MAYBE

Problem:
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 *(x,0()) -> 0()
 *(x,s(y)) -> +(*(x,y),x)
 ge(x,0()) -> true()
 ge(0(),s(y)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 fact(x) -> iffact(x,ge(x,s(s(0()))))
 iffact(x,true()) -> *(x,fact(-(x,s(0()))))
 iffact(x,false()) -> s(0())

Proof:
 DP Processor:
  DPs:
   +#(x,s(y)) -> +#(x,y)
   *#(x,s(y)) -> *#(x,y)
   *#(x,s(y)) -> +#(*(x,y),x)
   ge#(s(x),s(y)) -> ge#(x,y)
   -#(s(x),s(y)) -> -#(x,y)
   fact#(x) -> ge#(x,s(s(0())))
   fact#(x) -> iffact#(x,ge(x,s(s(0()))))
   iffact#(x,true()) -> -#(x,s(0()))
   iffact#(x,true()) -> fact#(-(x,s(0())))
   iffact#(x,true()) -> *#(x,fact(-(x,s(0()))))
  TRS:
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   *(x,0()) -> 0()
   *(x,s(y)) -> +(*(x,y),x)
   ge(x,0()) -> true()
   ge(0(),s(y)) -> false()
   ge(s(x),s(y)) -> ge(x,y)
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   fact(x) -> iffact(x,ge(x,s(s(0()))))
   iffact(x,true()) -> *(x,fact(-(x,s(0()))))
   iffact(x,false()) -> s(0())
  TDG Processor:
   DPs:
    +#(x,s(y)) -> +#(x,y)
    *#(x,s(y)) -> *#(x,y)
    *#(x,s(y)) -> +#(*(x,y),x)
    ge#(s(x),s(y)) -> ge#(x,y)
    -#(s(x),s(y)) -> -#(x,y)
    fact#(x) -> ge#(x,s(s(0())))
    fact#(x) -> iffact#(x,ge(x,s(s(0()))))
    iffact#(x,true()) -> -#(x,s(0()))
    iffact#(x,true()) -> fact#(-(x,s(0())))
    iffact#(x,true()) -> *#(x,fact(-(x,s(0()))))
   TRS:
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    *(x,0()) -> 0()
    *(x,s(y)) -> +(*(x,y),x)
    ge(x,0()) -> true()
    ge(0(),s(y)) -> false()
    ge(s(x),s(y)) -> ge(x,y)
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
    fact(x) -> iffact(x,ge(x,s(s(0()))))
    iffact(x,true()) -> *(x,fact(-(x,s(0()))))
    iffact(x,false()) -> s(0())
   graph:
    iffact#(x,true()) -> fact#(-(x,s(0()))) ->
    fact#(x) -> iffact#(x,ge(x,s(s(0()))))
    iffact#(x,true()) -> fact#(-(x,s(0()))) ->
    fact#(x) -> ge#(x,s(s(0())))
    iffact#(x,true()) -> -#(x,s(0())) ->
    -#(s(x),s(y)) -> -#(x,y)
    iffact#(x,true()) -> *#(x,fact(-(x,s(0())))) ->
    *#(x,s(y)) -> +#(*(x,y),x)
    iffact#(x,true()) -> *#(x,fact(-(x,s(0())))) ->
    *#(x,s(y)) -> *#(x,y)
    fact#(x) -> iffact#(x,ge(x,s(s(0())))) ->
    iffact#(x,true()) -> *#(x,fact(-(x,s(0()))))
    fact#(x) -> iffact#(x,ge(x,s(s(0())))) ->
    iffact#(x,true()) -> fact#(-(x,s(0())))
    fact#(x) -> iffact#(x,ge(x,s(s(0())))) ->
    iffact#(x,true()) -> -#(x,s(0()))
    fact#(x) -> ge#(x,s(s(0()))) -> ge#(s(x),s(y)) -> ge#(x,y)
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
    ge#(s(x),s(y)) -> ge#(x,y) -> ge#(s(x),s(y)) -> ge#(x,y)
    *#(x,s(y)) -> *#(x,y) -> *#(x,s(y)) -> +#(*(x,y),x)
    *#(x,s(y)) -> *#(x,y) -> *#(x,s(y)) -> *#(x,y)
    *#(x,s(y)) -> +#(*(x,y),x) -> +#(x,s(y)) -> +#(x,y)
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
   SCC Processor:
    #sccs: 5
    #rules: 6
    #arcs: 15/100
    DPs:
     iffact#(x,true()) -> fact#(-(x,s(0())))
     fact#(x) -> iffact#(x,ge(x,s(s(0()))))
    TRS:
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(*(x,y),x)
     ge(x,0()) -> true()
     ge(0(),s(y)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     fact(x) -> iffact(x,ge(x,s(s(0()))))
     iffact(x,true()) -> *(x,fact(-(x,s(0()))))
     iffact(x,false()) -> s(0())
    Open
    
