MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if1(false(),x,y) -> true()
            if1(true(),x,y) -> if2(divides(x,y),x,y)
            if2(false(),x,y) -> test(x,s(y))
            if2(true(),x,y) -> false()
            prime(x) -> test(x,s(s(0())))
            test(x,y) -> if1(gt(x,y),x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div,divides,gt,if1,if2,prime,test} and constructors {0
            ,false,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          div#(0(),0(),z) -> c_1()
          div#(0(),s(x),z) -> c_2()
          div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
          div#(s(x),s(y),z) -> c_4(div#(x,y,z))
          divides#(x,y) -> c_5(div#(x,y,y))
          gt#(0(),y) -> c_6()
          gt#(s(x),0()) -> c_7()
          gt#(s(x),s(y)) -> c_8(gt#(x,y))
          if1#(false(),x,y) -> c_9()
          if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
          if2#(false(),x,y) -> c_11(test#(x,s(y)))
          if2#(true(),x,y) -> c_12()
          prime#(x) -> c_13(test#(x,s(s(0()))))
          test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(0(),0(),z) -> c_1()
            div#(0(),s(x),z) -> c_2()
            div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
            div#(s(x),s(y),z) -> c_4(div#(x,y,z))
            divides#(x,y) -> c_5(div#(x,y,y))
            gt#(0(),y) -> c_6()
            gt#(s(x),0()) -> c_7()
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(false(),x,y) -> c_9()
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            if2#(true(),x,y) -> c_12()
            prime#(x) -> c_13(test#(x,s(s(0()))))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if1(false(),x,y) -> true()
            if1(true(),x,y) -> if2(divides(x,y),x,y)
            if2(false(),x,y) -> test(x,s(y))
            if2(true(),x,y) -> false()
            prime(x) -> test(x,s(s(0())))
            test(x,y) -> if1(gt(x,y),x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          div(0(),0(),z) -> true()
          div(0(),s(x),z) -> false()
          div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
          div(s(x),s(y),z) -> div(x,y,z)
          divides(x,y) -> div(x,y,y)
          gt(0(),y) -> false()
          gt(s(x),0()) -> true()
          gt(s(x),s(y)) -> gt(x,y)
          div#(0(),0(),z) -> c_1()
          div#(0(),s(x),z) -> c_2()
          div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
          div#(s(x),s(y),z) -> c_4(div#(x,y,z))
          divides#(x,y) -> c_5(div#(x,y,y))
          gt#(0(),y) -> c_6()
          gt#(s(x),0()) -> c_7()
          gt#(s(x),s(y)) -> c_8(gt#(x,y))
          if1#(false(),x,y) -> c_9()
          if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
          if2#(false(),x,y) -> c_11(test#(x,s(y)))
          if2#(true(),x,y) -> c_12()
          prime#(x) -> c_13(test#(x,s(s(0()))))
          test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(0(),0(),z) -> c_1()
            div#(0(),s(x),z) -> c_2()
            div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
            div#(s(x),s(y),z) -> c_4(div#(x,y,z))
            divides#(x,y) -> c_5(div#(x,y,y))
            gt#(0(),y) -> c_6()
            gt#(s(x),0()) -> c_7()
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(false(),x,y) -> c_9()
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            if2#(true(),x,y) -> c_12()
            prime#(x) -> c_13(test#(x,s(s(0()))))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,6,7,9,12}
        by application of
          Pre({1,2,6,7,9,12}) = {4,5,8,10,14}.
        Here rules are labelled as follows:
          1: div#(0(),0(),z) -> c_1()
          2: div#(0(),s(x),z) -> c_2()
          3: div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
          4: div#(s(x),s(y),z) -> c_4(div#(x,y,z))
          5: divides#(x,y) -> c_5(div#(x,y,y))
          6: gt#(0(),y) -> c_6()
          7: gt#(s(x),0()) -> c_7()
          8: gt#(s(x),s(y)) -> c_8(gt#(x,y))
          9: if1#(false(),x,y) -> c_9()
          10: if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
          11: if2#(false(),x,y) -> c_11(test#(x,s(y)))
          12: if2#(true(),x,y) -> c_12()
          13: prime#(x) -> c_13(test#(x,s(s(0()))))
          14: test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
            div#(s(x),s(y),z) -> c_4(div#(x,y,z))
            divides#(x,y) -> c_5(div#(x,y,y))
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            prime#(x) -> c_13(test#(x,s(s(0()))))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak DPs:
            div#(0(),0(),z) -> c_1()
            div#(0(),s(x),z) -> c_2()
            gt#(0(),y) -> c_6()
            gt#(s(x),0()) -> c_7()
            if1#(false(),x,y) -> c_9()
            if2#(true(),x,y) -> c_12()
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
          
          2:S:div#(s(x),s(y),z) -> c_4(div#(x,y,z))
             -->_1 div#(0(),s(x),z) -> c_2():10
             -->_1 div#(0(),0(),z) -> c_1():9
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
             -->_1 div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z))):1
          
          3:S:divides#(x,y) -> c_5(div#(x,y,y))
             -->_1 div#(0(),s(x),z) -> c_2():10
             -->_1 div#(0(),0(),z) -> c_1():9
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
          
          4:S:gt#(s(x),s(y)) -> c_8(gt#(x,y))
             -->_1 gt#(s(x),0()) -> c_7():12
             -->_1 gt#(0(),y) -> c_6():11
             -->_1 gt#(s(x),s(y)) -> c_8(gt#(x,y)):4
          
          5:S:if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
             -->_1 if2#(false(),x,y) -> c_11(test#(x,s(y))):6
             -->_1 if2#(true(),x,y) -> c_12():14
             -->_2 divides#(x,y) -> c_5(div#(x,y,y)):3
          
          6:S:if2#(false(),x,y) -> c_11(test#(x,s(y)))
             -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):8
          
          7:S:prime#(x) -> c_13(test#(x,s(s(0()))))
             -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):8
          
          8:S:test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
             -->_1 if1#(false(),x,y) -> c_9():13
             -->_2 gt#(s(x),0()) -> c_7():12
             -->_2 gt#(0(),y) -> c_6():11
             -->_1 if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y)):5
             -->_2 gt#(s(x),s(y)) -> c_8(gt#(x,y)):4
          
          9:W:div#(0(),0(),z) -> c_1()
             
          
          10:W:div#(0(),s(x),z) -> c_2()
             
          
          11:W:gt#(0(),y) -> c_6()
             
          
          12:W:gt#(s(x),0()) -> c_7()
             
          
          13:W:if1#(false(),x,y) -> c_9()
             
          
          14:W:if2#(true(),x,y) -> c_12()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          14: if2#(true(),x,y) -> c_12()
          13: if1#(false(),x,y) -> c_9()
          11: gt#(0(),y) -> c_6()
          12: gt#(s(x),0()) -> c_7()
          9: div#(0(),0(),z) -> c_1()
          10: div#(0(),s(x),z) -> c_2()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
            div#(s(x),s(y),z) -> c_4(div#(x,y,z))
            divides#(x,y) -> c_5(div#(x,y,y))
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            prime#(x) -> c_13(test#(x,s(s(0()))))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
           -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
        
        2:S:div#(s(x),s(y),z) -> c_4(div#(x,y,z))
           -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
           -->_1 div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z))):1
        
        3:S:divides#(x,y) -> c_5(div#(x,y,y))
           -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
        
        4:S:gt#(s(x),s(y)) -> c_8(gt#(x,y))
           -->_1 gt#(s(x),s(y)) -> c_8(gt#(x,y)):4
        
        5:S:if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
           -->_1 if2#(false(),x,y) -> c_11(test#(x,s(y))):6
           -->_2 divides#(x,y) -> c_5(div#(x,y,y)):3
        
        6:S:if2#(false(),x,y) -> c_11(test#(x,s(y)))
           -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):8
        
        7:S:prime#(x) -> c_13(test#(x,s(s(0()))))
           -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):8
        
        8:S:test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
           -->_1 if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y)):5
           -->_2 gt#(s(x),s(y)) -> c_8(gt#(x,y)):4
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(7,prime#(x) -> c_13(test#(x,s(s(0())))))]
* Step 6: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
            div#(s(x),s(y),z) -> c_4(div#(x,y,z))
            divides#(x,y) -> c_5(div#(x,y,y))
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
              div#(s(x),s(y),z) -> c_4(div#(x,y,z))
          - Weak DPs:
              divides#(x,y) -> c_5(div#(x,y,y))
              gt#(s(x),s(y)) -> c_8(gt#(x,y))
              if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
              if2#(false(),x,y) -> c_11(test#(x,s(y)))
              test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
          - Weak TRS:
              div(0(),0(),z) -> true()
              div(0(),s(x),z) -> false()
              div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
              div(s(x),s(y),z) -> div(x,y,z)
              divides(x,y) -> div(x,y,y)
              gt(0(),y) -> false()
              gt(s(x),0()) -> true()
              gt(s(x),s(y)) -> gt(x,y)
          - Signature:
              {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
              ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
              ,c_12/0,c_13/1,c_14/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
              ,test#} and constructors {0,false,s,true}
        
        Problem (S)
          - Strict DPs:
              divides#(x,y) -> c_5(div#(x,y,y))
              gt#(s(x),s(y)) -> c_8(gt#(x,y))
              if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
              if2#(false(),x,y) -> c_11(test#(x,s(y)))
              test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
          - Weak DPs:
              div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
              div#(s(x),s(y),z) -> c_4(div#(x,y,z))
          - Weak TRS:
              div(0(),0(),z) -> true()
              div(0(),s(x),z) -> false()
              div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
              div(s(x),s(y),z) -> div(x,y,z)
              divides(x,y) -> div(x,y,y)
              gt(0(),y) -> false()
              gt(s(x),0()) -> true()
              gt(s(x),s(y)) -> gt(x,y)
          - Signature:
              {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
              ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
              ,c_12/0,c_13/1,c_14/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
              ,test#} and constructors {0,false,s,true}
** Step 6.a:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
            div#(s(x),s(y),z) -> c_4(div#(x,y,z))
        - Weak DPs:
            divides#(x,y) -> c_5(div#(x,y,y))
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
          
          2:S:div#(s(x),s(y),z) -> c_4(div#(x,y,z))
             -->_1 div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z))):1
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
          
          3:W:divides#(x,y) -> c_5(div#(x,y,y))
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
          
          4:W:gt#(s(x),s(y)) -> c_8(gt#(x,y))
             -->_1 gt#(s(x),s(y)) -> c_8(gt#(x,y)):4
          
          5:W:if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
             -->_2 divides#(x,y) -> c_5(div#(x,y,y)):3
             -->_1 if2#(false(),x,y) -> c_11(test#(x,s(y))):6
          
          6:W:if2#(false(),x,y) -> c_11(test#(x,s(y)))
             -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):8
          
          8:W:test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
             -->_2 gt#(s(x),s(y)) -> c_8(gt#(x,y)):4
             -->_1 if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y)):5
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: gt#(s(x),s(y)) -> c_8(gt#(x,y))
** Step 6.a:2: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
            div#(s(x),s(y),z) -> c_4(div#(x,y,z))
        - Weak DPs:
            divides#(x,y) -> c_5(div#(x,y,y))
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
          
          2:S:div#(s(x),s(y),z) -> c_4(div#(x,y,z))
             -->_1 div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z))):1
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
          
          3:W:divides#(x,y) -> c_5(div#(x,y,y))
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):2
          
          5:W:if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
             -->_2 divides#(x,y) -> c_5(div#(x,y,y)):3
             -->_1 if2#(false(),x,y) -> c_11(test#(x,s(y))):6
          
          6:W:if2#(false(),x,y) -> c_11(test#(x,s(y)))
             -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):8
          
          8:W:test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
             -->_1 if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y)):5
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          test#(x,y) -> c_14(if1#(gt(x,y),x,y))
** Step 6.a:3: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
          div#(s(x),s(y),z) -> c_4(div#(x,y,z))
      - Weak DPs:
          divides#(x,y) -> c_5(div#(x,y,y))
          if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
          if2#(false(),x,y) -> c_11(test#(x,s(y)))
          test#(x,y) -> c_14(if1#(gt(x,y),x,y))
      - Weak TRS:
          div(0(),0(),z) -> true()
          div(0(),s(x),z) -> false()
          div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
          div(s(x),s(y),z) -> div(x,y,z)
          divides(x,y) -> div(x,y,y)
          gt(0(),y) -> false()
          gt(s(x),0()) -> true()
          gt(s(x),s(y)) -> gt(x,y)
      - Signature:
          {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
          ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
          ,c_12/0,c_13/1,c_14/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
          ,test#} and constructors {0,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 6.b:1: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            divides#(x,y) -> c_5(div#(x,y,y))
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak DPs:
            div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
            div#(s(x),s(y),z) -> c_4(div#(x,y,z))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {3}.
        Here rules are labelled as follows:
          1: divides#(x,y) -> c_5(div#(x,y,y))
          2: gt#(s(x),s(y)) -> c_8(gt#(x,y))
          3: if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
          4: if2#(false(),x,y) -> c_11(test#(x,s(y)))
          5: test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
          6: div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
          7: div#(s(x),s(y),z) -> c_4(div#(x,y,z))
** Step 6.b:2: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak DPs:
            div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
            div#(s(x),s(y),z) -> c_4(div#(x,y,z))
            divides#(x,y) -> c_5(div#(x,y,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:gt#(s(x),s(y)) -> c_8(gt#(x,y))
             -->_1 gt#(s(x),s(y)) -> c_8(gt#(x,y)):1
          
          2:S:if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
             -->_2 divides#(x,y) -> c_5(div#(x,y,y)):7
             -->_1 if2#(false(),x,y) -> c_11(test#(x,s(y))):3
          
          3:S:if2#(false(),x,y) -> c_11(test#(x,s(y)))
             -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):4
          
          4:S:test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
             -->_1 if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y)):2
             -->_2 gt#(s(x),s(y)) -> c_8(gt#(x,y)):1
          
          5:W:div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):6
          
          6:W:div#(s(x),s(y),z) -> c_4(div#(x,y,z))
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):6
             -->_1 div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z))):5
          
          7:W:divides#(x,y) -> c_5(div#(x,y,y))
             -->_1 div#(s(x),s(y),z) -> c_4(div#(x,y,z)):6
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          7: divides#(x,y) -> c_5(div#(x,y,y))
          6: div#(s(x),s(y),z) -> c_4(div#(x,y,z))
          5: div#(s(x),0(),s(z)) -> c_3(div#(s(x),s(z),s(z)))
** Step 6.b:3: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/2,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:gt#(s(x),s(y)) -> c_8(gt#(x,y))
             -->_1 gt#(s(x),s(y)) -> c_8(gt#(x,y)):1
          
          2:S:if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y))
             -->_1 if2#(false(),x,y) -> c_11(test#(x,s(y))):3
          
          3:S:if2#(false(),x,y) -> c_11(test#(x,s(y)))
             -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):4
          
          4:S:test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
             -->_1 if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y),divides#(x,y)):2
             -->_2 gt#(s(x),s(y)) -> c_8(gt#(x,y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
** Step 6.b:4: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              gt#(s(x),s(y)) -> c_8(gt#(x,y))
          - Weak DPs:
              if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
              if2#(false(),x,y) -> c_11(test#(x,s(y)))
              test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
          - Weak TRS:
              div(0(),0(),z) -> true()
              div(0(),s(x),z) -> false()
              div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
              div(s(x),s(y),z) -> div(x,y,z)
              divides(x,y) -> div(x,y,y)
              gt(0(),y) -> false()
              gt(s(x),0()) -> true()
              gt(s(x),s(y)) -> gt(x,y)
          - Signature:
              {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
              ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1
              ,c_12/0,c_13/1,c_14/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
              ,test#} and constructors {0,false,s,true}
        
        Problem (S)
          - Strict DPs:
              if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
              if2#(false(),x,y) -> c_11(test#(x,s(y)))
              test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
          - Weak DPs:
              gt#(s(x),s(y)) -> c_8(gt#(x,y))
          - Weak TRS:
              div(0(),0(),z) -> true()
              div(0(),s(x),z) -> false()
              div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
              div(s(x),s(y),z) -> div(x,y,z)
              divides(x,y) -> div(x,y,y)
              gt(0(),y) -> false()
              gt(s(x),0()) -> true()
              gt(s(x),s(y)) -> gt(x,y)
          - Signature:
              {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
              ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1
              ,c_12/0,c_13/1,c_14/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
              ,test#} and constructors {0,false,s,true}
*** Step 6.b:4.a:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          gt#(s(x),s(y)) -> c_8(gt#(x,y))
      - Weak DPs:
          if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
          if2#(false(),x,y) -> c_11(test#(x,s(y)))
          test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
      - Weak TRS:
          div(0(),0(),z) -> true()
          div(0(),s(x),z) -> false()
          div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
          div(s(x),s(y),z) -> div(x,y,z)
          divides(x,y) -> div(x,y,y)
          gt(0(),y) -> false()
          gt(s(x),0()) -> true()
          gt(s(x),s(y)) -> gt(x,y)
      - Signature:
          {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
          ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1
          ,c_12/0,c_13/1,c_14/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
          ,test#} and constructors {0,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
*** Step 6.b:4.b:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak DPs:
            gt#(s(x),s(y)) -> c_8(gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
             -->_1 if2#(false(),x,y) -> c_11(test#(x,s(y))):2
          
          2:S:if2#(false(),x,y) -> c_11(test#(x,s(y)))
             -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):3
          
          3:S:test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
             -->_2 gt#(s(x),s(y)) -> c_8(gt#(x,y)):4
             -->_1 if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y)):1
          
          4:W:gt#(s(x),s(y)) -> c_8(gt#(x,y))
             -->_1 gt#(s(x),s(y)) -> c_8(gt#(x,y)):4
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: gt#(s(x),s(y)) -> c_8(gt#(x,y))
*** Step 6.b:4.b:2: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
            if2#(false(),x,y) -> c_11(test#(x,s(y)))
            test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            div(0(),0(),z) -> true()
            div(0(),s(x),z) -> false()
            div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
            div(s(x),s(y),z) -> div(x,y,z)
            divides(x,y) -> div(x,y,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
        - Signature:
            {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
            ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1
            ,c_12/0,c_13/1,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
            ,test#} and constructors {0,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
             -->_1 if2#(false(),x,y) -> c_11(test#(x,s(y))):2
          
          2:S:if2#(false(),x,y) -> c_11(test#(x,s(y)))
             -->_1 test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y)):3
          
          3:S:test#(x,y) -> c_14(if1#(gt(x,y),x,y),gt#(x,y))
             -->_1 if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          test#(x,y) -> c_14(if1#(gt(x,y),x,y))
*** Step 6.b:4.b:3: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          if1#(true(),x,y) -> c_10(if2#(divides(x,y),x,y))
          if2#(false(),x,y) -> c_11(test#(x,s(y)))
          test#(x,y) -> c_14(if1#(gt(x,y),x,y))
      - Weak TRS:
          div(0(),0(),z) -> true()
          div(0(),s(x),z) -> false()
          div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
          div(s(x),s(y),z) -> div(x,y,z)
          divides(x,y) -> div(x,y,y)
          gt(0(),y) -> false()
          gt(s(x),0()) -> true()
          gt(s(x),s(y)) -> gt(x,y)
      - Signature:
          {div/3,divides/2,gt/2,if1/3,if2/3,prime/1,test/2,div#/3,divides#/2,gt#/2,if1#/3,if2#/3,prime#/1
          ,test#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1
          ,c_12/0,c_13/1,c_14/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {div#,divides#,gt#,if1#,if2#,prime#
          ,test#} and constructors {0,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE