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