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

TRS termination of:
[1] g(A) -> A
[2] g(B) -> A
[3] g(B) -> B
[4] g(C) -> A
[5] g(C) -> B
[6] g(C) -> C
[7] foldB(t,0) -> t
[8] foldB(t,s(n)) -> f(foldB(t,n),B)
[9] foldC(t,0) -> t
[10] foldC(t,s(n)) -> f(foldC(t,n),C)
[11] f(t,x) -> f'(t,g(x))
[12] f'(triple(a,b,c),C) -> triple(a,b,s(c))
[13] f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
[14] f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
[15] f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
[16] fold(t,x,0) -> t
[17] fold(t,x,s(n)) -> f(fold(t,x,n),x)


Sub problem: 
guided: 

DP termination of:
<Marked_foldB(t,s(n)) , Marked_f(foldB(t,n),B)>
<Marked_foldB(t,s(n)) , Marked_foldB(t,n)>
<Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)>
<Marked_foldC(t,s(n)) , Marked_foldC(t,n)>
<Marked_f(t,x) , Marked_f'(t,g(x))>
<Marked_f(t,x) , Marked_g(x)>
<Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
<Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))>
<Marked_f'(triple(a,b,c),A) , Marked_foldB(triple(s(a),0,c),b)>
<Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)>
<Marked_fold(t,x,s(n)) , Marked_f(fold(t,x,n),x)>
<Marked_fold(t,x,s(n)) , Marked_fold(t,x,n)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_fold(t,x,s(n)) , Marked_fold(t,x,n)> 
      --> <Marked_fold(t,x,s(n)) , Marked_fold(t,x,n)>
}

{  <Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)> 
      --> <Marked_foldC(t,s(n)) , Marked_foldC(t,n)>
  <Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)> 
     --> <Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)>
  <Marked_f'(triple(a,b,c),A) , Marked_foldB(triple(s(a),0,c),b)> 
     --> <Marked_foldB(t,s(n)) , Marked_foldB(t,n)>
  <Marked_f'(triple(a,b,c),A) , Marked_foldB(triple(s(a),0,c),b)> 
     --> <Marked_foldB(t,s(n)) , Marked_f(foldB(t,n),B)>
  <Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))> 
     --> <Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)>
  <Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)> 
     --> <Marked_f(t,x) , Marked_f'(t,g(x))>
  <Marked_f(t,x) , Marked_f'(t,g(x))> 
     --> <Marked_f'(triple(a,b,c),A) , Marked_foldB(triple(s(a),0,c),b)>
  <Marked_f(t,x) , Marked_f'(t,g(x))> 
     --> <Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))>
  <Marked_f(t,x) , Marked_f'(t,g(x))> 
     --> <Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
  <Marked_foldC(t,s(n)) , Marked_foldC(t,n)> 
     --> <Marked_foldC(t,s(n)) , Marked_foldC(t,n)>
  <Marked_foldC(t,s(n)) , Marked_foldC(t,n)> 
     --> <Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)>
  <Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)> 
     --> <Marked_f(t,x) , Marked_f'(t,g(x))>
  <Marked_foldB(t,s(n)) , Marked_foldB(t,n)> 
     --> <Marked_foldB(t,s(n)) , Marked_foldB(t,n)>
  <Marked_foldB(t,s(n)) , Marked_foldB(t,n)> 
     --> <Marked_foldB(t,s(n)) , Marked_f(foldB(t,n),B)>
  <Marked_foldB(t,s(n)) , Marked_f(foldB(t,n),B)> 
     --> <Marked_f(t,x) , Marked_f'(t,g(x))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_fold -> 3

