MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            add(0(),x) -> x
            add(s(x),y) -> s(add(x,y))
            cond1(true(),x,y) -> cond2(gr(x,0()),x,y)
            cond2(false(),x,y) -> cond3(gr(y,0()),x,y)
            cond2(true(),x,y) -> cond1(gr(add(x,y),0()),p(x),y)
            cond3(false(),x,y) -> cond1(gr(add(x,y),0()),x,y)
            cond3(true(),x,y) -> cond1(gr(add(x,y),0()),x,p(y))
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {add/2,cond1/3,cond2/3,cond3/3,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add,cond1,cond2,cond3,gr,p} and constructors {0,false,s
            ,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          add#(0(),x) -> c_1()
          add#(s(x),y) -> c_2(add#(x,y))
          cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0()))
          cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0()))
          cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x))
          cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y))
          cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y))
          gr#(0(),x) -> c_8()
          gr#(s(x),0()) -> c_9()
          gr#(s(x),s(y)) -> c_10(gr#(x,y))
          p#(0()) -> c_11()
          p#(s(x)) -> c_12()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            add#(0(),x) -> c_1()
            add#(s(x),y) -> c_2(add#(x,y))
            cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0()))
            cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0()))
            cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x))
            cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y))
            cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y))
            gr#(0(),x) -> c_8()
            gr#(s(x),0()) -> c_9()
            gr#(s(x),s(y)) -> c_10(gr#(x,y))
            p#(0()) -> c_11()
            p#(s(x)) -> c_12()
        - Weak TRS:
            add(0(),x) -> x
            add(s(x),y) -> s(add(x,y))
            cond1(true(),x,y) -> cond2(gr(x,0()),x,y)
            cond2(false(),x,y) -> cond3(gr(y,0()),x,y)
            cond2(true(),x,y) -> cond1(gr(add(x,y),0()),p(x),y)
            cond3(false(),x,y) -> cond1(gr(add(x,y),0()),x,y)
            cond3(true(),x,y) -> cond1(gr(add(x,y),0()),x,p(y))
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {add/2,cond1/3,cond2/3,cond3/3,gr/2,p/1,add#/2,cond1#/3,cond2#/3,cond3#/3,gr#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,c_1/0,c_2/1,c_3/2,c_4/2,c_5/4,c_6/3,c_7/4,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,cond1#,cond2#,cond3#,gr#,p#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          add(0(),x) -> x
          add(s(x),y) -> s(add(x,y))
          gr(0(),x) -> false()
          gr(s(x),0()) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
          add#(0(),x) -> c_1()
          add#(s(x),y) -> c_2(add#(x,y))
          cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0()))
          cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0()))
          cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x))
          cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y))
          cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y))
          gr#(0(),x) -> c_8()
          gr#(s(x),0()) -> c_9()
          gr#(s(x),s(y)) -> c_10(gr#(x,y))
          p#(0()) -> c_11()
          p#(s(x)) -> c_12()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            add#(0(),x) -> c_1()
            add#(s(x),y) -> c_2(add#(x,y))
            cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0()))
            cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0()))
            cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x))
            cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y))
            cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y))
            gr#(0(),x) -> c_8()
            gr#(s(x),0()) -> c_9()
            gr#(s(x),s(y)) -> c_10(gr#(x,y))
            p#(0()) -> c_11()
            p#(s(x)) -> c_12()
        - Weak TRS:
            add(0(),x) -> x
            add(s(x),y) -> s(add(x,y))
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {add/2,cond1/3,cond2/3,cond3/3,gr/2,p/1,add#/2,cond1#/3,cond2#/3,cond3#/3,gr#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,c_1/0,c_2/1,c_3/2,c_4/2,c_5/4,c_6/3,c_7/4,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,cond1#,cond2#,cond3#,gr#,p#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,8,9,11,12}
        by application of
          Pre({1,8,9,11,12}) = {2,3,4,5,6,7,10}.
        Here rules are labelled as follows:
          1: add#(0(),x) -> c_1()
          2: add#(s(x),y) -> c_2(add#(x,y))
          3: cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0()))
          4: cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0()))
          5: cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x))
          6: cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y))
          7: cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y))
          8: gr#(0(),x) -> c_8()
          9: gr#(s(x),0()) -> c_9()
          10: gr#(s(x),s(y)) -> c_10(gr#(x,y))
          11: p#(0()) -> c_11()
          12: p#(s(x)) -> c_12()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            add#(s(x),y) -> c_2(add#(x,y))
            cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0()))
            cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0()))
            cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x))
            cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y))
            cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y))
            gr#(s(x),s(y)) -> c_10(gr#(x,y))
        - Weak DPs:
            add#(0(),x) -> c_1()
            gr#(0(),x) -> c_8()
            gr#(s(x),0()) -> c_9()
            p#(0()) -> c_11()
            p#(s(x)) -> c_12()
        - Weak TRS:
            add(0(),x) -> x
            add(s(x),y) -> s(add(x,y))
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {add/2,cond1/3,cond2/3,cond3/3,gr/2,p/1,add#/2,cond1#/3,cond2#/3,cond3#/3,gr#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,c_1/0,c_2/1,c_3/2,c_4/2,c_5/4,c_6/3,c_7/4,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,cond1#,cond2#,cond3#,gr#,p#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:add#(s(x),y) -> c_2(add#(x,y))
             -->_1 add#(0(),x) -> c_1():8
             -->_1 add#(s(x),y) -> c_2(add#(x,y)):1
          
          2:S:cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0()))
             -->_1 cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x)):4
             -->_1 cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0())):3
             -->_2 gr#(s(x),0()) -> c_9():10
             -->_2 gr#(0(),x) -> c_8():9
          
          3:S:cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0()))
             -->_1 cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y)):6
             -->_1 cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y)):5
             -->_2 gr#(s(x),0()) -> c_9():10
             -->_2 gr#(0(),x) -> c_8():9
          
          4:S:cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x))
             -->_4 p#(s(x)) -> c_12():12
             -->_4 p#(0()) -> c_11():11
             -->_2 gr#(s(x),0()) -> c_9():10
             -->_2 gr#(0(),x) -> c_8():9
             -->_3 add#(0(),x) -> c_1():8
             -->_1 cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0())):2
             -->_3 add#(s(x),y) -> c_2(add#(x,y)):1
          
          5:S:cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y))
             -->_2 gr#(s(x),0()) -> c_9():10
             -->_2 gr#(0(),x) -> c_8():9
             -->_3 add#(0(),x) -> c_1():8
             -->_1 cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0())):2
             -->_3 add#(s(x),y) -> c_2(add#(x,y)):1
          
          6:S:cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y))
             -->_4 p#(s(x)) -> c_12():12
             -->_4 p#(0()) -> c_11():11
             -->_2 gr#(s(x),0()) -> c_9():10
             -->_2 gr#(0(),x) -> c_8():9
             -->_3 add#(0(),x) -> c_1():8
             -->_1 cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0())):2
             -->_3 add#(s(x),y) -> c_2(add#(x,y)):1
          
          7:S:gr#(s(x),s(y)) -> c_10(gr#(x,y))
             -->_1 gr#(s(x),0()) -> c_9():10
             -->_1 gr#(0(),x) -> c_8():9
             -->_1 gr#(s(x),s(y)) -> c_10(gr#(x,y)):7
          
          8:W:add#(0(),x) -> c_1()
             
          
          9:W:gr#(0(),x) -> c_8()
             
          
          10:W:gr#(s(x),0()) -> c_9()
             
          
          11:W:p#(0()) -> c_11()
             
          
          12:W:p#(s(x)) -> c_12()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: gr#(0(),x) -> c_8()
          10: gr#(s(x),0()) -> c_9()
          11: p#(0()) -> c_11()
          12: p#(s(x)) -> c_12()
          8: add#(0(),x) -> c_1()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            add#(s(x),y) -> c_2(add#(x,y))
            cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0()))
            cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0()))
            cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x))
            cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y))
            cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y))
            gr#(s(x),s(y)) -> c_10(gr#(x,y))
        - Weak TRS:
            add(0(),x) -> x
            add(s(x),y) -> s(add(x,y))
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {add/2,cond1/3,cond2/3,cond3/3,gr/2,p/1,add#/2,cond1#/3,cond2#/3,cond3#/3,gr#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,c_1/0,c_2/1,c_3/2,c_4/2,c_5/4,c_6/3,c_7/4,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,cond1#,cond2#,cond3#,gr#,p#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:add#(s(x),y) -> c_2(add#(x,y))
             -->_1 add#(s(x),y) -> c_2(add#(x,y)):1
          
          2:S:cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0()))
             -->_1 cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x)):4
             -->_1 cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0())):3
          
          3:S:cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y),gr#(y,0()))
             -->_1 cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y)):6
             -->_1 cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y)):5
          
          4:S:cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),gr#(add(x,y),0()),add#(x,y),p#(x))
             -->_1 cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0())):2
             -->_3 add#(s(x),y) -> c_2(add#(x,y)):1
          
          5:S:cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),gr#(add(x,y),0()),add#(x,y))
             -->_1 cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0())):2
             -->_3 add#(s(x),y) -> c_2(add#(x,y)):1
          
          6:S:cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),gr#(add(x,y),0()),add#(x,y),p#(y))
             -->_1 cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y),gr#(x,0())):2
             -->_3 add#(s(x),y) -> c_2(add#(x,y)):1
          
          7:S:gr#(s(x),s(y)) -> c_10(gr#(x,y))
             -->_1 gr#(s(x),s(y)) -> c_10(gr#(x,y)):7
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y))
          cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y))
          cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),add#(x,y))
          cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),add#(x,y))
          cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),add#(x,y))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          add#(s(x),y) -> c_2(add#(x,y))
          cond1#(true(),x,y) -> c_3(cond2#(gr(x,0()),x,y))
          cond2#(false(),x,y) -> c_4(cond3#(gr(y,0()),x,y))
          cond2#(true(),x,y) -> c_5(cond1#(gr(add(x,y),0()),p(x),y),add#(x,y))
          cond3#(false(),x,y) -> c_6(cond1#(gr(add(x,y),0()),x,y),add#(x,y))
          cond3#(true(),x,y) -> c_7(cond1#(gr(add(x,y),0()),x,p(y)),add#(x,y))
          gr#(s(x),s(y)) -> c_10(gr#(x,y))
      - Weak TRS:
          add(0(),x) -> x
          add(s(x),y) -> s(add(x,y))
          gr(0(),x) -> false()
          gr(s(x),0()) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
      - Signature:
          {add/2,cond1/3,cond2/3,cond3/3,gr/2,p/1,add#/2,cond1#/3,cond2#/3,cond3#/3,gr#/2,p#/1} / {0/0,false/0,s/1
          ,true/0,c_1/0,c_2/1,c_3/1,c_4/1,c_5/2,c_6/2,c_7/2,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {add#,cond1#,cond2#,cond3#,gr#,p#} and constructors {0
          ,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE