MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(*(x,y),y)
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            fact(0()) -> s(0())
            fact(s(x)) -> *(s(x),fact(p(s(x))))
            p(s(x)) -> x
        - Signature:
            {*/2,+/2,fact/1,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+,fact,p} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(0(),y) -> c_1()
          *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y))
          +#(x,0()) -> c_3()
          +#(x,s(y)) -> c_4(+#(x,y))
          fact#(0()) -> c_5()
          fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))),p#(s(x)))
          p#(s(x)) -> c_7()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(0(),y) -> c_1()
            *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y))
            +#(x,0()) -> c_3()
            +#(x,s(y)) -> c_4(+#(x,y))
            fact#(0()) -> c_5()
            fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))),p#(s(x)))
            p#(s(x)) -> c_7()
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(*(x,y),y)
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            fact(0()) -> s(0())
            fact(s(x)) -> *(s(x),fact(p(s(x))))
            p(s(x)) -> x
        - Signature:
            {*/2,+/2,fact/1,p/1,*#/2,+#/2,fact#/1,p#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/3,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,fact#,p#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,5,7}
        by application of
          Pre({1,3,5,7}) = {2,4,6}.
        Here rules are labelled as follows:
          1: *#(0(),y) -> c_1()
          2: *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y))
          3: +#(x,0()) -> c_3()
          4: +#(x,s(y)) -> c_4(+#(x,y))
          5: fact#(0()) -> c_5()
          6: fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))),p#(s(x)))
          7: p#(s(x)) -> c_7()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y))
            +#(x,s(y)) -> c_4(+#(x,y))
            fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))),p#(s(x)))
        - Weak DPs:
            *#(0(),y) -> c_1()
            +#(x,0()) -> c_3()
            fact#(0()) -> c_5()
            p#(s(x)) -> c_7()
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(*(x,y),y)
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            fact(0()) -> s(0())
            fact(s(x)) -> *(s(x),fact(p(s(x))))
            p(s(x)) -> x
        - Signature:
            {*/2,+/2,fact/1,p/1,*#/2,+#/2,fact#/1,p#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/3,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,fact#,p#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y))
             -->_1 +#(x,s(y)) -> c_4(+#(x,y)):2
             -->_1 +#(x,0()) -> c_3():5
             -->_2 *#(0(),y) -> c_1():4
             -->_2 *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y)):1
          
          2:S:+#(x,s(y)) -> c_4(+#(x,y))
             -->_1 +#(x,0()) -> c_3():5
             -->_1 +#(x,s(y)) -> c_4(+#(x,y)):2
          
          3:S:fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))),p#(s(x)))
             -->_3 p#(s(x)) -> c_7():7
             -->_2 fact#(0()) -> c_5():6
             -->_2 fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))),p#(s(x))):3
             -->_1 *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y)):1
          
          4:W:*#(0(),y) -> c_1()
             
          
          5:W:+#(x,0()) -> c_3()
             
          
          6:W:fact#(0()) -> c_5()
             
          
          7:W:p#(s(x)) -> c_7()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: fact#(0()) -> c_5()
          7: p#(s(x)) -> c_7()
          4: *#(0(),y) -> c_1()
          5: +#(x,0()) -> c_3()
* Step 4: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y))
            +#(x,s(y)) -> c_4(+#(x,y))
            fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))),p#(s(x)))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(*(x,y),y)
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            fact(0()) -> s(0())
            fact(s(x)) -> *(s(x),fact(p(s(x))))
            p(s(x)) -> x
        - Signature:
            {*/2,+/2,fact/1,p/1,*#/2,+#/2,fact#/1,p#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/3,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,fact#,p#} and constructors {0,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:*#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y))
             -->_1 +#(x,s(y)) -> c_4(+#(x,y)):2
             -->_2 *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y)):1
          
          2:S:+#(x,s(y)) -> c_4(+#(x,y))
             -->_1 +#(x,s(y)) -> c_4(+#(x,y)):2
          
          3:S:fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))),p#(s(x)))
             -->_2 fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))),p#(s(x))):3
             -->_1 *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))))
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          *#(s(x),y) -> c_2(+#(*(x,y),y),*#(x,y))
          +#(x,s(y)) -> c_4(+#(x,y))
          fact#(s(x)) -> c_6(*#(s(x),fact(p(s(x)))),fact#(p(s(x))))
      - Weak TRS:
          *(0(),y) -> 0()
          *(s(x),y) -> +(*(x,y),y)
          +(x,0()) -> x
          +(x,s(y)) -> s(+(x,y))
          fact(0()) -> s(0())
          fact(s(x)) -> *(s(x),fact(p(s(x))))
          p(s(x)) -> x
      - Signature:
          {*/2,+/2,fact/1,p/1,*#/2,+#/2,fact#/1,p#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/2,c_7/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {*#,+#,fact#,p#} and constructors {0,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE