/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 minus(X,s(Y)) -> pred(minus(X,Y))
 minus(X,0()) -> X
 pred(s(X)) -> X
 le(s(X),s(Y)) -> le(X,Y)
 le(s(X),0()) -> false()
 le(0(),Y) -> true()
 gcd(0(),Y) -> 0()
 gcd(s(X),0()) -> s(X)
 gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
 if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
 if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))

Proof:
 DP Processor:
  DPs:
   minus#(X,s(Y)) -> minus#(X,Y)
   minus#(X,s(Y)) -> pred#(minus(X,Y))
   le#(s(X),s(Y)) -> le#(X,Y)
   gcd#(s(X),s(Y)) -> le#(Y,X)
   gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
   if#(true(),s(X),s(Y)) -> minus#(X,Y)
   if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y))
   if#(false(),s(X),s(Y)) -> minus#(Y,X)
   if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X))
  TRS:
   minus(X,s(Y)) -> pred(minus(X,Y))
   minus(X,0()) -> X
   pred(s(X)) -> X
   le(s(X),s(Y)) -> le(X,Y)
   le(s(X),0()) -> false()
   le(0(),Y) -> true()
   gcd(0(),Y) -> 0()
   gcd(s(X),0()) -> s(X)
   gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
   if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
   if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
  TDG Processor:
   DPs:
    minus#(X,s(Y)) -> minus#(X,Y)
    minus#(X,s(Y)) -> pred#(minus(X,Y))
    le#(s(X),s(Y)) -> le#(X,Y)
    gcd#(s(X),s(Y)) -> le#(Y,X)
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
    if#(true(),s(X),s(Y)) -> minus#(X,Y)
    if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y))
    if#(false(),s(X),s(Y)) -> minus#(Y,X)
    if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X))
   TRS:
    minus(X,s(Y)) -> pred(minus(X,Y))
    minus(X,0()) -> X
    pred(s(X)) -> X
    le(s(X),s(Y)) -> le(X,Y)
    le(s(X),0()) -> false()
    le(0(),Y) -> true()
    gcd(0(),Y) -> 0()
    gcd(s(X),0()) -> s(X)
    gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
    if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
    if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
   graph:
    if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) ->
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
    if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) ->
    gcd#(s(X),s(Y)) -> le#(Y,X)
    if#(true(),s(X),s(Y)) -> minus#(X,Y) ->
    minus#(X,s(Y)) -> pred#(minus(X,Y))
    if#(true(),s(X),s(Y)) -> minus#(X,Y) ->
    minus#(X,s(Y)) -> minus#(X,Y)
    if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X)) ->
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
    if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X)) ->
    gcd#(s(X),s(Y)) -> le#(Y,X)
    if#(false(),s(X),s(Y)) -> minus#(Y,X) ->
    minus#(X,s(Y)) -> pred#(minus(X,Y))
    if#(false(),s(X),s(Y)) -> minus#(Y,X) ->
    minus#(X,s(Y)) -> minus#(X,Y)
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) ->
    if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X))
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) ->
    if#(false(),s(X),s(Y)) -> minus#(Y,X)
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) ->
    if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y))
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) ->
    if#(true(),s(X),s(Y)) -> minus#(X,Y)
    gcd#(s(X),s(Y)) -> le#(Y,X) -> le#(s(X),s(Y)) -> le#(X,Y)
    le#(s(X),s(Y)) -> le#(X,Y) -> le#(s(X),s(Y)) -> le#(X,Y)
    minus#(X,s(Y)) -> minus#(X,Y) ->
    minus#(X,s(Y)) -> pred#(minus(X,Y))
    minus#(X,s(Y)) -> minus#(X,Y) -> minus#(X,s(Y)) -> minus#(X,Y)
   SCC Processor:
    #sccs: 3
    #rules: 5
    #arcs: 16/81
    DPs:
     if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y))
     gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
     if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X))
    TRS:
     minus(X,s(Y)) -> pred(minus(X,Y))
     minus(X,0()) -> X
     pred(s(X)) -> X
     le(s(X),s(Y)) -> le(X,Y)
     le(s(X),0()) -> false()
     le(0(),Y) -> true()
     gcd(0(),Y) -> 0()
     gcd(s(X),0()) -> s(X)
     gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
     if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
     if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
    Subterm Criterion Processor:
     simple projection:
      pi(minus) = [0,0,0]
      pi(pred) = 0
      pi(gcd#) = [0,0,0,1]
      pi(if#) = [1,1,2]
     problem:
      DPs:
       
      TRS:
       minus(X,s(Y)) -> pred(minus(X,Y))
       minus(X,0()) -> X
       pred(s(X)) -> X
       le(s(X),s(Y)) -> le(X,Y)
       le(s(X),0()) -> false()
       le(0(),Y) -> true()
       gcd(0(),Y) -> 0()
       gcd(s(X),0()) -> s(X)
       gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
       if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
       if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
     Qed
    
    DPs:
     minus#(X,s(Y)) -> minus#(X,Y)
    TRS:
     minus(X,s(Y)) -> pred(minus(X,Y))
     minus(X,0()) -> X
     pred(s(X)) -> X
     le(s(X),s(Y)) -> le(X,Y)
     le(s(X),0()) -> false()
     le(0(),Y) -> true()
     gcd(0(),Y) -> 0()
     gcd(s(X),0()) -> s(X)
     gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
     if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
     if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 1
     problem:
      DPs:
       
      TRS:
       minus(X,s(Y)) -> pred(minus(X,Y))
       minus(X,0()) -> X
       pred(s(X)) -> X
       le(s(X),s(Y)) -> le(X,Y)
       le(s(X),0()) -> false()
       le(0(),Y) -> true()
       gcd(0(),Y) -> 0()
       gcd(s(X),0()) -> s(X)
       gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
       if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
       if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
     Qed
    
    DPs:
     le#(s(X),s(Y)) -> le#(X,Y)
    TRS:
     minus(X,s(Y)) -> pred(minus(X,Y))
     minus(X,0()) -> X
     pred(s(X)) -> X
     le(s(X),s(Y)) -> le(X,Y)
     le(s(X),0()) -> false()
     le(0(),Y) -> true()
     gcd(0(),Y) -> 0()
     gcd(s(X),0()) -> s(X)
     gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
     if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
     if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
    Subterm Criterion Processor:
     simple projection:
      pi(le#) = 0
     problem:
      DPs:
       
      TRS:
       minus(X,s(Y)) -> pred(minus(X,Y))
       minus(X,0()) -> X
       pred(s(X)) -> X
       le(s(X),s(Y)) -> le(X,Y)
       le(s(X),0()) -> false()
       le(0(),Y) -> true()
       gcd(0(),Y) -> 0()
       gcd(s(X),0()) -> s(X)
       gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
       if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
       if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
     Qed