
  less_leaves(leaf,cons(w,z)) >= true ;
  less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),concat(w,z)) ;
  less_leaves(x,leaf) >= false ;
  Marked_minus(s(x),s(y)) >= Marked_minus(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_minus(s(x),s(y)) > Marked_minus(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: minus(s(x),s(y)) >= minus(x,y)
constraint: minus(x,0) >= x
constraint: quot(0,s(y)) >= 0
constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y)))
constraint: app(nil,y) >= y
constraint: app(add(n,x),y) >= add(n,app(x,y))
constraint: reverse(nil) >= nil
constraint: reverse(add(n,x)) >= app(reverse(x),add(n,nil))
constraint: shuffle(nil) >= nil
constraint: shuffle(add(n,x)) >= add(n,shuffle(reverse(x)))
constraint: concat(leaf,y) >= y
constraint: concat(cons(u,v),y) >= cons(u,concat(v,y))
constraint: less_leaves(leaf,cons(w,z)) >= true
constraint: less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),
                                                 concat(w,z))
constraint: less_leaves(x,leaf) >= false
constraint: Marked_minus(s(x),s(y)) >= Marked_minus(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  quot(0,s(y)) >= 0 ;
  quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuffle(nil) >= nil ;
  shuffle(add(n,x)) >= add(n,shuffle(reverse(x))) ;
  concat(leaf,y) >= y ;
  concat(cons(u,v),y) >= cons(u,concat(v,y)) ;
  less_leaves(leaf,cons(w,z)) >= true ;
  less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),concat(w,z)) ;
  less_leaves(x,leaf) >= false ;
  Marked_shuffle(add(n,x)) >= Marked_shuffle(reverse(x)) ;
 }
 + Disjunctions:{ 
{
  Marked_shuffle(add(n,x)) > Marked_shuffle(reverse(x)) ;
 }
 } 
=== 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: minus(s(x),s(y)) >= minus(x,y)
constraint: minus(x,0) >= x
constraint: quot(0,s(y)) >= 0
constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y)))
constraint: app(nil,y) >= y
constraint: app(add(n,x),y) >= add(n,app(x,y))
constraint: reverse(nil) >= nil
constraint: reverse(add(n,x)) >= app(reverse(x),add(n,nil))
constraint: shuffle(nil) >= nil
constraint: shuffle(add(n,x)) >= add(n,shuffle(reverse(x)))
constraint: concat(leaf,y) >= y
constraint: concat(cons(u,v),y) >= cons(u,concat(v,y))
constraint: less_leaves(leaf,cons(w,z)) >= true
constraint: less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),
                                                 concat(w,z))
constraint: less_leaves(x,leaf) >= false
constraint: Marked_shuffle(add(n,x)) >= Marked_shuffle(reverse(x))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  quot(0,s(y)) >= 0 ;
  quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuffle(nil) >= nil ;
  shuffle(add(n,x)) >= add(n,shuffle(reverse(x))) ;
  concat(leaf,y) >= y ;
  concat(cons(u,v),y) >= cons(u,concat(v,y)) ;
  less_leaves(leaf,cons(w,z)) >= true ;
  less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),concat(w,z)) ;
  less_leaves(x,leaf) >= false ;
  Marked_reverse(add(n,x)) >= Marked_reverse(x) ;
 }
 + Disjunctions:{ 
{
  Marked_reverse(add(n,x)) > Marked_reverse(x) ;
 }
 } 
=== 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: minus(s(x),s(y)) >= minus(x,y)
constraint: minus(x,0) >= x
constraint: quot(0,s(y)) >= 0
constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y)))
constraint: app(nil,y) >= y
constraint: app(add(n,x),y) >= add(n,app(x,y))
constraint: reverse(nil) >= nil
constraint: reverse(add(n,x)) >= app(reverse(x),add(n,nil))
constraint: shuffle(nil) >= nil
constraint: shuffle(add(n,x)) >= add(n,shuffle(reverse(x)))
constraint: concat(leaf,y) >= y
constraint: concat(cons(u,v),y) >= cons(u,concat(v,y))
constraint: less_leaves(leaf,cons(w,z)) >= true
constraint: less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),
                                                 concat(w,z))
constraint: less_leaves(x,leaf) >= false
constraint: Marked_reverse(add(n,x)) >= Marked_reverse(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  quot(0,s(y)) >= 0 ;
  quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuffle(nil) >= nil ;
  shuffle(add(n,x)) >= add(n,shuffle(reverse(x))) ;
  concat(leaf,y) >= y ;
  concat(cons(u,v),y) >= cons(u,concat(v,y)) ;
  less_leaves(leaf,cons(w,z)) >= true ;
  less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),concat(w,z)) ;
  less_leaves(x,leaf) >= false ;
  Marked_app(add(n,x),y) >= Marked_app(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_app(add(n,x),y) > Marked_app(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: minus(s(x),s(y)) >= minus(x,y)
constraint: minus(x,0) >= x
constraint: quot(0,s(y)) >= 0
constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y)))
constraint: app(nil,y) >= y
constraint: app(add(n,x),y) >= add(n,app(x,y))
constraint: reverse(nil) >= nil
constraint: reverse(add(n,x)) >= app(reverse(x),add(n,nil))
constraint: shuffle(nil) >= nil
constraint: shuffle(add(n,x)) >= add(n,shuffle(reverse(x)))
constraint: concat(leaf,y) >= y
constraint: concat(cons(u,v),y) >= cons(u,concat(v,y))
constraint: less_leaves(leaf,cons(w,z)) >= true
constraint: less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),
                                                 concat(w,z))
constraint: less_leaves(x,leaf) >= false
constraint: Marked_app(add(n,x),y) >= Marked_app(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  quot(0,s(y)) >= 0 ;
  quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuffle(nil) >= nil ;
  shuffle(add(n,x)) >= add(n,shuffle(reverse(x))) ;
  concat(leaf,y) >= y ;
  concat(cons(u,v),y) >= cons(u,concat(v,y)) ;
  less_leaves(leaf,cons(w,z)) >= true ;
  less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),concat(w,z)) ;
  less_leaves(x,leaf) >= false ;
  Marked_less_leaves(cons(u,v),cons(w,z)) >= Marked_less_leaves(concat(u,v),
                                              concat(w,z)) ;
 }
 + Disjunctions:{ 
{
  Marked_less_leaves(cons(u,v),cons(w,z)) > Marked_less_leaves(concat(u,v),
                                             concat(w,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: minus(s(x),s(y)) >= minus(x,y)
constraint: minus(x,0) >= x
constraint: quot(0,s(y)) >= 0
constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y)))
constraint: app(nil,y) >= y
constraint: app(add(n,x),y) >= add(n,app(x,y))
constraint: reverse(nil) >= nil
constraint: reverse(add(n,x)) >= app(reverse(x),add(n,nil))
constraint: shuffle(nil) >= nil
constraint: shuffle(add(n,x)) >= add(n,shuffle(reverse(x)))
constraint: concat(leaf,y) >= y
constraint: concat(cons(u,v),y) >= cons(u,concat(v,y))
constraint: less_leaves(leaf,cons(w,z)) >= true
constraint: less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),
                                                 concat(w,z))
constraint: less_leaves(x,leaf) >= false
constraint: Marked_less_leaves(cons(u,v),cons(w,z)) >= Marked_less_leaves(
                                                        concat(u,v),
                                                        concat(w,z))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  quot(0,s(y)) >= 0 ;
  quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuffle(nil) >= nil ;
  shuffle(add(n,x)) >= add(n,shuffle(reverse(x))) ;
  concat(leaf,y) >= y ;
  concat(cons(u,v),y) >= cons(u,concat(v,y)) ;
  less_leaves(leaf,cons(w,z)) >= true ;
  less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),concat(w,z)) ;
  less_leaves(x,leaf) >= false ;
  Marked_concat(cons(u,v),y) >= Marked_concat(v,y) ;
 }
 + Disjunctions:{ 
{
  Marked_concat(cons(u,v),y) > Marked_concat(v,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: minus(s(x),s(y)) >= minus(x,y)
constraint: minus(x,0) >= x
constraint: quot(0,s(y)) >= 0
constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y)))
constraint: app(nil,y) >= y
constraint: app(add(n,x),y) >= add(n,app(x,y))
constraint: reverse(nil) >= nil
constraint: reverse(add(n,x)) >= app(reverse(x),add(n,nil))
constraint: shuffle(nil) >= nil
constraint: shuffle(add(n,x)) >= add(n,shuffle(reverse(x)))
constraint: concat(leaf,y) >= y
constraint: concat(cons(u,v),y) >= cons(u,concat(v,y))
constraint: less_leaves(leaf,cons(w,z)) >= true
constraint: less_leaves(cons(u,v),cons(w,z)) >= less_leaves(concat(u,v),
                                                 concat(w,z))
constraint: less_leaves(x,leaf) >= false
constraint: Marked_concat(cons(u,v),y) >= Marked_concat(v,y)
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:
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] minus(x,0) -> x
[2] minus(s(x),s(y)) -> minus(x,y)
[3] quot(0,s(y)) -> 0
[4] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
[5] app(nil,y) -> y
[6] app(add(n,x),y) -> add(n,app(x,y))
[7] reverse(nil) -> nil
[8] reverse(add(n,x)) -> app(reverse(x),add(n,nil))
[9] shuffle(nil) -> nil
[10] shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
[11] concat(leaf,y) -> y
[12] concat(cons(u,v),y) -> cons(u,concat(v,y))
[13] less_leaves(x,leaf) -> false
[14] less_leaves(leaf,cons(w,z)) -> true
[15] less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))>
<Marked_quot(s(x),s(y)) , Marked_minus(x,y)>
<Marked_app(add(n,x),y) , Marked_app(x,y)>
<Marked_reverse(add(n,x)) , Marked_app(reverse(x),add(n,nil))>
<Marked_reverse(add(n,x)) , Marked_reverse(x)>
<Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))>
<Marked_shuffle(add(n,x)) , Marked_reverse(x)>
<Marked_concat(cons(u,v),y) , Marked_concat(v,y)>
<Marked_less_leaves(cons(u,v),cons(w,z)) , Marked_less_leaves(concat(u,v),
                                            concat(w,z))>
<Marked_less_leaves(cons(u,v),cons(w,z)) , Marked_concat(u,v)>
<Marked_less_leaves(cons(u,v),cons(w,z)) , Marked_concat(w,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_quot(s(x),s(y)) , Marked_quot(minus(x,y),s(y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0,X1) = 1*X0 + 0; 
 [ shuffle ] (X0) = 0; 
 [ app ] (X0,X1) = 2*X1 + 0; 
 [ Marked_quot ] (X0,X1) = 2*X0 + 0; 
 [ false ] () = 2 + 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ leaf ] () = 3 + 0; 
 [ add ] (X0,X1) = 0; 
 [ true ] () = 0; 
 [ 0 ] () = 0; 
 [ concat ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ nil ] () = 0; 
 [ less_leaves ] (X0,X1) = 3 + 1*X1 + 0; 
 [ quot ] (X0,X1) = 1 + 2*X0 + 0; 
 [ cons ] (X0,X1) = 1 + 2*X0 + 1*X1 + 0; 
 [ reverse ] (X0) = 0; 
 ]} 
{
 
DP termination of:
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0,X1) = 1*X0 + 0; 
 [ shuffle ] (X0) = 0; 
