/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 DP Processor:
  DPs:
   times#(x,s(y)) -> times#(x,y)
   times#(x,s(y)) -> plus#(times(x,y),x)
   plus#(x,s(y)) -> plus#(x,y)
   plus#(s(x),y) -> plus#(x,y)
  TRS:
   times(x,0()) -> 0()
   times(x,s(y)) -> plus(times(x,y),x)
   plus(x,0()) -> x
   plus(0(),x) -> x
   plus(x,s(y)) -> s(plus(x,y))
   plus(s(x),y) -> s(plus(x,y))
  TDG Processor:
   DPs:
    times#(x,s(y)) -> times#(x,y)
    times#(x,s(y)) -> plus#(times(x,y),x)
    plus#(x,s(y)) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,y)
   TRS:
    times(x,0()) -> 0()
    times(x,s(y)) -> plus(times(x,y),x)
    plus(x,0()) -> x
    plus(0(),x) -> x
    plus(x,s(y)) -> s(plus(x,y))
    plus(s(x),y) -> s(plus(x,y))
   graph:
    plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,y) -> plus#(x,s(y)) -> plus#(x,y)
    plus#(x,s(y)) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y)
    plus#(x,s(y)) -> plus#(x,y) -> plus#(x,s(y)) -> plus#(x,y)
    times#(x,s(y)) -> plus#(times(x,y),x) ->
    plus#(s(x),y) -> plus#(x,y)
    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)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 8/16
    DPs:
     times#(x,s(y)) -> times#(x,y)
    TRS:
     times(x,0()) -> 0()
     times(x,s(y)) -> plus(times(x,y),x)
     plus(x,0()) -> x
     plus(0(),x) -> x
     plus(x,s(y)) -> s(plus(x,y))
     plus(s(x),y) -> s(plus(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(times#) = 1
     problem:
      DPs:
       
      TRS:
       times(x,0()) -> 0()
       times(x,s(y)) -> plus(times(x,y),x)
       plus(x,0()) -> x
       plus(0(),x) -> x
       plus(x,s(y)) -> s(plus(x,y))
       plus(s(x),y) -> s(plus(x,y))
     Qed
    
    DPs:
     plus#(s(x),y) -> plus#(x,y)
     plus#(x,s(y)) -> plus#(x,y)
    TRS:
     times(x,0()) -> 0()
     times(x,s(y)) -> plus(times(x,y),x)
     plus(x,0()) -> x
     plus(0(),x) -> x
     plus(x,s(y)) -> s(plus(x,y))
     plus(s(x),y) -> s(plus(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 0
     problem:
      DPs:
       plus#(x,s(y)) -> plus#(x,y)
      TRS:
       times(x,0()) -> 0()
       times(x,s(y)) -> plus(times(x,y),x)
       plus(x,0()) -> x
       plus(0(),x) -> x
       plus(x,s(y)) -> s(plus(x,y))
       plus(s(x),y) -> s(plus(x,y))
     Subterm Criterion Processor:
      simple projection:
       pi(plus#) = 1
      problem:
       DPs:
        
       TRS:
        times(x,0()) -> 0()
        times(x,s(y)) -> plus(times(x,y),x)
        plus(x,0()) -> x
        plus(0(),x) -> x
        plus(x,s(y)) -> s(plus(x,y))
        plus(s(x),y) -> s(plus(x,y))
      Qed