MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y,z,u) -> if2(le(y,s(u)),x,y,s(z),s(u))
            if(true(),x,y,z,u) -> u
            if2(false(),x,y,z,u) -> modIter(x,y,z,u)
            if2(true(),x,y,z,u) -> modIter(x,y,z,0())
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            mod(x,0()) -> modZeroErro()
            mod(x,s(y)) -> modIter(x,s(y),0(),0())
            modIter(x,s(y),z,u) -> if(le(x,z),x,s(y),z,u)
        - Signature:
            {if/5,if2/5,le/2,mod/2,modIter/4} / {0/0,false/0,modZeroErro/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if,if2,le,mod,modIter} and constructors {0,false
            ,modZeroErro,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
          if#(true(),x,y,z,u) -> c_2()
          if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
          if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
          le#(0(),y) -> c_5()
          le#(s(x),0()) -> c_6()
          le#(s(x),s(y)) -> c_7(le#(x,y))
          mod#(x,0()) -> c_8()
          mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0()))
          modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
            if#(true(),x,y,z,u) -> c_2()
            if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
            if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
            le#(0(),y) -> c_5()
            le#(s(x),0()) -> c_6()
            le#(s(x),s(y)) -> c_7(le#(x,y))
            mod#(x,0()) -> c_8()
            mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0()))
            modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
        - Weak TRS:
            if(false(),x,y,z,u) -> if2(le(y,s(u)),x,y,s(z),s(u))
            if(true(),x,y,z,u) -> u
            if2(false(),x,y,z,u) -> modIter(x,y,z,u)
            if2(true(),x,y,z,u) -> modIter(x,y,z,0())
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            mod(x,0()) -> modZeroErro()
            mod(x,s(y)) -> modIter(x,s(y),0(),0())
            modIter(x,s(y),z,u) -> if(le(x,z),x,s(y),z,u)
        - Signature:
            {if/5,if2/5,le/2,mod/2,modIter/4,if#/5,if2#/5,le#/2,mod#/2,modIter#/4} / {0/0,false/0,modZeroErro/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,if2#,le#,mod#,modIter#} and constructors {0,false
            ,modZeroErro,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
          if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
          if#(true(),x,y,z,u) -> c_2()
          if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
          if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
          le#(0(),y) -> c_5()
          le#(s(x),0()) -> c_6()
          le#(s(x),s(y)) -> c_7(le#(x,y))
          mod#(x,0()) -> c_8()
          mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0()))
          modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
            if#(true(),x,y,z,u) -> c_2()
            if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
            if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
            le#(0(),y) -> c_5()
            le#(s(x),0()) -> c_6()
            le#(s(x),s(y)) -> c_7(le#(x,y))
            mod#(x,0()) -> c_8()
            mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0()))
            modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/5,if2/5,le/2,mod/2,modIter/4,if#/5,if2#/5,le#/2,mod#/2,modIter#/4} / {0/0,false/0,modZeroErro/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,if2#,le#,mod#,modIter#} and constructors {0,false
            ,modZeroErro,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,5,6,8}
        by application of
          Pre({2,5,6,8}) = {1,7,10}.
        Here rules are labelled as follows:
          1: if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
          2: if#(true(),x,y,z,u) -> c_2()
          3: if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
          4: if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
          5: le#(0(),y) -> c_5()
          6: le#(s(x),0()) -> c_6()
          7: le#(s(x),s(y)) -> c_7(le#(x,y))
          8: mod#(x,0()) -> c_8()
          9: mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0()))
          10: modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
            if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
            if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
            le#(s(x),s(y)) -> c_7(le#(x,y))
            mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0()))
            modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
        - Weak DPs:
            if#(true(),x,y,z,u) -> c_2()
            le#(0(),y) -> c_5()
            le#(s(x),0()) -> c_6()
            mod#(x,0()) -> c_8()
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/5,if2/5,le/2,mod/2,modIter/4,if#/5,if2#/5,le#/2,mod#/2,modIter#/4} / {0/0,false/0,modZeroErro/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,if2#,le#,mod#,modIter#} and constructors {0,false
            ,modZeroErro,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
             -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):4
             -->_1 if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0())):3
             -->_1 if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u)):2
             -->_2 le#(0(),y) -> c_5():8
          
          2:S:if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
             -->_1 modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z)):6
          
          3:S:if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
             -->_1 modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z)):6
          
          4:S:le#(s(x),s(y)) -> c_7(le#(x,y))
             -->_1 le#(s(x),0()) -> c_6():9
             -->_1 le#(0(),y) -> c_5():8
             -->_1 le#(s(x),s(y)) -> c_7(le#(x,y)):4
          
          5:S:mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0()))
             -->_1 modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z)):6
          
          6:S:modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
             -->_2 le#(s(x),0()) -> c_6():9
             -->_2 le#(0(),y) -> c_5():8
             -->_1 if#(true(),x,y,z,u) -> c_2():7
             -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):4
             -->_1 if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u))):1
          
          7:W:if#(true(),x,y,z,u) -> c_2()
             
          
          8:W:le#(0(),y) -> c_5()
             
          
          9:W:le#(s(x),0()) -> c_6()
             
          
          10:W:mod#(x,0()) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          10: mod#(x,0()) -> c_8()
          7: if#(true(),x,y,z,u) -> c_2()
          8: le#(0(),y) -> c_5()
          9: le#(s(x),0()) -> c_6()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
            if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
            if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
            le#(s(x),s(y)) -> c_7(le#(x,y))
            mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0()))
            modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/5,if2/5,le/2,mod/2,modIter/4,if#/5,if2#/5,le#/2,mod#/2,modIter#/4} / {0/0,false/0,modZeroErro/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,if2#,le#,mod#,modIter#} and constructors {0,false
            ,modZeroErro,s,true}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
           -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):4
           -->_1 if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0())):3
           -->_1 if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u)):2
        
        2:S:if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
           -->_1 modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z)):6
        
        3:S:if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
           -->_1 modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z)):6
        
        4:S:le#(s(x),s(y)) -> c_7(le#(x,y))
           -->_1 le#(s(x),s(y)) -> c_7(le#(x,y)):4
        
        5:S:mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0()))
           -->_1 modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z)):6
        
        6:S:modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
           -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):4
           -->_1 if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u))):1
        
        
        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).
        
        [(5,mod#(x,s(y)) -> c_9(modIter#(x,s(y),0(),0())))]
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          if#(false(),x,y,z,u) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u)),le#(y,s(u)))
          if2#(false(),x,y,z,u) -> c_3(modIter#(x,y,z,u))
          if2#(true(),x,y,z,u) -> c_4(modIter#(x,y,z,0()))
          le#(s(x),s(y)) -> c_7(le#(x,y))
          modIter#(x,s(y),z,u) -> c_10(if#(le(x,z),x,s(y),z,u),le#(x,z))
      - Weak TRS:
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
      - Signature:
          {if/5,if2/5,le/2,mod/2,modIter/4,if#/5,if2#/5,le#/2,mod#/2,modIter#/4} / {0/0,false/0,modZeroErro/0,s/1
          ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {if#,if2#,le#,mod#,modIter#} and constructors {0,false
          ,modZeroErro,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE