MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
            cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
            cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,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:
            {and/2,cond1/3,cond2/3,eq/2,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,cond1,cond2,eq,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()
          cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0()))
          cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y),and#(eq(x,y),gr(x,0())),eq#(x,y),gr#(x,0()))
          cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y))
          eq#(0(),0()) -> c_7()
          eq#(0(),s(x)) -> c_8()
          eq#(s(x),0()) -> c_9()
          eq#(s(x),s(y)) -> c_10(eq#(x,y))
          gr#(0(),x) -> c_11()
          gr#(s(x),0()) -> c_12()
          gr#(s(x),s(y)) -> c_13(gr#(x,y))
          p#(0()) -> c_14()
          p#(s(x)) -> c_15()
        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()
            cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0()))
            cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y),and#(eq(x,y),gr(x,0())),eq#(x,y),gr#(x,0()))
            cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y))
            eq#(0(),0()) -> c_7()
            eq#(0(),s(x)) -> c_8()
            eq#(s(x),0()) -> c_9()
            eq#(s(x),s(y)) -> c_10(eq#(x,y))
            gr#(0(),x) -> c_11()
            gr#(s(x),0()) -> c_12()
            gr#(s(x),s(y)) -> c_13(gr#(x,y))
            p#(0()) -> c_14()
            p#(s(x)) -> c_15()
        - Weak TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
            cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
            cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,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:
            {and/2,cond1/3,cond2/3,eq/2,gr/2,p/1,and#/2,cond1#/3,cond2#/3,eq#/2,gr#/2,p#/1} / {0/0,false/0,s/1,true/0
            ,c_1/0,c_2/0,c_3/0,c_4/2,c_5/4,c_6/4,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,cond1#,cond2#,eq#,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()
          eq(0(),0()) -> true()
          eq(0(),s(x)) -> false()
          eq(s(x),0()) -> false()
          eq(s(x),s(y)) -> eq(x,y)
          gr(0(),x) -> 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()
          cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0()))
          cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y),and#(eq(x,y),gr(x,0())),eq#(x,y),gr#(x,0()))
          cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y))
          eq#(0(),0()) -> c_7()
          eq#(0(),s(x)) -> c_8()
          eq#(s(x),0()) -> c_9()
          eq#(s(x),s(y)) -> c_10(eq#(x,y))
          gr#(0(),x) -> c_11()
          gr#(s(x),0()) -> c_12()
          gr#(s(x),s(y)) -> c_13(gr#(x,y))
          p#(0()) -> c_14()
          p#(s(x)) -> c_15()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            and#(x,false()) -> c_1()
            and#(false(),x) -> c_2()
            and#(true(),true()) -> c_3()
            cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0()))
            cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y),and#(eq(x,y),gr(x,0())),eq#(x,y),gr#(x,0()))
            cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y))
            eq#(0(),0()) -> c_7()
            eq#(0(),s(x)) -> c_8()
            eq#(s(x),0()) -> c_9()
            eq#(s(x),s(y)) -> c_10(eq#(x,y))
            gr#(0(),x) -> c_11()
            gr#(s(x),0()) -> c_12()
            gr#(s(x),s(y)) -> c_13(gr#(x,y))
            p#(0()) -> c_14()
            p#(s(x)) -> c_15()
        - Weak TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond1/3,cond2/3,eq/2,gr/2,p/1,and#/2,cond1#/3,cond2#/3,eq#/2,gr#/2,p#/1} / {0/0,false/0,s/1,true/0
            ,c_1/0,c_2/0,c_3/0,c_4/2,c_5/4,c_6/4,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,cond1#,cond2#,eq#,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
          {1,2,3,7,8,9,11,12,14,15}
        by application of
          Pre({1,2,3,7,8,9,11,12,14,15}) = {4,5,6,10,13}.
        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: cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0()))
          5: cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y)
                                       ,and#(eq(x,y),gr(x,0()))
                                       ,eq#(x,y)
                                       ,gr#(x,0()))
          6: cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y))
          7: eq#(0(),0()) -> c_7()
          8: eq#(0(),s(x)) -> c_8()
          9: eq#(s(x),0()) -> c_9()
          10: eq#(s(x),s(y)) -> c_10(eq#(x,y))
          11: gr#(0(),x) -> c_11()
          12: gr#(s(x),0()) -> c_12()
          13: gr#(s(x),s(y)) -> c_13(gr#(x,y))
          14: p#(0()) -> c_14()
          15: p#(s(x)) -> c_15()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0()))
            cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y),and#(eq(x,y),gr(x,0())),eq#(x,y),gr#(x,0()))
            cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y))
            eq#(s(x),s(y)) -> c_10(eq#(x,y))
            gr#(s(x),s(y)) -> c_13(gr#(x,y))
        - Weak DPs:
            and#(x,false()) -> c_1()
            and#(false(),x) -> c_2()
            and#(true(),true()) -> c_3()
            eq#(0(),0()) -> c_7()
            eq#(0(),s(x)) -> c_8()
            eq#(s(x),0()) -> c_9()
            gr#(0(),x) -> c_11()
            gr#(s(x),0()) -> c_12()
            p#(0()) -> c_14()
            p#(s(x)) -> c_15()
        - Weak TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond1/3,cond2/3,eq/2,gr/2,p/1,and#/2,cond1#/3,cond2#/3,eq#/2,gr#/2,p#/1} / {0/0,false/0,s/1,true/0
            ,c_1/0,c_2/0,c_3/0,c_4/2,c_5/4,c_6/4,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,cond1#,cond2#,eq#,gr#,p#} and constructors {0,false
            ,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0()))
             -->_1 cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y)):3
             -->_1 cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y)
                                             ,and#(eq(x,y),gr(x,0()))
                                             ,eq#(x,y)
                                             ,gr#(x,0())):2
             -->_2 gr#(s(x),0()) -> c_12():13
             -->_2 gr#(0(),x) -> c_11():12
          
          2:S:cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y)
                                        ,and#(eq(x,y),gr(x,0()))
                                        ,eq#(x,y)
                                        ,gr#(x,0()))
             -->_3 eq#(s(x),s(y)) -> c_10(eq#(x,y)):4
             -->_4 gr#(s(x),0()) -> c_12():13
             -->_4 gr#(0(),x) -> c_11():12
             -->_3 eq#(s(x),0()) -> c_9():11
             -->_3 eq#(0(),s(x)) -> c_8():10
             -->_3 eq#(0(),0()) -> c_7():9
             -->_2 and#(true(),true()) -> c_3():8
             -->_2 and#(false(),x) -> c_2():7
             -->_2 and#(x,false()) -> c_1():6
             -->_1 cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0())):1
          
          3:S:cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y))
             -->_4 p#(s(x)) -> c_15():15
             -->_3 p#(s(x)) -> c_15():15
             -->_4 p#(0()) -> c_14():14
             -->_3 p#(0()) -> c_14():14
             -->_2 gr#(s(x),0()) -> c_12():13
             -->_2 gr#(0(),x) -> c_11():12
             -->_1 cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y)):3
             -->_1 cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y)
                                             ,and#(eq(x,y),gr(x,0()))
                                             ,eq#(x,y)
                                             ,gr#(x,0())):2
          
          4:S:eq#(s(x),s(y)) -> c_10(eq#(x,y))
             -->_1 eq#(s(x),0()) -> c_9():11
             -->_1 eq#(0(),s(x)) -> c_8():10
             -->_1 eq#(0(),0()) -> c_7():9
             -->_1 eq#(s(x),s(y)) -> c_10(eq#(x,y)):4
          
          5:S:gr#(s(x),s(y)) -> c_13(gr#(x,y))
             -->_1 gr#(s(x),0()) -> c_12():13
             -->_1 gr#(0(),x) -> c_11():12
             -->_1 gr#(s(x),s(y)) -> c_13(gr#(x,y)):5
          
          6:W:and#(x,false()) -> c_1()
             
          
          7:W:and#(false(),x) -> c_2()
             
          
          8:W:and#(true(),true()) -> c_3()
             
          
          9:W:eq#(0(),0()) -> c_7()
             
          
          10:W:eq#(0(),s(x)) -> c_8()
             
          
          11:W:eq#(s(x),0()) -> c_9()
             
          
          12:W:gr#(0(),x) -> c_11()
             
          
          13:W:gr#(s(x),0()) -> c_12()
             
          
          14:W:p#(0()) -> c_14()
             
          
          15:W:p#(s(x)) -> c_15()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: and#(x,false()) -> c_1()
          7: and#(false(),x) -> c_2()
          8: and#(true(),true()) -> c_3()
          9: eq#(0(),0()) -> c_7()
          10: eq#(0(),s(x)) -> c_8()
          11: eq#(s(x),0()) -> c_9()
          12: gr#(0(),x) -> c_11()
          13: gr#(s(x),0()) -> c_12()
          14: p#(0()) -> c_14()
          15: p#(s(x)) -> c_15()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0()))
            cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y),and#(eq(x,y),gr(x,0())),eq#(x,y),gr#(x,0()))
            cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y))
            eq#(s(x),s(y)) -> c_10(eq#(x,y))
            gr#(s(x),s(y)) -> c_13(gr#(x,y))
        - Weak TRS:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond1/3,cond2/3,eq/2,gr/2,p/1,and#/2,cond1#/3,cond2#/3,eq#/2,gr#/2,p#/1} / {0/0,false/0,s/1,true/0
            ,c_1/0,c_2/0,c_3/0,c_4/2,c_5/4,c_6/4,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,cond1#,cond2#,eq#,gr#,p#} and constructors {0,false
            ,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0()))
             -->_1 cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y)):3
             -->_1 cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y)
                                             ,and#(eq(x,y),gr(x,0()))
                                             ,eq#(x,y)
                                             ,gr#(x,0())):2
          
          2:S:cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y)
                                        ,and#(eq(x,y),gr(x,0()))
                                        ,eq#(x,y)
                                        ,gr#(x,0()))
             -->_3 eq#(s(x),s(y)) -> c_10(eq#(x,y)):4
             -->_1 cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y),gr#(y,0())):1
          
          3:S:cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y))
             -->_1 cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)),gr#(y,0()),p#(x),p#(y)):3
             -->_1 cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y)
                                             ,and#(eq(x,y),gr(x,0()))
                                             ,eq#(x,y)
                                             ,gr#(x,0())):2
          
          4:S:eq#(s(x),s(y)) -> c_10(eq#(x,y))
             -->_1 eq#(s(x),s(y)) -> c_10(eq#(x,y)):4
          
          5:S:gr#(s(x),s(y)) -> c_13(gr#(x,y))
             -->_1 gr#(s(x),s(y)) -> c_13(gr#(x,y)):5
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y))
          cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y),eq#(x,y))
          cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          cond1#(true(),x,y) -> c_4(cond2#(gr(y,0()),x,y))
          cond2#(false(),x,y) -> c_5(cond1#(and(eq(x,y),gr(x,0())),x,y),eq#(x,y))
          cond2#(true(),x,y) -> c_6(cond2#(gr(y,0()),p(x),p(y)))
          eq#(s(x),s(y)) -> c_10(eq#(x,y))
          gr#(s(x),s(y)) -> c_13(gr#(x,y))
      - Weak TRS:
          and(x,false()) -> false()
          and(false(),x) -> false()
          and(true(),true()) -> true()
          eq(0(),0()) -> true()
          eq(0(),s(x)) -> false()
          eq(s(x),0()) -> false()
          eq(s(x),s(y)) -> eq(x,y)
          gr(0(),x) -> false()
          gr(s(x),0()) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
      - Signature:
          {and/2,cond1/3,cond2/3,eq/2,gr/2,p/1,and#/2,cond1#/3,cond2#/3,eq#/2,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_5/2,c_6/1,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {and#,cond1#,cond2#,eq#,gr#,p#} and constructors {0,false
          ,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE