MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            cond1(true(),x,y,z) -> cond2(gr(x,0()),x,y,z)
            cond2(false(),x,y,z) -> cond3(gr(y,0()),x,y,z)
            cond2(true(),x,y,z) -> cond1(or(gr(x,z),gr(y,z)),p(x),y,z)
            cond3(false(),x,y,z) -> cond1(or(gr(x,z),gr(y,z)),x,y,z)
            cond3(true(),x,y,z) -> cond1(or(gr(x,z),gr(y,z)),x,p(y),z)
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            or(x,true()) -> true()
            or(false(),false()) -> false()
            or(true(),x) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/4,cond2/4,cond3/4,gr/2,or/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1,cond2,cond3,gr,or,p} and constructors {0,false,s
            ,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0()))
          cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0()))
          cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                     ,or#(gr(x,z),gr(y,z))
                                     ,gr#(x,z)
                                     ,gr#(y,z)
                                     ,p#(x))
          cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),or#(gr(x,z),gr(y,z)),gr#(x,z),gr#(y,z))
          cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                     ,or#(gr(x,z),gr(y,z))
                                     ,gr#(x,z)
                                     ,gr#(y,z)
                                     ,p#(y))
          gr#(0(),x) -> c_6()
          gr#(s(x),0()) -> c_7()
          gr#(s(x),s(y)) -> c_8(gr#(x,y))
          or#(x,true()) -> c_9()
          or#(false(),false()) -> c_10()
          or#(true(),x) -> c_11()
          p#(0()) -> c_12()
          p#(s(x)) -> c_13()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0()))
            cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0()))
            cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                       ,or#(gr(x,z),gr(y,z))
                                       ,gr#(x,z)
                                       ,gr#(y,z)
                                       ,p#(x))
            cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),or#(gr(x,z),gr(y,z)),gr#(x,z),gr#(y,z))
            cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                       ,or#(gr(x,z),gr(y,z))
                                       ,gr#(x,z)
                                       ,gr#(y,z)
                                       ,p#(y))
            gr#(0(),x) -> c_6()
            gr#(s(x),0()) -> c_7()
            gr#(s(x),s(y)) -> c_8(gr#(x,y))
            or#(x,true()) -> c_9()
            or#(false(),false()) -> c_10()
            or#(true(),x) -> c_11()
            p#(0()) -> c_12()
            p#(s(x)) -> c_13()
        - Weak TRS:
            cond1(true(),x,y,z) -> cond2(gr(x,0()),x,y,z)
            cond2(false(),x,y,z) -> cond3(gr(y,0()),x,y,z)
            cond2(true(),x,y,z) -> cond1(or(gr(x,z),gr(y,z)),p(x),y,z)
            cond3(false(),x,y,z) -> cond1(or(gr(x,z),gr(y,z)),x,y,z)
            cond3(true(),x,y,z) -> cond1(or(gr(x,z),gr(y,z)),x,p(y),z)
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            or(x,true()) -> true()
            or(false(),false()) -> false()
            or(true(),x) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/4,cond2/4,cond3/4,gr/2,or/2,p/1,cond1#/4,cond2#/4,cond3#/4,gr#/2,or#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/2,c_3/5,c_4/4,c_5/5,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0,c_11/0,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1#,cond2#,cond3#,gr#,or#,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)
          or(x,true()) -> true()
          or(false(),false()) -> false()
          or(true(),x) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
          cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0()))
          cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0()))
          cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                     ,or#(gr(x,z),gr(y,z))
                                     ,gr#(x,z)
                                     ,gr#(y,z)
                                     ,p#(x))
          cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),or#(gr(x,z),gr(y,z)),gr#(x,z),gr#(y,z))
          cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                     ,or#(gr(x,z),gr(y,z))
                                     ,gr#(x,z)
                                     ,gr#(y,z)
                                     ,p#(y))
          gr#(0(),x) -> c_6()
          gr#(s(x),0()) -> c_7()
          gr#(s(x),s(y)) -> c_8(gr#(x,y))
          or#(x,true()) -> c_9()
          or#(false(),false()) -> c_10()
          or#(true(),x) -> c_11()
          p#(0()) -> c_12()
          p#(s(x)) -> c_13()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0()))
            cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0()))
            cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                       ,or#(gr(x,z),gr(y,z))
                                       ,gr#(x,z)
                                       ,gr#(y,z)
                                       ,p#(x))
            cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),or#(gr(x,z),gr(y,z)),gr#(x,z),gr#(y,z))
            cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                       ,or#(gr(x,z),gr(y,z))
                                       ,gr#(x,z)
                                       ,gr#(y,z)
                                       ,p#(y))
            gr#(0(),x) -> c_6()
            gr#(s(x),0()) -> c_7()
            gr#(s(x),s(y)) -> c_8(gr#(x,y))
            or#(x,true()) -> c_9()
            or#(false(),false()) -> c_10()
            or#(true(),x) -> c_11()
            p#(0()) -> c_12()
            p#(s(x)) -> c_13()
        - Weak TRS:
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            or(x,true()) -> true()
            or(false(),false()) -> false()
            or(true(),x) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/4,cond2/4,cond3/4,gr/2,or/2,p/1,cond1#/4,cond2#/4,cond3#/4,gr#/2,or#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/2,c_3/5,c_4/4,c_5/5,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0,c_11/0,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1#,cond2#,cond3#,gr#,or#,p#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {6,7,9,10,11,12,13}
        by application of
          Pre({6,7,9,10,11,12,13}) = {1,2,3,4,5,8}.
        Here rules are labelled as follows:
          1: cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0()))
          2: cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0()))
          3: cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                        ,or#(gr(x,z),gr(y,z))
                                        ,gr#(x,z)
                                        ,gr#(y,z)
                                        ,p#(x))
          4: cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),or#(gr(x,z),gr(y,z)),gr#(x,z),gr#(y,z))
          5: cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                        ,or#(gr(x,z),gr(y,z))
                                        ,gr#(x,z)
                                        ,gr#(y,z)
                                        ,p#(y))
          6: gr#(0(),x) -> c_6()
          7: gr#(s(x),0()) -> c_7()
          8: gr#(s(x),s(y)) -> c_8(gr#(x,y))
          9: or#(x,true()) -> c_9()
          10: or#(false(),false()) -> c_10()
          11: or#(true(),x) -> c_11()
          12: p#(0()) -> c_12()
          13: p#(s(x)) -> c_13()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0()))
            cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0()))
            cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                       ,or#(gr(x,z),gr(y,z))
                                       ,gr#(x,z)
                                       ,gr#(y,z)
                                       ,p#(x))
            cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),or#(gr(x,z),gr(y,z)),gr#(x,z),gr#(y,z))
            cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                       ,or#(gr(x,z),gr(y,z))
                                       ,gr#(x,z)
                                       ,gr#(y,z)
                                       ,p#(y))
            gr#(s(x),s(y)) -> c_8(gr#(x,y))
        - Weak DPs:
            gr#(0(),x) -> c_6()
            gr#(s(x),0()) -> c_7()
            or#(x,true()) -> c_9()
            or#(false(),false()) -> c_10()
            or#(true(),x) -> c_11()
            p#(0()) -> c_12()
            p#(s(x)) -> c_13()
        - Weak TRS:
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            or(x,true()) -> true()
            or(false(),false()) -> false()
            or(true(),x) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/4,cond2/4,cond3/4,gr/2,or/2,p/1,cond1#/4,cond2#/4,cond3#/4,gr#/2,or#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/2,c_3/5,c_4/4,c_5/5,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0,c_11/0,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1#,cond2#,cond3#,gr#,or#,p#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0()))
             -->_1 cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                              ,or#(gr(x,z),gr(y,z))
                                              ,gr#(x,z)
                                              ,gr#(y,z)
                                              ,p#(x)):3
             -->_1 cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0())):2
             -->_2 gr#(s(x),0()) -> c_7():8
             -->_2 gr#(0(),x) -> c_6():7
          
          2:S:cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0()))
             -->_1 cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                              ,or#(gr(x,z),gr(y,z))
                                              ,gr#(x,z)
                                              ,gr#(y,z)
                                              ,p#(y)):5
             -->_1 cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z)
                                               ,or#(gr(x,z),gr(y,z))
                                               ,gr#(x,z)
                                               ,gr#(y,z)):4
             -->_2 gr#(s(x),0()) -> c_7():8
             -->_2 gr#(0(),x) -> c_6():7
          
          3:S:cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                         ,or#(gr(x,z),gr(y,z))
                                         ,gr#(x,z)
                                         ,gr#(y,z)
                                         ,p#(x))
             -->_4 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_3 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_5 p#(s(x)) -> c_13():13
             -->_5 p#(0()) -> c_12():12
             -->_2 or#(true(),x) -> c_11():11
             -->_2 or#(false(),false()) -> c_10():10
             -->_2 or#(x,true()) -> c_9():9
             -->_4 gr#(s(x),0()) -> c_7():8
             -->_3 gr#(s(x),0()) -> c_7():8
             -->_4 gr#(0(),x) -> c_6():7
             -->_3 gr#(0(),x) -> c_6():7
             -->_1 cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0())):1
          
          4:S:cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),or#(gr(x,z),gr(y,z)),gr#(x,z),gr#(y,z))
             -->_4 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_3 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_2 or#(true(),x) -> c_11():11
             -->_2 or#(false(),false()) -> c_10():10
             -->_2 or#(x,true()) -> c_9():9
             -->_4 gr#(s(x),0()) -> c_7():8
             -->_3 gr#(s(x),0()) -> c_7():8
             -->_4 gr#(0(),x) -> c_6():7
             -->_3 gr#(0(),x) -> c_6():7
             -->_1 cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0())):1
          
          5:S:cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                         ,or#(gr(x,z),gr(y,z))
                                         ,gr#(x,z)
                                         ,gr#(y,z)
                                         ,p#(y))
             -->_4 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_3 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_5 p#(s(x)) -> c_13():13
             -->_5 p#(0()) -> c_12():12
             -->_2 or#(true(),x) -> c_11():11
             -->_2 or#(false(),false()) -> c_10():10
             -->_2 or#(x,true()) -> c_9():9
             -->_4 gr#(s(x),0()) -> c_7():8
             -->_3 gr#(s(x),0()) -> c_7():8
             -->_4 gr#(0(),x) -> c_6():7
             -->_3 gr#(0(),x) -> c_6():7
             -->_1 cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0())):1
          
          6:S:gr#(s(x),s(y)) -> c_8(gr#(x,y))
             -->_1 gr#(s(x),0()) -> c_7():8
             -->_1 gr#(0(),x) -> c_6():7
             -->_1 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
          
          7:W:gr#(0(),x) -> c_6()
             
          
          8:W:gr#(s(x),0()) -> c_7()
             
          
          9:W:or#(x,true()) -> c_9()
             
          
          10:W:or#(false(),false()) -> c_10()
             
          
          11:W:or#(true(),x) -> c_11()
             
          
          12:W:p#(0()) -> c_12()
             
          
          13:W:p#(s(x)) -> c_13()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: or#(x,true()) -> c_9()
          10: or#(false(),false()) -> c_10()
          11: or#(true(),x) -> c_11()
          12: p#(0()) -> c_12()
          13: p#(s(x)) -> c_13()
          7: gr#(0(),x) -> c_6()
          8: gr#(s(x),0()) -> c_7()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0()))
            cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0()))
            cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                       ,or#(gr(x,z),gr(y,z))
                                       ,gr#(x,z)
                                       ,gr#(y,z)
                                       ,p#(x))
            cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),or#(gr(x,z),gr(y,z)),gr#(x,z),gr#(y,z))
            cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                       ,or#(gr(x,z),gr(y,z))
                                       ,gr#(x,z)
                                       ,gr#(y,z)
                                       ,p#(y))
            gr#(s(x),s(y)) -> c_8(gr#(x,y))
        - Weak TRS:
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            or(x,true()) -> true()
            or(false(),false()) -> false()
            or(true(),x) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/4,cond2/4,cond3/4,gr/2,or/2,p/1,cond1#/4,cond2#/4,cond3#/4,gr#/2,or#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/2,c_3/5,c_4/4,c_5/5,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0,c_11/0,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1#,cond2#,cond3#,gr#,or#,p#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0()))
             -->_1 cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                              ,or#(gr(x,z),gr(y,z))
                                              ,gr#(x,z)
                                              ,gr#(y,z)
                                              ,p#(x)):3
             -->_1 cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0())):2
          
          2:S:cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z),gr#(y,0()))
             -->_1 cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                              ,or#(gr(x,z),gr(y,z))
                                              ,gr#(x,z)
                                              ,gr#(y,z)
                                              ,p#(y)):5
             -->_1 cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z)
                                               ,or#(gr(x,z),gr(y,z))
                                               ,gr#(x,z)
                                               ,gr#(y,z)):4
          
          3:S:cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z)
                                         ,or#(gr(x,z),gr(y,z))
                                         ,gr#(x,z)
                                         ,gr#(y,z)
                                         ,p#(x))
             -->_4 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_3 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_1 cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0())):1
          
          4:S:cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),or#(gr(x,z),gr(y,z)),gr#(x,z),gr#(y,z))
             -->_4 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_3 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_1 cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0())):1
          
          5:S:cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z)
                                         ,or#(gr(x,z),gr(y,z))
                                         ,gr#(x,z)
                                         ,gr#(y,z)
                                         ,p#(y))
             -->_4 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_3 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
             -->_1 cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z),gr#(x,0())):1
          
          6:S:gr#(s(x),s(y)) -> c_8(gr#(x,y))
             -->_1 gr#(s(x),s(y)) -> c_8(gr#(x,y)):6
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z))
          cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z))
          cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z),gr#(x,z),gr#(y,z))
          cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),gr#(x,z),gr#(y,z))
          cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z),gr#(x,z),gr#(y,z))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          cond1#(true(),x,y,z) -> c_1(cond2#(gr(x,0()),x,y,z))
          cond2#(false(),x,y,z) -> c_2(cond3#(gr(y,0()),x,y,z))
          cond2#(true(),x,y,z) -> c_3(cond1#(or(gr(x,z),gr(y,z)),p(x),y,z),gr#(x,z),gr#(y,z))
          cond3#(false(),x,y,z) -> c_4(cond1#(or(gr(x,z),gr(y,z)),x,y,z),gr#(x,z),gr#(y,z))
          cond3#(true(),x,y,z) -> c_5(cond1#(or(gr(x,z),gr(y,z)),x,p(y),z),gr#(x,z),gr#(y,z))
          gr#(s(x),s(y)) -> c_8(gr#(x,y))
      - Weak TRS:
          gr(0(),x) -> false()
          gr(s(x),0()) -> true()
          gr(s(x),s(y)) -> gr(x,y)
          or(x,true()) -> true()
          or(false(),false()) -> false()
          or(true(),x) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
      - Signature:
          {cond1/4,cond2/4,cond3/4,gr/2,or/2,p/1,cond1#/4,cond2#/4,cond3#/4,gr#/2,or#/2,p#/1} / {0/0,false/0,s/1
          ,true/0,c_1/1,c_2/1,c_3/3,c_4/3,c_5/3,c_6/0,c_7/0,c_8/1,c_9/0,c_10/0,c_11/0,c_12/0,c_13/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {cond1#,cond2#,cond3#,gr#,or#,p#} and constructors {0
          ,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE