MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
            gr(0(),x) -> false()
            gr(0(),0()) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond/3,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,cond,gr,p} and constructors {0,false,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          and#(x,false()) -> c_1()
          and#(false(),x) -> c_2()
          and#(true(),true()) -> c_3()
          cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                  ,and#(gr(x,0()),gr(y,0()))
                                  ,gr#(x,0())
                                  ,gr#(y,0())
                                  ,p#(x)
                                  ,p#(y))
          gr#(0(),x) -> c_5()
          gr#(0(),0()) -> c_6()
          gr#(s(x),0()) -> c_7()
          gr#(s(x),s(y)) -> c_8(gr#(x,y))
          p#(0()) -> c_9()
          p#(s(x)) -> c_10()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            and#(x,false()) -> c_1()
            and#(false(),x) -> c_2()
            and#(true(),true()) -> c_3()
            cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                    ,and#(gr(x,0()),gr(y,0()))
                                    ,gr#(x,0())
                                    ,gr#(y,0())
                                    ,p#(x)
                                    ,p#(y))
            gr#(0(),x) -> c_5()
            gr#(0(),0()) -> c_6()
            gr#(s(x),0()) -> c_7()
            gr#(s(x),s(y)) -> c_8(gr#(x,y))
            p#(0()) -> c_9()
            p#(s(x)) -> c_10()
        - Weak TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
            gr(0(),x) -> false()
            gr(0(),0()) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond/3,gr/2,p/1,and#/2,cond#/3,gr#/2,p#/1} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/0,c_4/6,c_5/0
            ,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,cond#,gr#,p#} and constructors {0,false,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          and(x,false()) -> false()
          and(false(),x) -> false()
          and(true(),true()) -> true()
          gr(0(),x) -> false()
          gr(0(),0()) -> false()
          gr(s(x),0()) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
          and#(x,false()) -> c_1()
          and#(false(),x) -> c_2()
          and#(true(),true()) -> c_3()
          cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                  ,and#(gr(x,0()),gr(y,0()))
                                  ,gr#(x,0())
                                  ,gr#(y,0())
                                  ,p#(x)
                                  ,p#(y))
          gr#(0(),x) -> c_5()
          gr#(0(),0()) -> c_6()
          gr#(s(x),0()) -> c_7()
          gr#(s(x),s(y)) -> c_8(gr#(x,y))
          p#(0()) -> c_9()
          p#(s(x)) -> c_10()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            and#(x,false()) -> c_1()
            and#(false(),x) -> c_2()
            and#(true(),true()) -> c_3()
            cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                    ,and#(gr(x,0()),gr(y,0()))
                                    ,gr#(x,0())
                                    ,gr#(y,0())
                                    ,p#(x)
                                    ,p#(y))
            gr#(0(),x) -> c_5()
            gr#(0(),0()) -> c_6()
            gr#(s(x),0()) -> c_7()
            gr#(s(x),s(y)) -> c_8(gr#(x,y))
            p#(0()) -> c_9()
            p#(s(x)) -> c_10()
        - Weak TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            gr(0(),x) -> false()
            gr(0(),0()) -> false()
            gr(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond/3,gr/2,p/1,and#/2,cond#/3,gr#/2,p#/1} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/0,c_4/6,c_5/0
            ,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,cond#,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
          {1,2,3,5,6,7,9,10}
        by application of
          Pre({1,2,3,5,6,7,9,10}) = {4,8}.
        Here rules are labelled as follows:
          1: and#(x,false()) -> c_1()
          2: and#(false(),x) -> c_2()
          3: and#(true(),true()) -> c_3()
          4: cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                     ,and#(gr(x,0()),gr(y,0()))
                                     ,gr#(x,0())
                                     ,gr#(y,0())
                                     ,p#(x)
                                     ,p#(y))
          5: gr#(0(),x) -> c_5()
          6: gr#(0(),0()) -> c_6()
          7: gr#(s(x),0()) -> c_7()
          8: gr#(s(x),s(y)) -> c_8(gr#(x,y))
          9: p#(0()) -> c_9()
          10: p#(s(x)) -> c_10()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                    ,and#(gr(x,0()),gr(y,0()))
                                    ,gr#(x,0())
                                    ,gr#(y,0())
                                    ,p#(x)
                                    ,p#(y))
            gr#(s(x),s(y)) -> c_8(gr#(x,y))
        - Weak DPs:
            and#(x,false()) -> c_1()
            and#(false(),x) -> c_2()
            and#(true(),true()) -> c_3()
            gr#(0(),x) -> c_5()
            gr#(0(),0()) -> c_6()
            gr#(s(x),0()) -> c_7()
            p#(0()) -> c_9()
            p#(s(x)) -> c_10()
        - Weak TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            gr(0(),x) -> false()
            gr(0(),0()) -> false()
            gr(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond/3,gr/2,p/1,and#/2,cond#/3,gr#/2,p#/1} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/0,c_4/6,c_5/0
            ,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,cond#,gr#,p#} and constructors {0,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                      ,and#(gr(x,0()),gr(y,0()))
                                      ,gr#(x,0())
                                      ,gr#(y,0())
                                      ,p#(x)
                                      ,p#(y))
             -->_6 p#(s(x)) -> c_10():10
             -->_5 p#(s(x)) -> c_10():10
             -->_6 p#(0()) -> c_9():9
             -->_5 p#(0()) -> c_9():9
             -->_4 gr#(s(x),0()) -> c_7():8
             -->_3 gr#(s(x),0()) -> c_7():8
             -->_4 gr#(0(),0()) -> c_6():7
             -->_3 gr#(0(),0()) -> c_6():7
             -->_4 gr#(0(),x) -> c_5():6
             -->_3 gr#(0(),x) -> c_5():6
             -->_2 and#(true(),true()) -> c_3():5
             -->_2 and#(false(),x) -> c_2():4
             -->_2 and#(x,false()) -> c_1():3
             -->_1 cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                           ,and#(gr(x,0()),gr(y,0()))
                                           ,gr#(x,0())
                                           ,gr#(y,0())
                                           ,p#(x)
                                           ,p#(y)):1
          
          2:S:gr#(s(x),s(y)) -> c_8(gr#(x,y))
             -->_1 gr#(s(x),0()) -> c_7():8
             -->_1 gr#(0(),0()) -> c_6():7
             -->_1 gr#(0(),x) -> c_5():6
             -->_1 gr#(s(x),s(y)) -> c_8(gr#(x,y)):2
          
          3:W:and#(x,false()) -> c_1()
             
          
          4:W:and#(false(),x) -> c_2()
             
          
          5:W:and#(true(),true()) -> c_3()
             
          
          6:W:gr#(0(),x) -> c_5()
             
          
          7:W:gr#(0(),0()) -> c_6()
             
          
          8:W:gr#(s(x),0()) -> c_7()
             
          
          9:W:p#(0()) -> c_9()
             
          
          10:W:p#(s(x)) -> c_10()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: and#(x,false()) -> c_1()
          4: and#(false(),x) -> c_2()
          5: and#(true(),true()) -> c_3()
          6: gr#(0(),x) -> c_5()
          7: gr#(0(),0()) -> c_6()
          8: gr#(s(x),0()) -> c_7()
          9: p#(0()) -> c_9()
          10: p#(s(x)) -> c_10()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                    ,and#(gr(x,0()),gr(y,0()))
                                    ,gr#(x,0())
                                    ,gr#(y,0())
                                    ,p#(x)
                                    ,p#(y))
            gr#(s(x),s(y)) -> c_8(gr#(x,y))
        - Weak TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            gr(0(),x) -> false()
            gr(0(),0()) -> false()
            gr(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond/3,gr/2,p/1,and#/2,cond#/3,gr#/2,p#/1} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/0,c_4/6,c_5/0
            ,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,cond#,gr#,p#} and constructors {0,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                      ,and#(gr(x,0()),gr(y,0()))
                                      ,gr#(x,0())
                                      ,gr#(y,0())
                                      ,p#(x)
                                      ,p#(y))
             -->_1 cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
                                           ,and#(gr(x,0()),gr(y,0()))
                                           ,gr#(x,0())
                                           ,gr#(y,0())
                                           ,p#(x)
                                           ,p#(y)):1
          
          2:S:gr#(s(x),s(y)) -> c_8(gr#(x,y))
             -->_1 gr#(s(x),s(y)) -> c_8(gr#(x,y)):2
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          cond#(true(),x,y) -> c_4(cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)))
          gr#(s(x),s(y)) -> c_8(gr#(x,y))
      - Weak TRS:
          and(x,false()) -> false()
          and(false(),x) -> false()
          and(true(),true()) -> true()
          gr(0(),x) -> false()
          gr(0(),0()) -> false()
          gr(s(x),0()) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
      - Signature:
          {and/2,cond/3,gr/2,p/1,and#/2,cond#/3,gr#/2,p#/1} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/0,c_4/1,c_5/0
          ,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {and#,cond#,gr#,p#} and constructors {0,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE