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


--------------------------------------------------------------------------------


YES

Problem:
 times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
 times(x,0()) -> 0()
 times(x,s(y)) -> plus(times(x,y),x)
 plus(x,0()) -> x
 plus(x,s(y)) -> s(plus(x,y))

Proof:
 DP Processor:
  DPs:
   times#(x,plus(y,s(z))) -> times#(x,s(z))
   times#(x,plus(y,s(z))) -> times#(s(z),0())
   times#(x,plus(y,s(z))) -> plus#(y,times(s(z),0()))
   times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
   times#(x,plus(y,s(z))) -> plus#(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
   times#(x,s(y)) -> times#(x,y)
   times#(x,s(y)) -> plus#(times(x,y),x)
   plus#(x,s(y)) -> plus#(x,y)
  TRS:
   times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
   times(x,0()) -> 0()
   times(x,s(y)) -> plus(times(x,y),x)
   plus(x,0()) -> x
   plus(x,s(y)) -> s(plus(x,y))
  TDG Processor:
   DPs:
    times#(x,plus(y,s(z))) -> times#(x,s(z))
    times#(x,plus(y,s(z))) -> times#(s(z),0())
    times#(x,plus(y,s(z))) -> plus#(y,times(s(z),0()))
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
    times#(x,plus(y,s(z))) -> plus#(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
    times#(x,s(y)) -> times#(x,y)
    times#(x,s(y)) -> plus#(times(x,y),x)
    plus#(x,s(y)) -> plus#(x,y)
   TRS:
    times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
    times(x,0()) -> 0()
    times(x,s(y)) -> plus(times(x,y),x)
    plus(x,0()) -> x
    plus(x,s(y)) -> s(plus(x,y))
   graph:
    plus#(x,s(y)) -> plus#(x,y) ->
    plus#(x,s(y)) -> plus#(x,y)
    times#(x,plus(y,s(z))) -> plus#(times(x,plus(y,times(s(z),0()))),times(x,s(z))) ->
    plus#(x,s(y)) -> plus#(x,y)
    times#(x,plus(y,s(z))) -> plus#(y,times(s(z),0())) ->
    plus#(x,s(y)) -> plus#(x,y)
    times#(x,plus(y,s(z))) -> times#(s(z),0()) ->
    times#(x,s(y)) -> plus#(times(x,y),x)
    times#(x,plus(y,s(z))) -> times#(s(z),0()) ->
    times#(x,s(y)) -> times#(x,y)
    times#(x,plus(y,s(z))) -> times#(s(z),0()) ->
    times#(x,plus(y,s(z))) -> plus#(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
    times#(x,plus(y,s(z))) -> times#(s(z),0()) ->
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
    times#(x,plus(y,s(z))) -> times#(s(z),0()) ->
    times#(x,plus(y,s(z))) -> plus#(y,times(s(z),0()))
    times#(x,plus(y,s(z))) -> times#(s(z),0()) ->
    times#(x,plus(y,s(z))) -> times#(s(z),0())
    times#(x,plus(y,s(z))) -> times#(s(z),0()) ->
    times#(x,plus(y,s(z))) -> times#(x,s(z))
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
    times#(x,s(y)) -> plus#(times(x,y),x)
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
    times#(x,s(y)) -> times#(x,y)
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
    times#(x,plus(y,s(z))) -> plus#(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
    times#(x,plus(y,s(z))) -> plus#(y,times(s(z),0()))
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
    times#(x,plus(y,s(z))) -> times#(s(z),0())
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
    times#(x,plus(y,s(z))) -> times#(x,s(z))
    times#(x,plus(y,s(z))) -> times#(x,s(z)) ->
    times#(x,s(y)) -> plus#(times(x,y),x)
    times#(x,plus(y,s(z))) -> times#(x,s(z)) ->
    times#(x,s(y)) -> times#(x,y)
    times#(x,plus(y,s(z))) -> times#(x,s(z)) ->
    times#(x,plus(y,s(z))) -> plus#(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
    times#(x,plus(y,s(z))) -> times#(x,s(z)) ->
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
    times#(x,plus(y,s(z))) -> times#(x,s(z)) ->
    times#(x,plus(y,s(z))) -> plus#(y,times(s(z),0()))
    times#(x,plus(y,s(z))) -> times#(x,s(z)) ->
    times#(x,plus(y,s(z))) -> times#(s(z),0())
    times#(x,plus(y,s(z))) -> times#(x,s(z)) ->
    times#(x,plus(y,s(z))) -> times#(x,s(z))
    times#(x,s(y)) -> plus#(times(x,y),x) ->
    plus#(x,s(y)) -> plus#(x,y)
    times#(x,s(y)) -> times#(x,y) ->
    times#(x,s(y)) -> plus#(times(x,y),x)
    times#(x,s(y)) -> times#(x,y) -> times#(x,s(y)) -> times#(x,y)
    times#(x,s(y)) -> times#(x,y) ->
    times#(x,plus(y,s(z))) -> plus#(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
    times#(x,s(y)) -> times#(x,y) ->
    times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
    times#(x,s(y)) -> times#(x,y) ->
    times#(x,plus(y,s(z))) -> plus#(y,times(s(z),0()))
    times#(x,s(y)) -> times#(x,y) ->
    times#(x,plus(y,s(z))) -> times#(s(z),0())
    times#(x,s(y)) -> times#(x,y) -> times#(x,plus(y,s(z))) -> times#(x,s(z))
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 32/64
    DPs:
     times#(x,plus(y,s(z))) -> times#(s(z),0())
     times#(x,plus(y,s(z))) -> times#(x,s(z))
     times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
     times#(x,s(y)) -> times#(x,y)
    TRS:
     times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
     times(x,0()) -> 0()
     times(x,s(y)) -> plus(times(x,y),x)
     plus(x,0()) -> x
     plus(x,s(y)) -> s(plus(x,y))
    EDG Processor:
     DPs:
      times#(x,plus(y,s(z))) -> times#(s(z),0())
      times#(x,plus(y,s(z))) -> times#(x,s(z))
      times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
      times#(x,s(y)) -> times#(x,y)
     TRS:
      times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
      times(x,0()) -> 0()
      times(x,s(y)) -> plus(times(x,y),x)
      plus(x,0()) -> x
      plus(x,s(y)) -> s(plus(x,y))
     graph:
      times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
      times#(x,plus(y,s(z))) -> times#(x,s(z))
      times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
      times#(x,plus(y,s(z))) -> times#(s(z),0())
      times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
      times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
      times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0()))) ->
      times#(x,s(y)) -> times#(x,y)
      times#(x,plus(y,s(z))) -> times#(x,s(z)) ->
      times#(x,s(y)) -> times#(x,y)
      times#(x,s(y)) -> times#(x,y) ->
      times#(x,plus(y,s(z))) -> times#(x,s(z))
      times#(x,s(y)) -> times#(x,y) ->
      times#(x,plus(y,s(z))) -> times#(s(z),0())
      times#(x,s(y)) -> times#(x,y) ->
      times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
      times#(x,s(y)) -> times#(x,y) -> times#(x,s(y)) -> times#(x,y)
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 9/16
      DPs:
       times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
       times#(x,s(y)) -> times#(x,y)
       times#(x,plus(y,s(z))) -> times#(x,s(z))
      TRS:
       times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
       times(x,0()) -> 0()
       times(x,s(y)) -> plus(times(x,y),x)
       plus(x,0()) -> x
       plus(x,s(y)) -> s(plus(x,y))
      Usable Rule Processor:
       DPs:
        times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
        times#(x,s(y)) -> times#(x,y)
        times#(x,plus(y,s(z))) -> times#(x,s(z))
       TRS:
        times(x,0()) -> 0()
        plus(x,0()) -> x
        plus(x,s(y)) -> s(plus(x,y))
       Semantic Labeling Processor:
        dimension: 1
        usable rules:
         
