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

TRS termination of:
[1] active(f(x)) -> mark(x)
[2] top(active(c)) -> top(mark(c))
[3] top(mark(x)) -> top(check(x))
[4] check(f(x)) -> f(check(x))
[5] check(x) -> start(match(f(X),x))
[6] match(f(x),f(y)) -> f(match(x,y))
[7] match(X,x) -> proper(x)
[8] proper(c) -> ok(c)
[9] proper(f(x)) -> f(proper(x))
[10] f(ok(x)) -> ok(f(x))
[11] start(ok(x)) -> found(x)
[12] f(found(x)) -> found(f(x))
[13] top(found(x)) -> top(active(x))
[14] active(f(x)) -> f(active(x))
[15] f(mark(x)) -> mark(f(x))


Sub problem: 
guided: 

DP termination of:
<Marked_top(active(c)) , Marked_top(mark(c))>
<Marked_top(mark(x)) , Marked_top(check(x))>
<Marked_top(mark(x)) , Marked_check(x)>
<Marked_check(f(x)) , Marked_f(check(x))>
<Marked_check(f(x)) , Marked_check(x)>
<Marked_check(x) , Marked_start(match(f(X),x))>
<Marked_check(x) , Marked_match(f(X),x)>
<Marked_check(x) , Marked_f(X)>
<Marked_match(f(x),f(y)) , Marked_f(match(x,y))>
<Marked_match(f(x),f(y)) , Marked_match(x,y)>
<Marked_match(X,x) , Marked_proper(x)>
<Marked_proper(f(x)) , Marked_f(proper(x))>
<Marked_proper(f(x)) , Marked_proper(x)>
<Marked_f(ok(x)) , Marked_f(x)>
<Marked_f(found(x)) , Marked_f(x)>
<Marked_top(found(x)) , Marked_top(active(x))>
<Marked_top(found(x)) , Marked_active(x)>
<Marked_active(f(x)) , Marked_f(active(x))>
<Marked_active(f(x)) , Marked_active(x)>
<Marked_f(mark(x)) , Marked_f(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 6 components:

{  <Marked_top(found(x)) , Marked_top(active(x))> 
      --> <Marked_top(found(x)) , Marked_top(active(x))>
  <Marked_top(found(x)) , Marked_top(active(x))> 
     --> <Marked_top(mark(x)) , Marked_top(check(x))>
  <Marked_top(found(x)) , Marked_top(active(x))> 
     --> <Marked_top(active(c)) , Marked_top(mark(c))>
  <Marked_top(mark(x)) , Marked_top(check(x))> 
     --> <Marked_top(found(x)) , Marked_top(active(x))>
  <Marked_top(mark(x)) , Marked_top(check(x))> 
     --> <Marked_top(mark(x)) , Marked_top(check(x))>
  <Marked_top(mark(x)) , Marked_top(check(x))> 
     --> <Marked_top(active(c)) , Marked_top(mark(c))>
  <Marked_top(active(c)) , Marked_top(mark(c))> 
     --> <Marked_top(mark(x)) , Marked_top(check(x))>
}

{  <Marked_check(f(x)) , Marked_check(x)> 
      --> <Marked_check(f(x)) , Marked_check(x)>
}

{  <Marked_match(f(x),f(y)) , Marked_match(x,y)> 
      --> <Marked_match(f(x),f(y)) , Marked_match(x,y)>
}

{  <Marked_proper(f(x)) , Marked_proper(x)> 
      --> <Marked_proper(f(x)) , Marked_proper(x)>
}

{  <Marked_active(f(x)) , Marked_active(x)> 
      --> <Marked_active(f(x)) , Marked_active(x)>
}

{  <Marked_f(mark(x)) , Marked_f(x)> --> <Marked_f(mark(x)) , Marked_f(x)>
  <Marked_f(mark(x)) , Marked_f(x)> --> <Marked_f(found(x)) , Marked_f(x)>
  <Marked_f(mark(x)) , Marked_f(x)> --> <Marked_f(ok(x)) , Marked_f(x)>
  <Marked_f(found(x)) , Marked_f(x)> --> <Marked_f(mark(x)) , Marked_f(x)>
  <Marked_f(found(x)) , Marked_f(x)> --> <Marked_f(found(x)) , Marked_f(x)>
  <Marked_f(found(x)) , Marked_f(x)> --> <Marked_f(ok(x)) , Marked_f(x)>
  <Marked_f(ok(x)) , Marked_f(x)> --> <Marked_f(mark(x)) , Marked_f(x)>
  <Marked_f(ok(x)) , Marked_f(x)> --> <Marked_f(found(x)) , Marked_f(x)>
  <Marked_f(ok(x)) , Marked_f(x)> --> <Marked_f(ok(x)) , Marked_f(x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  active(f(x)) >= mark(x) ;
  active(f(x)) >= f(active(x)) ;
  f(mark(x)) >= mark(f(x)) ;
  f(ok(x)) >= ok(f(x)) ;
  f(found(x)) >= found(f(x)) ;
  top(mark(x)) >= top(check(x)) ;
  top(active(c)) >= top(mark(c)) ;
  top(found(x)) >= top(active(x)) ;
  check(f(x)) >= f(check(x)) ;
  check(x) >= start(match(f(X),x)) ;
  start(ok(x)) >= found(x) ;
  match(f(x),f(y)) >= f(match(x,y)) ;
  match(X,x) >= proper(x) ;
  proper(f(x)) >= f(proper(x)) ;
  proper(c) >= ok(c) ;
  Marked_top(mark(x)) >= Marked_top(check(x)) ;
  Marked_top(active(c)) >= Marked_top(mark(c)) ;
  Marked_top(found(x)) >= Marked_top(active(x)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(x)) > Marked_top(check(x)) ;
 }
{
  Marked_top(active(c)) > Marked_top(mark(c)) ;
 }
{
  Marked_top(found(x)) > Marked_top(active(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: active(f(x)) >= mark(x)
constraint: active(f(x)) >= f(active(x))
constraint: f(mark(x)) >= mark(f(x))
constraint: f(ok(x)) >= ok(f(x))
constraint: f(found(x)) >= found(f(x))
constraint: top(mark(x)) >= top(check(x))
constraint: top(active(c)) >= top(mark(c))
constraint: top(found(x)) >= top(active(x))
constraint: check(f(x)) >= f(check(x))
constraint: check(x) >= start(match(f(X),x))
constraint: start(ok(x)) >= found(x)
constraint: match(f(x),f(y)) >= f(match(x,y))
constraint: match(X,x) >= proper(x)
constraint: proper(f(x)) >= f(proper(x))
constraint: proper(c) >= ok(c)
constraint: Marked_top(mark(x)) >= Marked_top(check(x))
constraint: Marked_top(active(c)) >= Marked_top(mark(c))
constraint: Marked_top(found(x)) >= Marked_top(active(x))
APPLY CRITERIA (Subterm criterion)

ST: Marked_check -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_match -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_proper -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_active -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_top(found(x)) , Marked_top(active(x))> 
      --> <Marked_top(found(x)) , Marked_top(active(x))>
  <Marked_top(found(x)) , Marked_top(active(x))> 
     --> <Marked_top(mark(x)) , Marked_top(check(x))>
  <Marked_top(mark(x)) , Marked_top(check(x))> 
     --> <Marked_top(found(x)) , Marked_top(active(x))>
  <Marked_top(mark(x)) , Marked_top(check(x))> 
     --> <Marked_top(mark(x)) , Marked_top(check(x))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  active(f(x)) >= mark(x) ;
  active(f(x)) >= f(active(x)) ;
  f(mark(x)) >= mark(f(x)) ;
  f(ok(x)) >= ok(f(x)) ;
  f(found(x)) >= found(f(x)) ;
  top(mark(x)) >= top(check(x)) ;
  top(active(c)) >= top(mark(c)) ;
  top(found(x)) >= top(active(x)) ;
  check(f(x)) >= f(check(x)) ;
  check(x) >= start(match(f(X),x)) ;
  start(ok(x)) >= found(x) ;
  match(f(x),f(y)) >= f(match(x,y)) ;
  match(X,x) >= proper(x) ;
  proper(f(x)) >= f(proper(x)) ;
  proper(c) >= ok(c) ;
  Marked_top(mark(x)) >= Marked_top(check(x)) ;
  Marked_top(found(x)) >= Marked_top(active(x)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(x)) > Marked_top(check(x)) ;
 }
{
  Marked_top(found(x)) > Marked_top(active(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: active(f(x)) >= mark(x)
constraint: active(f(x)) >= f(active(x))
constraint: f(mark(x)) >= mark(f(x))
constraint: f(ok(x)) >= ok(f(x))
constraint: f(found(x)) >= found(f(x))
constraint: top(mark(x)) >= top(check(x))
constraint: top(active(c)) >= top(mark(c))
constraint: top(found(x)) >= top(active(x))
constraint: check(f(x)) >= f(check(x))
constraint: check(x) >= start(match(f(X),x))
constraint: start(ok(x)) >= found(x)
constraint: match(f(x),f(y)) >= f(match(x,y))
constraint: match(X,x) >= proper(x)
constraint: proper(f(x)) >= f(proper(x))
constraint: proper(c) >= ok(c)
constraint: Marked_top(mark(x)) >= Marked_top(check(x))
constraint: Marked_top(found(x)) >= Marked_top(active(x))
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] active(f(x)) -> mark(x)
[2] top(active(c)) -> top(mark(c))
[3] top(mark(x)) -> top(check(x))
[4] check(f(x)) -> f(check(x))
[5] check(x) -> start(match(f(X),x))
[6] match(f(x),f(y)) -> f(match(x,y))
[7] match(X,x) -> proper(x)
[8] proper(c) -> ok(c)
[9] proper(f(x)) -> f(proper(x))
[10] f(ok(x)) -> ok(f(x))
[11] start(ok(x)) -> found(x)
[12] f(found(x)) -> found(f(x))
[13] top(found(x)) -> top(active(x))
[14] active(f(x)) -> f(active(x))
[15] f(mark(x)) -> mark(f(x))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_top(active(c)) , Marked_top(mark(c))>
<Marked_top(mark(x)) , Marked_top(check(x))>
<Marked_top(mark(x)) , Marked_check(x)>
<Marked_check(f(x)) , Marked_f(check(x))>
<Marked_check(f(x)) , Marked_check(x)>
<Marked_check(x) , Marked_start(match(f(X),x))>
<Marked_check(x) , Marked_match(f(X),x)>
<Marked_check(x) , Marked_f(X)>
<Marked_match(f(x),f(y)) , Marked_f(match(x,y))>
<Marked_match(f(x),f(y)) , Marked_match(x,y)>
<Marked_match(X,x) , Marked_proper(x)>
<Marked_proper(f(x)) , Marked_f(proper(x))>
<Marked_proper(f(x)) , Marked_proper(x)>
<Marked_f(ok(x)) , Marked_f(x)>
<Marked_f(found(x)) , Marked_f(x)>
<Marked_top(found(x)) , Marked_top(active(x))>
<Marked_top(found(x)) , Marked_active(x)>
<Marked_active(f(x)) , Marked_f(active(x))>
<Marked_active(f(x)) , Marked_active(x)>
<Marked_f(mark(x)) , Marked_f(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_top(active(c)) , Marked_top(mark(c))>
<Marked_top(mark(x)) , Marked_top(check(x))>
<Marked_top(found(x)) , Marked_top(active(x))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ X ] () = 3; 
 [ c ] () = 2; 
 [ f ] (X0) = 0; 
 [ ok ] (X0) = 1*X0; 
 [ start ] (X0) = 1*X0; 
 [ Marked_top ] (X0) = 2*X0; 
 [ active ] (X0) = 1*X0; 
 [ proper ] (X0) = 2; 
 [ check ] (X0) = 0; 
 [ top ] (X0) = 0; 
 [ found ] (X0) = 1*X0; 
 [ match ] (X0,X1) = 3*X0; 
 removing <Marked_top(active(c)),Marked_top(mark(c))>
 [ {
      
     DP termination of:
     <Marked_top(mark(x)) , Marked_top(check(x))>
<Marked_top(found(x)) , Marked_top(active(x))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_top(mark(x)) , Marked_top(check(x))>
<Marked_top(found(x)) , Marked_top(active(x))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 2 + 2*X0 + 0; 
 [ X ] () = 0; 
 [ c ] () = 3 + 0; 
 [ f ] (X0) = 2 + 2*X0 + 0; 
 [ ok ] (X0) = 3 + 1*X0 + 0; 
 [ start ] (X0) = 1*X0 + 0; 
 [ Marked_top ] (X0) = 2*X0 + 0; 
 [ active ] (X0) = 1*X0 + 0; 
 [ proper ] (X0) = 2*X0 + 0; 
 [ check ] (X0) = 2*X0 + 0; 
 [ top ] (X0) = 0; 
 [ found ] (X0) = 3 + 1*X0 + 0; 
 [ match ] (X0,X1) = 2*X1 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_check(f(x)) , Marked_check(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_match(f(x),f(y)) , Marked_match(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_proper(f(x)) , Marked_proper(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_active(f(x)) , Marked_active(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_f(ok(x)) , Marked_f(x)>
<Marked_f(found(x)) , Marked_f(x)>
<Marked_f(mark(x)) , Marked_f(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.142361 seconds (real time)
Cime Exit Status: 0