 [ app ] (X0,X1) = 2*X1 + 0; 
 [ false ] () = 2 + 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ leaf ] () = 3 + 0; 
 [ add ] (X0,X1) = 0; 
 [ true ] () = 0; 
 [ 0 ] () = 0; 
 [ concat ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ nil ] () = 0; 
 [ Marked_minus ] (X0,X1) = 1*X0 + 0; 
 [ less_leaves ] (X0,X1) = 3 + 1*X1 + 0; 
 [ quot ] (X0,X1) = 1 + 2*X0 + 0; 
 [ cons ] (X0,X1) = 1 + 2*X0 + 1*X1 + 0; 
 [ reverse ] (X0) = 0; 
 ]} 
{
 
DP termination of:
<Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0,X1) = 2*X0 + 0; 
 [ shuffle ] (X0) = 1*X0 + 0; 
 [ app ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ false ] () = 3 + 0; 
 [ s ] (X0) = 2*X0 + 0; 
 [ leaf ] () = 3 + 0; 
 [ add ] (X0,X1) = 1 + 1*X1 + 0; 
 [ true ] () = 3 + 0; 
 [ 0 ] () = 0; 
 [ Marked_shuffle ] (X0) = 1*X0 + 0; 
 [ concat ] (X0,X1) = 2*X1 + 0; 
 [ nil ] () = 0; 
 [ less_leaves ] (X0,X1) = 3 + 0; 
 [ quot ] (X0,X1) = 0; 
 [ cons ] (X0,X1) = 0; 
 [ reverse ] (X0) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_reverse(add(n,x)) , Marked_reverse(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0,X1) = 1*X0 + 0; 
 [ shuffle ] (X0) = 2*X0 + 0; 
 [ app ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ false ] () = 3 + 0; 
 [ s ] (X0) = 2*X0 + 0; 
 [ Marked_reverse ] (X0) = 3*X0 + 0; 
 [ leaf ] () = 3 + 0; 
 [ add ] (X0,X1) = 1 + 1*X1 + 0; 
 [ true ] () = 3 + 0; 
 [ 0 ] () = 0; 
 [ concat ] (X0,X1) = 2*X1 + 0; 
 [ nil ] () = 0; 
 [ less_leaves ] (X0,X1) = 3 + 0; 
 [ quot ] (X0,X1) = 0; 
 [ cons ] (X0,X1) = 0; 
 [ reverse ] (X0) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_app(add(n,x),y) , Marked_app(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0,X1) = 1*X0 + 0; 
 [ shuffle ] (X0) = 2 + 2*X0 + 0; 
 [ app ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ false ] () = 3 + 0; 
 [ s ] (X0) = 2*X0 + 0; 
 [ leaf ] () = 3 + 0; 
 [ add ] (X0,X1) = 2 + 1*X1 + 0; 
 [ true ] () = 3 + 0; 
 [ 0 ] () = 0; 
 [ concat ] (X0,X1) = 2*X1 + 0; 
 [ nil ] () = 0; 
 [ less_leaves ] (X0,X1) = 3 + 0; 
 [ quot ] (X0,X1) = 0; 
 [ Marked_app ] (X0,X1) = 3*X0 + 0; 
 [ cons ] (X0,X1) = 0; 
 [ reverse ] (X0) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_less_leaves(cons(u,v),cons(w,z)) , Marked_less_leaves(concat(u,v),
                                            concat(w,z))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0,X1) = 2*X0 + 0; 
 [ shuffle ] (X0) = 0; 
 [ app ] (X0,X1) = 2*X1 + 0; 
 [ false ] () = 3 + 0; 
 [ s ] (X0) = 2*X0 + 0; 
 [ leaf ] () = 3 + 0; 
 [ add ] (X0,X1) = 0; 
 [ true ] () = 0; 
 [ 0 ] () = 0; 
 [ concat ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ nil ] () = 0; 
 [ less_leaves ] (X0,X1) = 3 + 1*X1 + 0; 
 [ quot ] (X0,X1) = 0; 
 [ cons ] (X0,X1) = 1 + 2*X0 + 1*X1 + 0; 
 [ reverse ] (X0) = 0; 
 [ Marked_less_leaves ] (X0,X1) = 1*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_concat(cons(u,v),y) , Marked_concat(v,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0,X1) = 1*X0 + 0; 
 [ Marked_concat ] (X0,X1) = 3*X0 + 0; 
 [ shuffle ] (X0) = 0; 
 [ app ] (X0,X1) = 2*X1 + 0; 
 [ false ] () = 3 + 0; 
 [ s ] (X0) = 2*X0 + 0; 
 [ leaf ] () = 3 + 0; 
 [ add ] (X0,X1) = 0; 
 [ true ] () = 3 + 0; 
 [ 0 ] () = 0; 
 [ concat ] (X0,X1) = 1 + 3*X0 + 2*X1 + 0; 
 [ nil ] () = 0; 
 [ less_leaves ] (X0,X1) = 3 + 0; 
 [ quot ] (X0,X1) = 0; 
 [ cons ] (X0,X1) = 1 + 1*X1 + 0; 
 [ reverse ] (X0) = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.492260 seconds (real time)
Cime Exit Status: 0