        interpretation:
         [0] = 0,
         
         [times](x0, x1) = x0,
         
         [plus](x0, x1) = 2x0 + x1 + 2,
         
         [s](x0) = x0
         labeled:
          times#
          s
         usable (for model):
          times#
          plus
          s
          times
          0
         argument filtering:
          pi(s) = []
          pi(plus) = []
          pi(times) = []
          pi(0) = []
          pi(times#) = []
        precedence:
         times# ~ 0 ~ times ~ plus ~ s
        problem:
         DPs:
          times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
          times#(x,s(y)) -> times#(x,y)
         TRS:
          times(x,0()) -> 0()
          plus(x,0()) -> x
          plus(x,s(y)) -> s(plus(x,y))
        Restore Modifier:
         DPs:
          times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
          times#(x,s(y)) -> times#(x,y)
         TRS:
          times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
          times(x,0()) -> 0()
          times(x,s(y)) -> plus(times(x,y),x)
          plus(x,0()) -> x
          plus(x,s(y)) -> s(plus(x,y))
         Usable Rule Processor:
          DPs:
           times#(x,plus(y,s(z))) -> times#(x,plus(y,times(s(z),0())))
           times#(x,s(y)) -> times#(x,y)
          TRS:
           times(x,0()) -> 0()
           plus(x,0()) -> x
           plus(x,s(y)) -> s(plus(x,y))
          Semantic Labeling Processor:
           dimension: 1
           usable rules:
            times(x,0()) -> 0()
            plus(x,0()) -> x
            plus(x,s(y)) -> s(plus(x,y))
           interpretation:
            [0] = 0,
            
            [times](x0, x1) = 1,
            
            [plus](x0, x1) = x0 + 1,
            
            [s](x0) = x0
            labeled:
            usable (for model):
            argument filtering:
             pi(s) = [0]
             pi(plus) = [0,1]
             pi(times) = []
             pi(0) = []
             pi(times#) = 1
           precedence:
            plus > s > times > times# ~ 0
           problem:
            DPs:
             
            TRS:
             times(x,0()) -> 0()
             plus(x,0()) -> x
             plus(x,s(y)) -> s(plus(x,y))
           Qed
    
    DPs:
     plus#(x,s(y)) -> plus#(x,y)
    TRS:
     times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
     times(x,0()) -> 0()
     times(x,s(y)) -> plus(times(x,y),x)
     plus(x,0()) -> x
     plus(x,s(y)) -> s(plus(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 1
     problem:
      DPs:
       
      TRS:
       times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
       times(x,0()) -> 0()
       times(x,s(y)) -> plus(times(x,y),x)
       plus(x,0()) -> x
       plus(x,s(y)) -> s(plus(x,y))
     Qed