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

TRS termination of:
[1] norm(nil) -> 0
[2] norm(g(x,y)) -> s(norm(x))
[3] f(x,nil) -> g(nil,x)
[4] f(x,g(y,z)) -> g(f(x,y),z)
[5] rem(nil,y) -> nil
[6] rem(g(x,y),0) -> g(x,y)
[7] rem(g(x,y),s(z)) -> rem(x,z)


Sub problem: 
guided: 

DP termination of:
<Marked_norm(g(x,y)) , Marked_norm(x)>
<Marked_f(x,g(y,z)) , Marked_f(x,y)>
<Marked_rem(g(x,y),s(z)) , Marked_rem(x,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_norm(g(x,y)) , Marked_norm(x)> 
      --> <Marked_norm(g(x,y)) , Marked_norm(x)>
}

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

{  <Marked_rem(g(x,y),s(z)) , Marked_rem(x,z)> 
      --> <Marked_rem(g(x,y),s(z)) , Marked_rem(x,z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  norm(nil) >= 0 ;
  norm(g(x,y)) >= s(norm(x)) ;
  f(x,nil) >= g(nil,x) ;
  f(x,g(y,z)) >= g(f(x,y),z) ;
  rem(nil,y) >= nil ;
  rem(g(x,y),0) >= g(x,y) ;
  rem(g(x,y),s(z)) >= rem(x,z) ;
  Marked_norm(g(x,y)) >= Marked_norm(x) ;
 }
 + Disjunctions:{ 
{
  Marked_norm(g(x,y)) > Marked_norm(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: norm(nil) >= 0
constraint: norm(g(x,y)) >= s(norm(x))
constraint: f(x,nil) >= g(nil,x)
constraint: f(x,g(y,z)) >= g(f(x,y),z)
constraint: rem(nil,y) >= nil
constraint: rem(g(x,y),0) >= g(x,y)
constraint: rem(g(x,y),s(z)) >= rem(x,z)
constraint: Marked_norm(g(x,y)) >= Marked_norm(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  norm(nil) >= 0 ;
  norm(g(x,y)) >= s(norm(x)) ;
  f(x,nil) >= g(nil,x) ;
  f(x,g(y,z)) >= g(f(x,y),z) ;
  rem(nil,y) >= nil ;
  rem(g(x,y),0) >= g(x,y) ;
  rem(g(x,y),s(z)) >= rem(x,z) ;
  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: norm(nil) >= 0
constraint: norm(g(x,y)) >= s(norm(x))
constraint: f(x,nil) >= g(nil,x)
constraint: f(x,g(y,z)) >= g(f(x,y),z)
constraint: rem(nil,y) >= nil
constraint: rem(g(x,y),0) >= g(x,y)
constraint: rem(g(x,y),s(z)) >= rem(x,z)
constraint: Marked_f(x,g(y,z)) >= Marked_f(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  norm(nil) >= 0 ;
  norm(g(x,y)) >= s(norm(x)) ;
  f(x,nil) >= g(nil,x) ;
  f(x,g(y,z)) >= g(f(x,y),z) ;
  rem(nil,y) >= nil ;
  rem(g(x,y),0) >= g(x,y) ;
  rem(g(x,y),s(z)) >= rem(x,z) ;
  Marked_rem(g(x,y),s(z)) >= Marked_rem(x,z) ;
 }
 + Disjunctions:{ 
{
  Marked_rem(g(x,y),s(z)) > Marked_rem(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: norm(nil) >= 0
constraint: norm(g(x,y)) >= s(norm(x))
constraint: f(x,nil) >= g(nil,x)
constraint: f(x,g(y,z)) >= g(f(x,y),z)
constraint: rem(nil,y) >= nil
constraint: rem(g(x,y),0) >= g(x,y)
constraint: rem(g(x,y),s(z)) >= rem(x,z)
constraint: Marked_rem(g(x,y),s(z)) >= Marked_rem(x,z)
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] norm(nil) -> 0
[2] norm(g(x,y)) -> s(norm(x))
[3] f(x,nil) -> g(nil,x)
[4] f(x,g(y,z)) -> g(f(x,y),z)
[5] rem(nil,y) -> nil
[6] rem(g(x,y),0) -> g(x,y)
[7] rem(g(x,y),s(z)) -> rem(x,z)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_norm(g(x,y)) , Marked_norm(x)>
<Marked_f(x,g(y,z)) , Marked_f(x,y)>
<Marked_rem(g(x,y),s(z)) , Marked_rem(x,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_norm(g(x,y)) , Marked_norm(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ g ] (X0,X1) = 1 + 3*X0 + 0; 
 [ nil ] () = 0; 
 [ rem ] (X0,X1) = 1*X0 + 0; 
 [ norm ] (X0) = 2*X0 + 0; 
 [ Marked_norm ] (X0) = 3*X0 + 0; 
 [ f ] (X0,X1) = 1 + 3*X1 + 0; 
 [ s ] (X0) = 2 + 0; 
 ]} 
{
 
DP termination of:
<Marked_f(x,g(y,z)) , Marked_f(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ Marked_f ] (X0,X1) = 3*X1 + 0; 
 [ g ] (X0,X1) = 2 + 3*X0 + 0; 
 [ nil ] () = 0; 
 [ rem ] (X0,X1) = 1*X0 + 0; 
 [ norm ] (X0) = 2 + 2*X0 + 0; 
 [ f ] (X0,X1) = 2 + 3*X1 + 0; 
 [ s ] (X0) = 0; 
 ]} 
{
 
DP termination of:
<Marked_rem(g(x,y),s(z)) , Marked_rem(x,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ g ] (X0,X1) = 2 + 2*X0 + 0; 
 [ nil ] () = 0; 
 [ rem ] (X0,X1) = 2*X0 + 0; 
 [ norm ] (X0) = 1 + 2*X0 + 0; 
 [ f ] (X0,X1) = 2 + 2*X1 + 0; 
 [ s ] (X0) = 1 + 1*X0 + 0; 
 [ Marked_rem ] (X0,X1) = 1*X1 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.065569 seconds (real time)
Cime Exit Status: 0