/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:
 f(x,0()) -> s(0())
 f(s(x),s(y)) -> s(f(x,y))
 g(0(),x) -> g(f(x,x),x)

Proof:
 DP Processor:
  DPs:
   f#(s(x),s(y)) -> f#(x,y)
   g#(0(),x) -> f#(x,x)
   g#(0(),x) -> g#(f(x,x),x)
  TRS:
   f(x,0()) -> s(0())
   f(s(x),s(y)) -> s(f(x,y))
   g(0(),x) -> g(f(x,x),x)
  TDG Processor:
   DPs:
    f#(s(x),s(y)) -> f#(x,y)
    g#(0(),x) -> f#(x,x)
    g#(0(),x) -> g#(f(x,x),x)
   TRS:
    f(x,0()) -> s(0())
    f(s(x),s(y)) -> s(f(x,y))
    g(0(),x) -> g(f(x,x),x)
   graph:
    g#(0(),x) -> g#(f(x,x),x) -> g#(0(),x) -> g#(f(x,x),x)
    g#(0(),x) -> g#(f(x,x),x) -> g#(0(),x) -> f#(x,x)
    g#(0(),x) -> f#(x,x) -> f#(s(x),s(y)) -> f#(x,y)
    f#(s(x),s(y)) -> f#(x,y) -> f#(s(x),s(y)) -> f#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 4/9
    DPs:
     g#(0(),x) -> g#(f(x,x),x)
    TRS:
     f(x,0()) -> s(0())
     f(s(x),s(y)) -> s(f(x,y))
     g(0(),x) -> g(f(x,x),x)
    EDG Processor:
     DPs:
      g#(0(),x) -> g#(f(x,x),x)
     TRS:
      f(x,0()) -> s(0())
      f(s(x),s(y)) -> s(f(x,y))
      g(0(),x) -> g(f(x,x),x)
     graph:
      
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 0/1
      
    
    DPs:
     f#(s(x),s(y)) -> f#(x,y)
    TRS:
     f(x,0()) -> s(0())
     f(s(x),s(y)) -> s(f(x,y))
     g(0(),x) -> g(f(x,x),x)
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 0
     problem:
      DPs:
       
      TRS:
       f(x,0()) -> s(0())
       f(s(x),s(y)) -> s(f(x,y))
       g(0(),x) -> g(f(x,x),x)
     Qed