/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:
 p(0()) -> 0()
 p(s(x)) -> x
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 minus(x,y) -> if(le(x,y),x,y)
 if(true(),x,y) -> 0()
 if(false(),x,y) -> s(minus(p(x),y))

Proof:
 DP Processor:
  DPs:
   le#(s(x),s(y)) -> le#(x,y)
   minus#(x,y) -> le#(x,y)
   minus#(x,y) -> if#(le(x,y),x,y)
   if#(false(),x,y) -> p#(x)
   if#(false(),x,y) -> minus#(p(x),y)
  TRS:
   p(0()) -> 0()
   p(s(x)) -> x
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   minus(x,y) -> if(le(x,y),x,y)
   if(true(),x,y) -> 0()
   if(false(),x,y) -> s(minus(p(x),y))
  TDG Processor:
   DPs:
    le#(s(x),s(y)) -> le#(x,y)
    minus#(x,y) -> le#(x,y)
    minus#(x,y) -> if#(le(x,y),x,y)
    if#(false(),x,y) -> p#(x)
    if#(false(),x,y) -> minus#(p(x),y)
   TRS:
    p(0()) -> 0()
    p(s(x)) -> x
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    minus(x,y) -> if(le(x,y),x,y)
    if(true(),x,y) -> 0()
    if(false(),x,y) -> s(minus(p(x),y))
   graph:
    if#(false(),x,y) -> minus#(p(x),y) ->
    minus#(x,y) -> if#(le(x,y),x,y)
    if#(false(),x,y) -> minus#(p(x),y) -> minus#(x,y) -> le#(x,y)
    minus#(x,y) -> if#(le(x,y),x,y) ->
    if#(false(),x,y) -> minus#(p(x),y)
    minus#(x,y) -> if#(le(x,y),x,y) -> if#(false(),x,y) -> p#(x)
    minus#(x,y) -> le#(x,y) -> le#(s(x),s(y)) -> le#(x,y)
    le#(s(x),s(y)) -> le#(x,y) -> le#(s(x),s(y)) -> le#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 6/25
    DPs:
     if#(false(),x,y) -> minus#(p(x),y)
     minus#(x,y) -> if#(le(x,y),x,y)
    TRS:
     p(0()) -> 0()
     p(s(x)) -> x
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     minus(x,y) -> if(le(x,y),x,y)
     if(true(),x,y) -> 0()
     if(false(),x,y) -> s(minus(p(x),y))
    Usable Rule Processor:
     DPs:
      if#(false(),x,y) -> minus#(p(x),y)
      minus#(x,y) -> if#(le(x,y),x,y)
     TRS:
      p(0()) -> 0()
      p(s(x)) -> x
      le(0(),y) -> true()
      le(s(x),0()) -> false()
      le(s(x),s(y)) -> le(x,y)
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       p(0()) -> 0()
       p(s(x)) -> x
       le(0(),y) -> true()
       le(s(x),0()) -> false()
       le(s(x),s(y)) -> le(x,y)
      interpretation:
       [if#](x0, x1, x2) = 2x0 + x1,
       
       [minus#](x0, x1) = 3x0 + 4,
       
       [false] = 2,
       
       [true] = 0,
       
       [le](x0, x1) = x0 + -6,
       
       [s](x0) = 7x0 + 2,
       
       [p](x0) = -7x0 + 0,
       
       [0] = 0
      orientation:
       if#(false(),x,y) = x + 4 >= -4x + 4 = minus#(p(x),y)
       
       minus#(x,y) = 3x + 4 >= 2x + -4 = if#(le(x,y),x,y)
       
       p(0()) = 0 >= 0 = 0()
       
       p(s(x)) = x + 0 >= x = x
       
       le(0(),y) = 0 >= 0 = true()
       
       le(s(x),0()) = 7x + 2 >= 2 = false()
       
       le(s(x),s(y)) = 7x + 2 >= x + -6 = le(x,y)
      problem:
       DPs:
        if#(false(),x,y) -> minus#(p(x),y)
       TRS:
        p(0()) -> 0()
        p(s(x)) -> x
        le(0(),y) -> true()
        le(s(x),0()) -> false()
        le(s(x),s(y)) -> le(x,y)
      Restore Modifier:
       DPs:
        if#(false(),x,y) -> minus#(p(x),y)
       TRS:
        p(0()) -> 0()
        p(s(x)) -> x
        le(0(),y) -> true()
        le(s(x),0()) -> false()
        le(s(x),s(y)) -> le(x,y)
        minus(x,y) -> if(le(x,y),x,y)
        if(true(),x,y) -> 0()
        if(false(),x,y) -> s(minus(p(x),y))
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 2/1
        
    
    DPs:
     le#(s(x),s(y)) -> le#(x,y)
    TRS:
     p(0()) -> 0()
     p(s(x)) -> x
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     minus(x,y) -> if(le(x,y),x,y)
     if(true(),x,y) -> 0()
     if(false(),x,y) -> s(minus(p(x),y))
    Subterm Criterion Processor:
     simple projection:
      pi(le#) = 0
     problem:
      DPs:
       
      TRS:
       p(0()) -> 0()
       p(s(x)) -> x
       le(0(),y) -> true()
       le(s(x),0()) -> false()
       le(s(x),s(y)) -> le(x,y)
       minus(x,y) -> if(le(x,y),x,y)
       if(true(),x,y) -> 0()
       if(false(),x,y) -> s(minus(p(x),y))
     Qed