MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(0(),x) -> 0()
            *(I(x),y) -> +(O(*(x,y)),y)
            *(O(x),y) -> O(*(x,y))
            +(x,0()) -> x
            +(0(),x) -> x
            +(I(x),I(y)) -> O(+(+(x,y),I(0())))
            +(I(x),O(y)) -> I(+(x,y))
            +(O(x),I(y)) -> I(+(x,y))
            +(O(x),O(y)) -> O(+(x,y))
            O(0()) -> 0()
        - Signature:
            {*/2,+/2,O/1} / {0/0,I/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+,O} and constructors {0,I}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(x,0()) -> c_1()
          *#(0(),x) -> c_2()
          *#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y))
          *#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y))
          +#(x,0()) -> c_5()
          +#(0(),x) -> c_6()
          +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y))
          +#(I(x),O(y)) -> c_8(+#(x,y))
          +#(O(x),I(y)) -> c_9(+#(x,y))
          +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y))
          O#(0()) -> c_11()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,0()) -> c_1()
            *#(0(),x) -> c_2()
            *#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y))
            *#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y))
            +#(x,0()) -> c_5()
            +#(0(),x) -> c_6()
            +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y))
            +#(I(x),O(y)) -> c_8(+#(x,y))
            +#(O(x),I(y)) -> c_9(+#(x,y))
            +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y))
            O#(0()) -> c_11()
        - Weak TRS:
            *(x,0()) -> 0()
            *(0(),x) -> 0()
            *(I(x),y) -> +(O(*(x,y)),y)
            *(O(x),y) -> O(*(x,y))
            +(x,0()) -> x
            +(0(),x) -> x
            +(I(x),I(y)) -> O(+(+(x,y),I(0())))
            +(I(x),O(y)) -> I(+(x,y))
            +(O(x),I(y)) -> I(+(x,y))
            +(O(x),O(y)) -> O(+(x,y))
            O(0()) -> 0()
        - Signature:
            {*/2,+/2,O/1,*#/2,+#/2,O#/1} / {0/0,I/1,c_1/0,c_2/0,c_3/3,c_4/2,c_5/0,c_6/0,c_7/3,c_8/1,c_9/1,c_10/2,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,O#} and constructors {0,I}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,5,6,11}
        by application of
          Pre({1,2,5,6,11}) = {3,4,7,8,9,10}.
        Here rules are labelled as follows:
          1: *#(x,0()) -> c_1()
          2: *#(0(),x) -> c_2()
          3: *#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y))
          4: *#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y))
          5: +#(x,0()) -> c_5()
          6: +#(0(),x) -> c_6()
          7: +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y))
          8: +#(I(x),O(y)) -> c_8(+#(x,y))
          9: +#(O(x),I(y)) -> c_9(+#(x,y))
          10: +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y))
          11: O#(0()) -> c_11()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y))
            *#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y))
            +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y))
            +#(I(x),O(y)) -> c_8(+#(x,y))
            +#(O(x),I(y)) -> c_9(+#(x,y))
            +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y))
        - Weak DPs:
            *#(x,0()) -> c_1()
            *#(0(),x) -> c_2()
            +#(x,0()) -> c_5()
            +#(0(),x) -> c_6()
            O#(0()) -> c_11()
        - Weak TRS:
            *(x,0()) -> 0()
            *(0(),x) -> 0()
            *(I(x),y) -> +(O(*(x,y)),y)
            *(O(x),y) -> O(*(x,y))
            +(x,0()) -> x
            +(0(),x) -> x
            +(I(x),I(y)) -> O(+(+(x,y),I(0())))
            +(I(x),O(y)) -> I(+(x,y))
            +(O(x),I(y)) -> I(+(x,y))
            +(O(x),O(y)) -> O(+(x,y))
            O(0()) -> 0()
        - Signature:
            {*/2,+/2,O/1,*#/2,+#/2,O#/1} / {0/0,I/1,c_1/0,c_2/0,c_3/3,c_4/2,c_5/0,c_6/0,c_7/3,c_8/1,c_9/1,c_10/2,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,O#} and constructors {0,I}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y))
             -->_1 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_1 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_1 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_1 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
             -->_3 *#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y)):2
             -->_2 O#(0()) -> c_11():11
             -->_1 +#(0(),x) -> c_6():10
             -->_1 +#(x,0()) -> c_5():9
             -->_3 *#(0(),x) -> c_2():8
             -->_3 *#(x,0()) -> c_1():7
             -->_3 *#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y)):1
          
          2:S:*#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y))
             -->_1 O#(0()) -> c_11():11
             -->_2 *#(0(),x) -> c_2():8
             -->_2 *#(x,0()) -> c_1():7
             -->_2 *#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y)):2
             -->_2 *#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y)):1
          
          3:S:+#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y))
             -->_3 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_3 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_2 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_3 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_1 O#(0()) -> c_11():11
             -->_3 +#(0(),x) -> c_6():10
             -->_2 +#(0(),x) -> c_6():10
             -->_3 +#(x,0()) -> c_5():9
             -->_3 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
             -->_2 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
          
          4:S:+#(I(x),O(y)) -> c_8(+#(x,y))
             -->_1 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_1 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_1 +#(0(),x) -> c_6():10
             -->_1 +#(x,0()) -> c_5():9
             -->_1 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_1 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
          
          5:S:+#(O(x),I(y)) -> c_9(+#(x,y))
             -->_1 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_1 +#(0(),x) -> c_6():10
             -->_1 +#(x,0()) -> c_5():9
             -->_1 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_1 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_1 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
          
          6:S:+#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y))
             -->_1 O#(0()) -> c_11():11
             -->_2 +#(0(),x) -> c_6():10
             -->_2 +#(x,0()) -> c_5():9
             -->_2 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_2 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_2 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_2 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
          
          7:W:*#(x,0()) -> c_1()
             
          
          8:W:*#(0(),x) -> c_2()
             
          
          9:W:+#(x,0()) -> c_5()
             
          
          10:W:+#(0(),x) -> c_6()
             
          
          11:W:O#(0()) -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          7: *#(x,0()) -> c_1()
          8: *#(0(),x) -> c_2()
          9: +#(x,0()) -> c_5()
          10: +#(0(),x) -> c_6()
          11: O#(0()) -> c_11()
* Step 4: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y))
            *#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y))
            +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y))
            +#(I(x),O(y)) -> c_8(+#(x,y))
            +#(O(x),I(y)) -> c_9(+#(x,y))
            +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y))
        - Weak TRS:
            *(x,0()) -> 0()
            *(0(),x) -> 0()
            *(I(x),y) -> +(O(*(x,y)),y)
            *(O(x),y) -> O(*(x,y))
            +(x,0()) -> x
            +(0(),x) -> x
            +(I(x),I(y)) -> O(+(+(x,y),I(0())))
            +(I(x),O(y)) -> I(+(x,y))
            +(O(x),I(y)) -> I(+(x,y))
            +(O(x),O(y)) -> O(+(x,y))
            O(0()) -> 0()
        - Signature:
            {*/2,+/2,O/1,*#/2,+#/2,O#/1} / {0/0,I/1,c_1/0,c_2/0,c_3/3,c_4/2,c_5/0,c_6/0,c_7/3,c_8/1,c_9/1,c_10/2,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,O#} and constructors {0,I}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:*#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y))
             -->_1 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_1 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_1 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_1 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
             -->_3 *#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y)):2
             -->_3 *#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y)):1
          
          2:S:*#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y))
             -->_2 *#(O(x),y) -> c_4(O#(*(x,y)),*#(x,y)):2
             -->_2 *#(I(x),y) -> c_3(+#(O(*(x,y)),y),O#(*(x,y)),*#(x,y)):1
          
          3:S:+#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y))
             -->_3 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_3 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_2 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_3 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_3 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
             -->_2 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
          
          4:S:+#(I(x),O(y)) -> c_8(+#(x,y))
             -->_1 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_1 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_1 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_1 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
          
          5:S:+#(O(x),I(y)) -> c_9(+#(x,y))
             -->_1 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_1 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_1 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_1 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
          
          6:S:+#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y))
             -->_2 +#(O(x),O(y)) -> c_10(O#(+(x,y)),+#(x,y)):6
             -->_2 +#(O(x),I(y)) -> c_9(+#(x,y)):5
             -->_2 +#(I(x),O(y)) -> c_8(+#(x,y)):4
             -->_2 +#(I(x),I(y)) -> c_7(O#(+(+(x,y),I(0()))),+#(+(x,y),I(0())),+#(x,y)):3
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          *#(I(x),y) -> c_3(+#(O(*(x,y)),y),*#(x,y))
          *#(O(x),y) -> c_4(*#(x,y))
          +#(I(x),I(y)) -> c_7(+#(+(x,y),I(0())),+#(x,y))
          +#(O(x),O(y)) -> c_10(+#(x,y))
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          *#(I(x),y) -> c_3(+#(O(*(x,y)),y),*#(x,y))
          *#(O(x),y) -> c_4(*#(x,y))
          +#(I(x),I(y)) -> c_7(+#(+(x,y),I(0())),+#(x,y))
          +#(I(x),O(y)) -> c_8(+#(x,y))
          +#(O(x),I(y)) -> c_9(+#(x,y))
          +#(O(x),O(y)) -> c_10(+#(x,y))
      - Weak TRS:
          *(x,0()) -> 0()
          *(0(),x) -> 0()
          *(I(x),y) -> +(O(*(x,y)),y)
          *(O(x),y) -> O(*(x,y))
          +(x,0()) -> x
          +(0(),x) -> x
          +(I(x),I(y)) -> O(+(+(x,y),I(0())))
          +(I(x),O(y)) -> I(+(x,y))
          +(O(x),I(y)) -> I(+(x,y))
          +(O(x),O(y)) -> O(+(x,y))
          O(0()) -> 0()
      - Signature:
          {*/2,+/2,O/1,*#/2,+#/2,O#/1} / {0/0,I/1,c_1/0,c_2/0,c_3/2,c_4/1,c_5/0,c_6/0,c_7/2,c_8/1,c_9/1,c_10/1,c_11/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {*#,+#,O#} and constructors {0,I}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE