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

TRS termination of:
[1] eq(0,0) -> true
[2] eq(0,s(X)) -> false
[3] eq(s(X),0) -> false
[4] eq(s(X),s(Y)) -> eq(X,Y)
[5] rm(N,nil) -> nil
[6] rm(N,add(M,X)) -> ifrm(eq(N,M),N,add(M,X))
[7] ifrm(true,N,add(M,X)) -> rm(N,X)
[8] ifrm(false,N,add(M,X)) -> add(M,rm(N,X))
[9] purge(nil) -> nil
[10] purge(add(N,X)) -> add(N,purge(rm(N,X)))


Sub problem: 
guided: 

DP termination of:
<Marked_eq(s(X),s(Y)) , Marked_eq(X,Y)>
<Marked_rm(N,add(M,X)) , Marked_ifrm(eq(N,M),N,add(M,X))>
<Marked_rm(N,add(M,X)) , Marked_eq(N,M)>
<Marked_ifrm(true,N,add(M,X)) , Marked_rm(N,X)>
<Marked_ifrm(false,N,add(M,X)) , Marked_rm(N,X)>
<Marked_purge(add(N,X)) , Marked_purge(rm(N,X))>
<Marked_purge(add(N,X)) , Marked_rm(N,X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_purge(add(N,X)) , Marked_purge(rm(N,X))> 
      --> <Marked_purge(add(N,X)) , Marked_purge(rm(N,X))>
}

{  <Marked_ifrm(false,N,add(M,X)) , Marked_rm(N,X)> 
      --> <Marked_rm(N,add(M,X)) , Marked_ifrm(eq(N,M),N,add(M,X))>
  <Marked_ifrm(true,N,add(M,X)) , Marked_rm(N,X)> 
     --> <Marked_rm(N,add(M,X)) , Marked_ifrm(eq(N,M),N,add(M,X))>
  <Marked_rm(N,add(M,X)) , Marked_ifrm(eq(N,M),N,add(M,X))> 
     --> <Marked_ifrm(false,N,add(M,X)) , Marked_rm(N,X)>
  <Marked_rm(N,add(M,X)) , Marked_ifrm(eq(N,M),N,add(M,X))> 
     --> <Marked_ifrm(true,N,add(M,X)) , Marked_rm(N,X)>
}

{  <Marked_eq(s(X),s(Y)) , Marked_eq(X,Y)> 
      --> <Marked_eq(s(X),s(Y)) , Marked_eq(X,Y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  eq(0,0) >= true ;
  eq(0,s(X)) >= false ;
  eq(s(X),0) >= false ;
  eq(s(X),s(Y)) >= eq(X,Y) ;
  rm(N,nil) >= nil ;
  rm(N,add(M,X)) >= ifrm(eq(N,M),N,add(M,X)) ;
  ifrm(true,N,add(M,X)) >= rm(N,X) ;
  ifrm(false,N,add(M,X)) >= add(M,rm(N,X)) ;
  purge(nil) >= nil ;
  purge(add(N,X)) >= add(N,purge(rm(N,X))) ;
  Marked_purge(add(N,X)) >= Marked_purge(rm(N,X)) ;
 }
 + Disjunctions:{ 
{
  Marked_purge(add(N,X)) > Marked_purge(rm(N,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: eq(0,0) >= true
constraint: eq(0,s(X)) >= false
constraint: eq(s(X),0) >= false
constraint: eq(s(X),s(Y)) >= eq(X,Y)
constraint: rm(N,nil) >= nil
constraint: rm(N,add(M,X)) >= ifrm(eq(N,M),N,add(M,X))
constraint: ifrm(true,N,add(M,X)) >= rm(N,X)
constraint: ifrm(false,N,add(M,X)) >= add(M,rm(N,X))
constraint: purge(nil) >= nil
constraint: purge(add(N,X)) >= add(N,purge(rm(N,X)))
constraint: Marked_purge(add(N,X)) >= Marked_purge(rm(N,X))
APPLY CRITERIA (Subterm criterion)

ST: Marked_ifrm -> 3
Marked_rm -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_eq -> 1

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] eq(0,0) -> true
[2] eq(0,s(X)) -> false
[3] eq(s(X),0) -> false
[4] eq(s(X),s(Y)) -> eq(X,Y)
[5] rm(N,nil) -> nil
[6] rm(N,add(M,X)) -> ifrm(eq(N,M),N,add(M,X))
[7] ifrm(true,N,add(M,X)) -> rm(N,X)
[8] ifrm(false,N,add(M,X)) -> add(M,rm(N,X))
[9] purge(nil) -> nil
[10] purge(add(N,X)) -> add(N,purge(rm(N,X)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_eq(s(X),s(Y)) , Marked_eq(X,Y)>
<Marked_rm(N,add(M,X)) , Marked_ifrm(eq(N,M),N,add(M,X))>
<Marked_rm(N,add(M,X)) , Marked_eq(N,M)>
<Marked_ifrm(true,N,add(M,X)) , Marked_rm(N,X)>
<Marked_ifrm(false,N,add(M,X)) , Marked_rm(N,X)>
<Marked_purge(add(N,X)) , Marked_purge(rm(N,X))>
<Marked_purge(add(N,X)) , Marked_rm(N,X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_purge(add(N,X)) , Marked_purge(rm(N,X))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ true ] () = 0; 
 [ add ] (X0,X1) = 2 + 1*X1 + 0; 
 [ s ] (X0) = 3*X0 + 0; 
 [ 0 ] () = 0; 
 [ Marked_purge ] (X0) = 3*X0 + 0; 
 [ rm ] (X0,X1) = 1*X1 + 0; 
 [ eq ] (X0,X1) = 0; 
 [ purge ] (X0) = 1*X0 + 0; 
 [ nil ] () = 0; 
 [ false ] () = 0; 
 [ ifrm ] (X0,X1,X2) = 1*X2 + 0; 
 ]} 
{
 
DP termination of:
<Marked_rm(N,add(M,X)) , Marked_ifrm(eq(N,M),N,add(M,X))>
<Marked_ifrm(true,N,add(M,X)) , Marked_rm(N,X)>
<Marked_ifrm(false,N,add(M,X)) , Marked_rm(N,X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_rm(N,add(M,X)) , Marked_ifrm(eq(N,M),N,add(M,X))>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
{
 
DP termination of:
<Marked_eq(s(X),s(Y)) , Marked_eq(X,Y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.060495 seconds (real time)
Cime Exit Status: 0