/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 -(0(),y) -> 0()
 -(x,0()) -> x
 -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0())
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   -#(x,s(y)) -> p#(s(y))
   -#(x,s(y)) -> -#(x,p(s(y)))
  TRS:
   -(0(),y) -> 0()
   -(x,0()) -> x
   -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0())
   p(0()) -> 0()
   p(s(x)) -> x
  TDG Processor:
   DPs:
    -#(x,s(y)) -> p#(s(y))
    -#(x,s(y)) -> -#(x,p(s(y)))
   TRS:
    -(0(),y) -> 0()
    -(x,0()) -> x
    -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0())
    p(0()) -> 0()
    p(s(x)) -> x
   graph:
    -#(x,s(y)) -> -#(x,p(s(y))) -> -#(x,s(y)) -> -#(x,p(s(y)))
    -#(x,s(y)) -> -#(x,p(s(y))) -> -#(x,s(y)) -> p#(s(y))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 2/4
    DPs:
     -#(x,s(y)) -> -#(x,p(s(y)))
    TRS:
     -(0(),y) -> 0()
     -(x,0()) -> x
     -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0())
     p(0()) -> 0()
     p(s(x)) -> x
    Usable Rule Processor:
     DPs:
      -#(x,s(y)) -> -#(x,p(s(y)))
     TRS:
      p(s(x)) -> x
     Semantic Labeling Processor:
      dimension: 2
      usable rules:
       
      interpretation:
                 [1 0]     [1]
       [p](x0) = [1 0]x0 + [0],
       
                 [1 1]     [0]
       [s](x0) = [1 1]x0 + [1]
       labeled:
        -#
       usable (for model):
        -#
        s
        p
       argument filtering:
        pi(s) = 0
        pi(p) = []
        pi(-#) = []
      precedence:
       -# ~ p ~ s
      problem:
       DPs:
        
       TRS:
        p(s(x)) -> x
      Qed