    DPs:
     *#(x,s(y)) -> *#(x,y)
    TRS:
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(*(x,y),x)
     ge(x,0()) -> true()
     ge(0(),s(y)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     fact(x) -> iffact(x,ge(x,s(s(0()))))
     iffact(x,true()) -> *(x,fact(-(x,s(0()))))
     iffact(x,false()) -> s(0())
    Subterm Criterion Processor:
     simple projection:
      pi(*#) = 1
     problem:
      DPs:
       
      TRS:
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(*(x,y),x)
       ge(x,0()) -> true()
       ge(0(),s(y)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       fact(x) -> iffact(x,ge(x,s(s(0()))))
       iffact(x,true()) -> *(x,fact(-(x,s(0()))))
       iffact(x,false()) -> s(0())
     Qed
    
    DPs:
     +#(x,s(y)) -> +#(x,y)
    TRS:
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(*(x,y),x)
     ge(x,0()) -> true()
     ge(0(),s(y)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     fact(x) -> iffact(x,ge(x,s(s(0()))))
     iffact(x,true()) -> *(x,fact(-(x,s(0()))))
     iffact(x,false()) -> s(0())
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     problem:
      DPs:
       
      TRS:
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(*(x,y),x)
       ge(x,0()) -> true()
       ge(0(),s(y)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       fact(x) -> iffact(x,ge(x,s(s(0()))))
       iffact(x,true()) -> *(x,fact(-(x,s(0()))))
       iffact(x,false()) -> s(0())
     Qed
    
    DPs:
     -#(s(x),s(y)) -> -#(x,y)
    TRS:
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(*(x,y),x)
     ge(x,0()) -> true()
     ge(0(),s(y)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     fact(x) -> iffact(x,ge(x,s(s(0()))))
     iffact(x,true()) -> *(x,fact(-(x,s(0()))))
     iffact(x,false()) -> s(0())
    Subterm Criterion Processor:
     simple projection:
      pi(-#) = 1
     problem:
      DPs:
       
      TRS:
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(*(x,y),x)
       ge(x,0()) -> true()
       ge(0(),s(y)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       fact(x) -> iffact(x,ge(x,s(s(0()))))
       iffact(x,true()) -> *(x,fact(-(x,s(0()))))
       iffact(x,false()) -> s(0())
     Qed
    
    DPs:
     ge#(s(x),s(y)) -> ge#(x,y)
    TRS:
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(*(x,y),x)
     ge(x,0()) -> true()
     ge(0(),s(y)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     fact(x) -> iffact(x,ge(x,s(s(0()))))
     iffact(x,true()) -> *(x,fact(-(x,s(0()))))
     iffact(x,false()) -> s(0())
    Subterm Criterion Processor:
     simple projection:
      pi(ge#) = 1
     problem:
      DPs:
       
      TRS:
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(*(x,y),x)
       ge(x,0()) -> true()
       ge(0(),s(y)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       fact(x) -> iffact(x,ge(x,s(s(0()))))
       iffact(x,true()) -> *(x,fact(-(x,s(0()))))
       iffact(x,false()) -> s(0())
     Qed