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  g(A) >= A ;
  g(B) >= A ;
  g(B) >= B ;
  g(C) >= A ;
  g(C) >= B ;
  g(C) >= C ;
  foldB(t,0) >= t ;
  foldB(t,s(n)) >= f(foldB(t,n),B) ;
  f(t,x) >= f'(t,g(x)) ;
  foldC(t,0) >= t ;
  foldC(t,s(n)) >= f(foldC(t,n),C) ;
  f'(triple(a,b,c),A) >= f''(foldB(triple(s(a),0,c),b)) ;
  f'(triple(a,b,c),B) >= f(triple(a,b,c),A) ;
  f'(triple(a,b,c),C) >= triple(a,b,s(c)) ;
  f''(triple(a,b,c)) >= foldC(triple(a,b,0),c) ;
  fold(t,x,0) >= t ;
  fold(t,x,s(n)) >= f(fold(t,x,n),x) ;
  Marked_f(t,x) >= Marked_f'(t,g(x)) ;
  Marked_f''(triple(a,b,c)) >= Marked_foldC(triple(a,b,0),c) ;
  Marked_foldC(t,s(n)) >= Marked_f(foldC(t,n),C) ;
  Marked_foldC(t,s(n)) >= Marked_foldC(t,n) ;
  Marked_f'(triple(a,b,c),A) >= Marked_f''(foldB(triple(s(a),0,c),b)) ;
  Marked_f'(triple(a,b,c),A) >= Marked_foldB(triple(s(a),0,c),b) ;
  Marked_f'(triple(a,b,c),B) >= Marked_f(triple(a,b,c),A) ;
  Marked_foldB(t,s(n)) >= Marked_f(foldB(t,n),B) ;
  Marked_foldB(t,s(n)) >= Marked_foldB(t,n) ;
 }
 + Disjunctions:{ 
{
  Marked_f(t,x) > Marked_f'(t,g(x)) ;
 }
{
  Marked_f''(triple(a,b,c)) > Marked_foldC(triple(a,b,0),c) ;
 }
{
  Marked_foldC(t,s(n)) > Marked_f(foldC(t,n),C) ;
 }
{
  Marked_foldC(t,s(n)) > Marked_foldC(t,n) ;
 }
{
  Marked_f'(triple(a,b,c),A) > Marked_f''(foldB(triple(s(a),0,c),b)) ;
 }
{
  Marked_f'(triple(a,b,c),A) > Marked_foldB(triple(s(a),0,c),b) ;
 }
{
  Marked_f'(triple(a,b,c),B) > Marked_f(triple(a,b,c),A) ;
 }
{
  Marked_foldB(t,s(n)) > Marked_f(foldB(t,n),B) ;
 }
{
  Marked_foldB(t,s(n)) > Marked_foldB(t,n) ;
 }
 } 
=== 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: g(A) >= A
constraint: g(B) >= A
constraint: g(B) >= B
constraint: g(C) >= A
constraint: g(C) >= B
constraint: g(C) >= C
constraint: foldB(t,0) >= t
constraint: foldB(t,s(n)) >= f(foldB(t,n),B)
constraint: f(t,x) >= f'(t,g(x))
constraint: foldC(t,0) >= t
constraint: foldC(t,s(n)) >= f(foldC(t,n),C)
constraint: f'(triple(a,b,c),A) >= f''(foldB(triple(s(a),0,c),b))
constraint: f'(triple(a,b,c),B) >= f(triple(a,b,c),A)
constraint: f'(triple(a,b,c),C) >= triple(a,b,s(c))
constraint: f''(triple(a,b,c)) >= foldC(triple(a,b,0),c)
constraint: fold(t,x,0) >= t
constraint: fold(t,x,s(n)) >= f(fold(t,x,n),x)
constraint: Marked_f(t,x) >= Marked_f'(t,g(x))
constraint: Marked_f''(triple(a,b,c)) >= Marked_foldC(triple(a,b,0),c)
constraint: Marked_foldC(t,s(n)) >= Marked_f(foldC(t,n),C)
constraint: Marked_foldC(t,s(n)) >= Marked_foldC(t,n)
constraint: Marked_f'(triple(a,b,c),A) >= Marked_f''(foldB(triple(s(a),0,c),b))
constraint: Marked_f'(triple(a,b,c),A) >= Marked_foldB(triple(s(a),0,c),b)
constraint: Marked_f'(triple(a,b,c),B) >= Marked_f(triple(a,b,c),A)
constraint: Marked_foldB(t,s(n)) >= Marked_f(foldB(t,n),B)
constraint: Marked_foldB(t,s(n)) >= Marked_foldB(t,n)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)> 
      --> <Marked_foldC(t,s(n)) , Marked_foldC(t,n)>
  <Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)> 
     --> <Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)>
  <Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))> 
     --> <Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)>
  <Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)> 
     --> <Marked_f(t,x) , Marked_f'(t,g(x))>
  <Marked_f(t,x) , Marked_f'(t,g(x))> 
     --> <Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))>
  <Marked_f(t,x) , Marked_f'(t,g(x))> 
     --> <Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
  <Marked_foldC(t,s(n)) , Marked_foldC(t,n)> 
     --> <Marked_foldC(t,s(n)) , Marked_foldC(t,n)>
  <Marked_foldC(t,s(n)) , Marked_foldC(t,n)> 
     --> <Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)>
  <Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)> 
     --> <Marked_f(t,x) , Marked_f'(t,g(x))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  g(A) >= A ;
  g(B) >= A ;
  g(B) >= B ;
  g(C) >= A ;
  g(C) >= B ;
  g(C) >= C ;
  foldB(t,0) >= t ;
  foldB(t,s(n)) >= f(foldB(t,n),B) ;
  f(t,x) >= f'(t,g(x)) ;
  foldC(t,0) >= t ;
  foldC(t,s(n)) >= f(foldC(t,n),C) ;
  f'(triple(a,b,c),A) >= f''(foldB(triple(s(a),0,c),b)) ;
  f'(triple(a,b,c),B) >= f(triple(a,b,c),A) ;
  f'(triple(a,b,c),C) >= triple(a,b,s(c)) ;
  f''(triple(a,b,c)) >= foldC(triple(a,b,0),c) ;
  fold(t,x,0) >= t ;
  fold(t,x,s(n)) >= f(fold(t,x,n),x) ;
  Marked_f(t,x) >= Marked_f'(t,g(x)) ;
  Marked_f''(triple(a,b,c)) >= Marked_foldC(triple(a,b,0),c) ;
  Marked_foldC(t,s(n)) >= Marked_f(foldC(t,n),C) ;
  Marked_foldC(t,s(n)) >= Marked_foldC(t,n) ;
  Marked_f'(triple(a,b,c),A) >= Marked_f''(foldB(triple(s(a),0,c),b)) ;
  Marked_f'(triple(a,b,c),B) >= Marked_f(triple(a,b,c),A) ;
 }
 + Disjunctions:{ 
{
  Marked_f(t,x) > Marked_f'(t,g(x)) ;
 }
{
  Marked_f''(triple(a,b,c)) > Marked_foldC(triple(a,b,0),c) ;
 }
{
  Marked_foldC(t,s(n)) > Marked_f(foldC(t,n),C) ;
 }
{
  Marked_foldC(t,s(n)) > Marked_foldC(t,n) ;
 }
{
  Marked_f'(triple(a,b,c),A) > Marked_f''(foldB(triple(s(a),0,c),b)) ;
 }
{
  Marked_f'(triple(a,b,c),B) > Marked_f(triple(a,b,c),A) ;
 }
 } 
=== 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: g(A) >= A
constraint: g(B) >= A
constraint: g(B) >= B
constraint: g(C) >= A
constraint: g(C) >= B
constraint: g(C) >= C
constraint: foldB(t,0) >= t
constraint: foldB(t,s(n)) >= f(foldB(t,n),B)
constraint: f(t,x) >= f'(t,g(x))
constraint: foldC(t,0) >= t
constraint: foldC(t,s(n)) >= f(foldC(t,n),C)
constraint: f'(triple(a,b,c),A) >= f''(foldB(triple(s(a),0,c),b))
constraint: f'(triple(a,b,c),B) >= f(triple(a,b,c),A)
constraint: f'(triple(a,b,c),C) >= triple(a,b,s(c))
constraint: f''(triple(a,b,c)) >= foldC(triple(a,b,0),c)
constraint: fold(t,x,0) >= t
constraint: fold(t,x,s(n)) >= f(fold(t,x,n),x)
constraint: Marked_f(t,x) >= Marked_f'(t,g(x))
constraint: Marked_f''(triple(a,b,c)) >= Marked_foldC(triple(a,b,0),c)
constraint: Marked_foldC(t,s(n)) >= Marked_f(foldC(t,n),C)
constraint: Marked_foldC(t,s(n)) >= Marked_foldC(t,n)
constraint: Marked_f'(triple(a,b,c),A) >= Marked_f''(foldB(triple(s(a),0,c),b))
constraint: Marked_f'(triple(a,b,c),B) >= Marked_f(triple(a,b,c),A)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)> 
      --> <Marked_f(t,x) , Marked_f'(t,g(x))>
  <Marked_f(t,x) , Marked_f'(t,g(x))> 
     --> <Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  g(A) >= A ;
  g(B) >= A ;
  g(B) >= B ;
  g(C) >= A ;
  g(C) >= B ;
  g(C) >= C ;
  foldB(t,0) >= t ;
  foldB(t,s(n)) >= f(foldB(t,n),B) ;
  f(t,x) >= f'(t,g(x)) ;
  foldC(t,0) >= t ;
  foldC(t,s(n)) >= f(foldC(t,n),C) ;
  f'(triple(a,b,c),A) >= f''(foldB(triple(s(a),0,c),b)) ;
  f'(triple(a,b,c),B) >= f(triple(a,b,c),A) ;
  f'(triple(a,b,c),C) >= triple(a,b,s(c)) ;
  f''(triple(a,b,c)) >= foldC(triple(a,b,0),c) ;
  fold(t,x,0) >= t ;
  fold(t,x,s(n)) >= f(fold(t,x,n),x) ;
  Marked_f(t,x) >= Marked_f'(t,g(x)) ;
  Marked_f'(triple(a,b,c),B) >= Marked_f(triple(a,b,c),A) ;
 }
 + Disjunctions:{ 
{
  Marked_f(t,x) > Marked_f'(t,g(x)) ;
 }
{
  Marked_f'(triple(a,b,c),B) > Marked_f(triple(a,b,c),A) ;
 }
 } 
=== 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: g(A) >= A
constraint: g(B) >= A
constraint: g(B) >= B
constraint: g(C) >= A
constraint: g(C) >= B
constraint: g(C) >= C
constraint: foldB(t,0) >= t
constraint: foldB(t,s(n)) >= f(foldB(t,n),B)
constraint: f(t,x) >= f'(t,g(x))
constraint: foldC(t,0) >= t
constraint: foldC(t,s(n)) >= f(foldC(t,n),C)
constraint: f'(triple(a,b,c),A) >= f''(foldB(triple(s(a),0,c),b))
constraint: f'(triple(a,b,c),B) >= f(triple(a,b,c),A)
constraint: f'(triple(a,b,c),C) >= triple(a,b,s(c))
constraint: f''(triple(a,b,c)) >= foldC(triple(a,b,0),c)
constraint: fold(t,x,0) >= t
constraint: fold(t,x,s(n)) >= f(fold(t,x,n),x)
constraint: Marked_f(t,x) >= Marked_f'(t,g(x))
constraint: Marked_f'(triple(a,b,c),B) >= Marked_f(triple(a,b,c),A)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] g(A) -> A
[2] g(B) -> A
[3] g(B) -> B
[4] g(C) -> A
[5] g(C) -> B
[6] g(C) -> C
[7] foldB(t,0) -> t
[8] foldB(t,s(n)) -> f(foldB(t,n),B)
[9] foldC(t,0) -> t
[10] foldC(t,s(n)) -> f(foldC(t,n),C)
[11] f(t,x) -> f'(t,g(x))
[12] f'(triple(a,b,c),C) -> triple(a,b,s(c))
[13] f'(triple(a,b,c),B) -> f(triple(a,b,c),A)
[14] f'(triple(a,b,c),A) -> f''(foldB(triple(s(a),0,c),b))
[15] f''(triple(a,b,c)) -> foldC(triple(a,b,0),c)
[16] fold(t,x,0) -> t
[17] fold(t,x,s(n)) -> f(fold(t,x,n),x)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_foldB(t,s(n)) , Marked_f(foldB(t,n),B)>
<Marked_foldB(t,s(n)) , Marked_foldB(t,n)>
<Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)>
<Marked_foldC(t,s(n)) , Marked_foldC(t,n)>
<Marked_f(t,x) , Marked_f'(t,g(x))>
<Marked_f(t,x) , Marked_g(x)>
<Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
<Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))>
<Marked_f'(triple(a,b,c),A) , Marked_foldB(triple(s(a),0,c),b)>
<Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)>
<Marked_fold(t,x,s(n)) , Marked_f(fold(t,x,n),x)>
<Marked_fold(t,x,s(n)) , Marked_fold(t,x,n)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_fold(t,x,s(n)) , Marked_fold(t,x,n)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_foldB(t,s(n)) , Marked_f(foldB(t,n),B)>
<Marked_foldB(t,s(n)) , Marked_foldB(t,n)>
<Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)>
<Marked_foldC(t,s(n)) , Marked_foldC(t,n)>
<Marked_f(t,x) , Marked_f'(t,g(x))>
<Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
<Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))>
<Marked_f'(triple(a,b,c),A) , Marked_foldB(triple(s(a),0,c),b)>
<Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ A ] () = 0; 
 [ Marked_foldC ] (X0,X1) = 1*X0 + 2; 
 [ foldC ] (X0,X1) = 1*X0; 
 [ foldB ] (X0,X1) = 2*X0; 
 [ fold ] (X0,X1,X2) = 1*X2 + 3*X1 + 3*X0; 
 [ B ] () = 0; 
 [ Marked_foldB ] (X0,X1) = 1*X1 + 2*X0 + 2; 
 [ triple ] (X0,X1,X2) = 1*X1; 
 [ f ] (X0,X1) = 1*X0; 
 [ Marked_f ] (X0,X1) = 1*X0 + 2; 
 [ g ] (X0) = 0; 
 [ Marked_f' ] (X0,X1) = 1*X0 + 2; 
 [ f' ] (X0,X1) = 1*X0; 
 [ 0 ] () = 0; 
 [ C ] () = 0; 
 [ f'' ] (X0) = 1*X0; 
 [ s ] (X0) = 2*X0 + 2; 
 [ Marked_f'' ] (X0) = 2*X0 + 2; 
 removing <Marked_foldB(t,s(n)),Marked_f(foldB(t,n),B)><Marked_foldB(t,s(n)),
Marked_foldB(t,n)>
 [ {
      
     DP termination of:
     <Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)>
<Marked_foldC(t,s(n)) , Marked_foldC(t,n)>
<Marked_f(t,x) , Marked_f'(t,g(x))>
<Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
<Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))>
<Marked_f'(triple(a,b,c),A) , Marked_foldB(triple(s(a),0,c),b)>
<Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_foldC(t,s(n)) , Marked_f(foldC(t,n),C)>
<Marked_foldC(t,s(n)) , Marked_foldC(t,n)>
<Marked_f(t,x) , Marked_f'(t,g(x))>
<Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
<Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))>
<Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ A ] () = 0; 
 [ Marked_foldC ] (X0,X1) = 1*X1 + 1*X0; 
 [ foldC ] (X0,X1) = 1*X1 + 1*X0; 
 [ foldB ] (X0,X1) = 1*X1 + 1*X0; 
 [ fold ] (X0,X1,X2) = 1*X2 + 3*X1 + 3*X0; 
 [ B ] () = 0; 
 [ triple ] (X0,X1,X2) = 1*X2 + 2*X1; 
 [ f ] (X0,X1) = 1*X0 + 1; 
 [ Marked_f ] (X0,X1) = 1*X0; 
 [ g ] (X0) = 0; 
 [ Marked_f' ] (X0,X1) = 1*X0; 
 [ f' ] (X0,X1) = 1*X0 + 1; 
 [ 0 ] () = 0; 
 [ C ] () = 0; 
 [ f'' ] (X0) = 1*X0; 
 [ s ] (X0) = 1*X0 + 1; 
 [ Marked_f'' ] (X0) = 1*X0; 
 removing <Marked_foldC(t,s(n)),Marked_f(foldC(t,n),C)><Marked_foldC(t,s(n)),
Marked_foldC(t,n)>
 [ {
      
     DP termination of:
     <Marked_f(t,x) , Marked_f'(t,g(x))>
<Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
<Marked_f'(triple(a,b,c),A) , Marked_f''(foldB(triple(s(a),0,c),b))>
<Marked_f''(triple(a,b,c)) , Marked_foldC(triple(a,b,0),c)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(t,x) , Marked_f'(t,g(x))>
<Marked_f'(triple(a,b,c),B) , Marked_f(triple(a,b,c),A)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ A ] () = 0; 
 [ foldC ] (X0,X1) = 2*X0; 
 [ foldB ] (X0,X1) = 2*X1 + 1*X0 + 2; 
 [ fold ] (X0,X1,X2) = 2*X2 + 3*X1 + 3*X0 + 2; 
 [ B ] () = 2; 
 [ triple ] (X0,X1,X2) = 0; 
 [ f ] (X0,X1) = 0; 
 [ Marked_f ] (X0,X1) = 2*X1 + 2; 
 [ g ] (X0) = 2*X0; 
 [ Marked_f' ] (X0,X1) = 1*X1 + 2; 
 [ f' ] (X0,X1) = 0; 
 [ 0 ] () = 0; 
 [ C ] () = 2; 
 [ f'' ] (X0) = 0; 
 [ s ] (X0) = 2; 
 removing <Marked_f'(triple(a,b,c),B),Marked_f(triple(a,b,c),A)>
 [ {
      
     DP termination of:
     <Marked_f(t,x) , Marked_f'(t,g(x))>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.389357 seconds (real time)
Cime Exit Status: 0