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