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


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YES

Problem:
 +(x,0()) -> x
 +(x,i(x)) -> 0()
 +(+(x,y),z) -> +(x,+(y,z))
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(+(x,y),z) -> +(*(x,z),*(y,z))

Proof:
 DP Processor:
  DPs:
   +#(+(x,y),z) -> +#(y,z)
   +#(+(x,y),z) -> +#(x,+(y,z))
   *#(x,+(y,z)) -> *#(x,z)
   *#(x,+(y,z)) -> *#(x,y)
   *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
   *#(+(x,y),z) -> *#(y,z)
   *#(+(x,y),z) -> *#(x,z)
   *#(+(x,y),z) -> +#(*(x,z),*(y,z))
  TRS:
   +(x,0()) -> x
   +(x,i(x)) -> 0()
   +(+(x,y),z) -> +(x,+(y,z))
   *(x,+(y,z)) -> +(*(x,y),*(x,z))
   *(+(x,y),z) -> +(*(x,z),*(y,z))
  TDG Processor:
   DPs:
    +#(+(x,y),z) -> +#(y,z)
    +#(+(x,y),z) -> +#(x,+(y,z))
    *#(x,+(y,z)) -> *#(x,z)
    *#(x,+(y,z)) -> *#(x,y)
    *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
    *#(+(x,y),z) -> *#(y,z)
    *#(+(x,y),z) -> *#(x,z)
    *#(+(x,y),z) -> +#(*(x,z),*(y,z))
   TRS:
    +(x,0()) -> x
    +(x,i(x)) -> 0()
    +(+(x,y),z) -> +(x,+(y,z))
    *(x,+(y,z)) -> +(*(x,y),*(x,z))
    *(+(x,y),z) -> +(*(x,z),*(y,z))
   graph:
    *#(+(x,y),z) -> *#(y,z) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z))
    *#(+(x,y),z) -> *#(y,z) -> *#(+(x,y),z) -> *#(x,z)
    *#(+(x,y),z) -> *#(y,z) -> *#(+(x,y),z) -> *#(y,z)
    *#(+(x,y),z) -> *#(y,z) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
    *#(+(x,y),z) -> *#(y,z) -> *#(x,+(y,z)) -> *#(x,y)
    *#(+(x,y),z) -> *#(y,z) -> *#(x,+(y,z)) -> *#(x,z)
    *#(+(x,y),z) -> *#(x,z) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z))
    *#(+(x,y),z) -> *#(x,z) -> *#(+(x,y),z) -> *#(x,z)
    *#(+(x,y),z) -> *#(x,z) -> *#(+(x,y),z) -> *#(y,z)
    *#(+(x,y),z) -> *#(x,z) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
    *#(+(x,y),z) -> *#(x,z) -> *#(x,+(y,z)) -> *#(x,y)
    *#(+(x,y),z) -> *#(x,z) -> *#(x,+(y,z)) -> *#(x,z)
    *#(+(x,y),z) -> +#(*(x,z),*(y,z)) ->
    +#(+(x,y),z) -> +#(x,+(y,z))
    *#(+(x,y),z) -> +#(*(x,z),*(y,z)) -> +#(+(x,y),z) -> +#(y,z)
    *#(x,+(y,z)) -> *#(x,z) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z))
    *#(x,+(y,z)) -> *#(x,z) -> *#(+(x,y),z) -> *#(x,z)
    *#(x,+(y,z)) -> *#(x,z) -> *#(+(x,y),z) -> *#(y,z)
    *#(x,+(y,z)) -> *#(x,z) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
    *#(x,+(y,z)) -> *#(x,z) -> *#(x,+(y,z)) -> *#(x,y)
    *#(x,+(y,z)) -> *#(x,z) -> *#(x,+(y,z)) -> *#(x,z)
    *#(x,+(y,z)) -> *#(x,y) -> *#(+(x,y),z) -> +#(*(x,z),*(y,z))
    *#(x,+(y,z)) -> *#(x,y) -> *#(+(x,y),z) -> *#(x,z)
    *#(x,+(y,z)) -> *#(x,y) -> *#(+(x,y),z) -> *#(y,z)
    *#(x,+(y,z)) -> *#(x,y) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
    *#(x,+(y,z)) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,y)
    *#(x,+(y,z)) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,z)
    *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) ->
    +#(+(x,y),z) -> +#(x,+(y,z))
    *#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(+(x,y),z) -> +#(y,z)
    +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(x,+(y,z))
    +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(y,z)
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z))
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(y,z)
   SCC Processor:
    #sccs: 2
    #rules: 6
    #arcs: 32/64
    DPs:
     *#(+(x,y),z) -> *#(y,z)
     *#(x,+(y,z)) -> *#(x,z)
     *#(x,+(y,z)) -> *#(x,y)
     *#(+(x,y),z) -> *#(x,z)
    TRS:
     +(x,0()) -> x
     +(x,i(x)) -> 0()
     +(+(x,y),z) -> +(x,+(y,z))
     *(x,+(y,z)) -> +(*(x,y),*(x,z))
     *(+(x,y),z) -> +(*(x,z),*(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(*#) = 0
     problem:
      DPs:
       *#(x,+(y,z)) -> *#(x,z)
       *#(x,+(y,z)) -> *#(x,y)
      TRS:
       +(x,0()) -> x
       +(x,i(x)) -> 0()
       +(+(x,y),z) -> +(x,+(y,z))
       *(x,+(y,z)) -> +(*(x,y),*(x,z))
       *(+(x,y),z) -> +(*(x,z),*(y,z))
     Subterm Criterion Processor:
      simple projection:
       pi(*#) = 1
      problem:
       DPs:
        
       TRS:
        +(x,0()) -> x
        +(x,i(x)) -> 0()
        +(+(x,y),z) -> +(x,+(y,z))
        *(x,+(y,z)) -> +(*(x,y),*(x,z))
        *(+(x,y),z) -> +(*(x,z),*(y,z))
      Qed
    
    DPs:
     +#(+(x,y),z) -> +#(y,z)
     +#(+(x,y),z) -> +#(x,+(y,z))
    TRS:
     +(x,0()) -> x
     +(x,i(x)) -> 0()
     +(+(x,y),z) -> +(x,+(y,z))
     *(x,+(y,z)) -> +(*(x,y),*(x,z))
     *(+(x,y),z) -> +(*(x,z),*(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 0
     problem:
      DPs:
       
      TRS:
       +(x,0()) -> x
       +(x,i(x)) -> 0()
       +(+(x,y),z) -> +(x,+(y,z))
       *(x,+(y,z)) -> +(*(x,y),*(x,z))
       *(+(x,y),z) -> +(*(x,z),*(y,z))
     Qed