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

TRS termination of:
[1] a__f(0) -> cons(0,f(s(0)))
[2] a__f(s(0)) -> a__f(a__p(s(0)))
[3] a__p(s(0)) -> 0
[4] mark(f(X)) -> a__f(mark(X))
[5] mark(p(X)) -> a__p(mark(X))
[6] mark(0) -> 0
[7] mark(cons(X1,X2)) -> cons(mark(X1),X2)
[8] mark(s(X)) -> s(mark(X))
[9] a__f(X) -> f(X)
[10] a__p(X) -> p(X)


Sub problem: 
guided: 

DP termination of:
<Marked_a__f(s(0)) , Marked_a__f(a__p(s(0)))>
<Marked_a__f(s(0)) , Marked_a__p(s(0))>
<Marked_mark(f(X)) , Marked_a__f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(p(X)) , Marked_a__p(mark(X))>
<Marked_mark(p(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_mark(s(X)) , Marked_mark(X)> 
      --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
}

{  <Marked_a__f(s(0)) , Marked_a__f(a__p(s(0)))> 
      --> <Marked_a__f(s(0)) , Marked_a__f(a__p(s(0)))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_mark -> 1

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__f(0) >= cons(0,f(s(0))) ;
  a__f(s(0)) >= a__f(a__p(s(0))) ;
  a__f(X) >= f(X) ;
  a__p(s(0)) >= 0 ;
  a__p(X) >= p(X) ;
  mark(cons(X1,X2)) >= cons(mark(X1),X2) ;
  mark(0) >= 0 ;
  mark(f(X)) >= a__f(mark(X)) ;
  mark(s(X)) >= s(mark(X)) ;
  mark(p(X)) >= a__p(mark(X)) ;
  Marked_a__f(s(0)) >= Marked_a__f(a__p(s(0))) ;
 }
 + Disjunctions:{ 
{
  Marked_a__f(s(0)) > Marked_a__f(a__p(s(0))) ;
 }
 } 
=== 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: a__f(0) >= cons(0,f(s(0)))
constraint: a__f(s(0)) >= a__f(a__p(s(0)))
constraint: a__f(X) >= f(X)
constraint: a__p(s(0)) >= 0
constraint: a__p(X) >= p(X)
constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2)
constraint: mark(0) >= 0
constraint: mark(f(X)) >= a__f(mark(X))
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(p(X)) >= a__p(mark(X))
constraint: Marked_a__f(s(0)) >= Marked_a__f(a__p(s(0)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__f(0) -> cons(0,f(s(0)))
[2] a__f(s(0)) -> a__f(a__p(s(0)))
[3] a__p(s(0)) -> 0
[4] mark(f(X)) -> a__f(mark(X))
[5] mark(p(X)) -> a__p(mark(X))
[6] mark(0) -> 0
[7] mark(cons(X1,X2)) -> cons(mark(X1),X2)
[8] mark(s(X)) -> s(mark(X))
[9] a__f(X) -> f(X)
[10] a__p(X) -> p(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__f(s(0)) , Marked_a__f(a__p(s(0)))>
<Marked_a__f(s(0)) , Marked_a__p(s(0))>
<Marked_mark(f(X)) , Marked_a__f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(p(X)) , Marked_a__p(mark(X))>
<Marked_mark(p(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(p(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_a__f(s(0)) , Marked_a__f(a__p(s(0)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ cons ] (X0,X1) = 2 + 0; 
 [ a__f ] (X0) = 2 + 0; 
 [ f ] (X0) = 2 + 0; 
 [ mark ] (X0) = 2 + 2*X0 + 0; 
 [ 0 ] () = 0; 
 [ Marked_a__f ] (X0) = 3*X0 + 0; 
 [ a__p ] (X0) = 0; 
 [ s ] (X0) = 2 + 0; 
 [ p ] (X0) = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.054025 seconds (real time)
Cime Exit Status: 0