/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:
 exp(x,0()) -> s(0())
 exp(x,s(y)) -> *(x,exp(x,y))
 *(0(),y) -> 0()
 *(s(x),y) -> +(y,*(x,y))
 -(0(),y) -> 0()
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)

Proof:
 DP Processor:
  DPs:
   exp#(x,s(y)) -> exp#(x,y)
   exp#(x,s(y)) -> *#(x,exp(x,y))
   *#(s(x),y) -> *#(x,y)
   -#(s(x),s(y)) -> -#(x,y)
  TRS:
   exp(x,0()) -> s(0())
   exp(x,s(y)) -> *(x,exp(x,y))
   *(0(),y) -> 0()
   *(s(x),y) -> +(y,*(x,y))
   -(0(),y) -> 0()
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
  TDG Processor:
   DPs:
    exp#(x,s(y)) -> exp#(x,y)
    exp#(x,s(y)) -> *#(x,exp(x,y))
    *#(s(x),y) -> *#(x,y)
    -#(s(x),s(y)) -> -#(x,y)
   TRS:
    exp(x,0()) -> s(0())
    exp(x,s(y)) -> *(x,exp(x,y))
    *(0(),y) -> 0()
    *(s(x),y) -> +(y,*(x,y))
    -(0(),y) -> 0()
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
   graph:
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
    *#(s(x),y) -> *#(x,y) -> *#(s(x),y) -> *#(x,y)
    exp#(x,s(y)) -> *#(x,exp(x,y)) -> *#(s(x),y) -> *#(x,y)
    exp#(x,s(y)) -> exp#(x,y) -> exp#(x,s(y)) -> *#(x,exp(x,y))
    exp#(x,s(y)) -> exp#(x,y) -> exp#(x,s(y)) -> exp#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 5/16
    DPs:
     exp#(x,s(y)) -> exp#(x,y)
    TRS:
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> *(x,exp(x,y))
     *(0(),y) -> 0()
     *(s(x),y) -> +(y,*(x,y))
     -(0(),y) -> 0()
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(exp#) = 1
     problem:
      DPs:
       
      TRS:
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> *(x,exp(x,y))
       *(0(),y) -> 0()
       *(s(x),y) -> +(y,*(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
     Qed
    
    DPs:
     *#(s(x),y) -> *#(x,y)
    TRS:
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> *(x,exp(x,y))
     *(0(),y) -> 0()
     *(s(x),y) -> +(y,*(x,y))
     -(0(),y) -> 0()
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(*#) = 0
     problem:
      DPs:
       
      TRS:
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> *(x,exp(x,y))
       *(0(),y) -> 0()
       *(s(x),y) -> +(y,*(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
     Qed
    
    DPs:
     -#(s(x),s(y)) -> -#(x,y)
    TRS:
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> *(x,exp(x,y))
     *(0(),y) -> 0()
     *(s(x),y) -> +(y,*(x,y))
     -(0(),y) -> 0()
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(-#) = 0
     problem:
      DPs:
       
      TRS:
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> *(x,exp(x,y))
       *(0(),y) -> 0()
       *(s(x),y) -> +(y,*(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
     Qed