/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
 +(minus(x),x) -> 0()
 minus(0()) -> 0()
 minus(minus(x)) -> x
 minus(+(x,y)) -> +(minus(y),minus(x))
 *(x,1()) -> x
 *(x,0()) -> 0()
 *(x,+(y,z)) -> +(*(x,y),*(x,z))
 *(x,minus(y)) -> minus(*(x,y))

Proof:
 DP Processor:
  DPs:
   minus#(+(x,y)) -> minus#(x)
   minus#(+(x,y)) -> minus#(y)
   minus#(+(x,y)) -> +#(minus(y),minus(x))
   *#(x,+(y,z)) -> *#(x,z)
   *#(x,+(y,z)) -> *#(x,y)
   *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
   *#(x,minus(y)) -> *#(x,y)
   *#(x,minus(y)) -> minus#(*(x,y))
  TRS:
   +(x,0()) -> x
   +(minus(x),x) -> 0()
   minus(0()) -> 0()
   minus(minus(x)) -> x
   minus(+(x,y)) -> +(minus(y),minus(x))
   *(x,1()) -> x
   *(x,0()) -> 0()
   *(x,+(y,z)) -> +(*(x,y),*(x,z))
   *(x,minus(y)) -> minus(*(x,y))
  TDG Processor:
   DPs:
    minus#(+(x,y)) -> minus#(x)
    minus#(+(x,y)) -> minus#(y)
    minus#(+(x,y)) -> +#(minus(y),minus(x))
    *#(x,+(y,z)) -> *#(x,z)
    *#(x,+(y,z)) -> *#(x,y)
    *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
    *#(x,minus(y)) -> *#(x,y)
    *#(x,minus(y)) -> minus#(*(x,y))
   TRS:
    +(x,0()) -> x
    +(minus(x),x) -> 0()
    minus(0()) -> 0()
    minus(minus(x)) -> x
    minus(+(x,y)) -> +(minus(y),minus(x))
    *(x,1()) -> x
    *(x,0()) -> 0()
    *(x,+(y,z)) -> +(*(x,y),*(x,z))
    *(x,minus(y)) -> minus(*(x,y))
   graph:
    *#(x,minus(y)) -> *#(x,y) -> *#(x,minus(y)) -> minus#(*(x,y))
    *#(x,minus(y)) -> *#(x,y) -> *#(x,minus(y)) -> *#(x,y)
    *#(x,minus(y)) -> *#(x,y) -> *#(x,+(y,z)) -> +#(*(x,y),*(x,z))
    *#(x,minus(y)) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,y)
    *#(x,minus(y)) -> *#(x,y) -> *#(x,+(y,z)) -> *#(x,z)
    *#(x,minus(y)) -> minus#(*(x,y)) ->
    minus#(+(x,y)) -> +#(minus(y),minus(x))
    *#(x,minus(y)) -> minus#(*(x,y)) -> minus#(+(x,y)) -> minus#(y)
    *#(x,minus(y)) -> minus#(*(x,y)) -> minus#(+(x,y)) -> minus#(x)
    *#(x,+(y,z)) -> *#(x,z) -> *#(x,minus(y)) -> minus#(*(x,y))
    *#(x,+(y,z)) -> *#(x,z) -> *#(x,minus(y)) -> *#(x,y)
    *#(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,minus(y)) -> minus#(*(x,y))
    *#(x,+(y,z)) -> *#(x,y) -> *#(x,minus(y)) -> *#(x,y)
    *#(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)
    minus#(+(x,y)) -> minus#(y) ->
    minus#(+(x,y)) -> +#(minus(y),minus(x))
    minus#(+(x,y)) -> minus#(y) -> minus#(+(x,y)) -> minus#(y)
    minus#(+(x,y)) -> minus#(y) -> minus#(+(x,y)) -> minus#(x)
    minus#(+(x,y)) -> minus#(x) ->
    minus#(+(x,y)) -> +#(minus(y),minus(x))
    minus#(+(x,y)) -> minus#(x) -> minus#(+(x,y)) -> minus#(y)
    minus#(+(x,y)) -> minus#(x) -> minus#(+(x,y)) -> minus#(x)
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 24/64
    DPs:
     *#(x,minus(y)) -> *#(x,y)
     *#(x,+(y,z)) -> *#(x,z)
     *#(x,+(y,z)) -> *#(x,y)
    TRS:
     +(x,0()) -> x
     +(minus(x),x) -> 0()
     minus(0()) -> 0()
     minus(minus(x)) -> x
     minus(+(x,y)) -> +(minus(y),minus(x))
     *(x,1()) -> x
     *(x,0()) -> 0()
     *(x,+(y,z)) -> +(*(x,y),*(x,z))
     *(x,minus(y)) -> minus(*(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(*#) = 1
     problem:
      DPs:
       
      TRS:
       +(x,0()) -> x
       +(minus(x),x) -> 0()
       minus(0()) -> 0()
       minus(minus(x)) -> x
       minus(+(x,y)) -> +(minus(y),minus(x))
       *(x,1()) -> x
       *(x,0()) -> 0()
       *(x,+(y,z)) -> +(*(x,y),*(x,z))
       *(x,minus(y)) -> minus(*(x,y))
     Qed
    
    DPs:
     minus#(+(x,y)) -> minus#(x)
     minus#(+(x,y)) -> minus#(y)
    TRS:
     +(x,0()) -> x
     +(minus(x),x) -> 0()
     minus(0()) -> 0()
     minus(minus(x)) -> x
     minus(+(x,y)) -> +(minus(y),minus(x))
     *(x,1()) -> x
     *(x,0()) -> 0()
     *(x,+(y,z)) -> +(*(x,y),*(x,z))
     *(x,minus(y)) -> minus(*(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 0
     problem:
      DPs:
       
      TRS:
       +(x,0()) -> x
       +(minus(x),x) -> 0()
       minus(0()) -> 0()
       minus(minus(x)) -> x
       minus(+(x,y)) -> +(minus(y),minus(x))
       *(x,1()) -> x
       *(x,0()) -> 0()
       *(x,+(y,z)) -> +(*(x,y),*(x,z))
       *(x,minus(y)) -> minus(*(x,y))
     Qed