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