MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            cond(false(),x,y) -> 0()
            cond(true(),x,y) -> s(minus(x,s(y)))
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
            minus(x,y) -> cond(gt(x,y),x,y)
        - Signature:
            {cond/3,gt/2,minus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond,gt,minus} and constructors {0,false,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          cond#(false(),x,y) -> c_1()
          cond#(true(),x,y) -> c_2(minus#(x,s(y)))
          gt#(0(),v) -> c_3()
          gt#(s(u),0()) -> c_4()
          gt#(s(u),s(v)) -> c_5(gt#(u,v))
          minus#(x,y) -> c_6(cond#(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:
            cond#(false(),x,y) -> c_1()
            cond#(true(),x,y) -> c_2(minus#(x,s(y)))
            gt#(0(),v) -> c_3()
            gt#(s(u),0()) -> c_4()
            gt#(s(u),s(v)) -> c_5(gt#(u,v))
            minus#(x,y) -> c_6(cond#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            cond(false(),x,y) -> 0()
            cond(true(),x,y) -> s(minus(x,s(y)))
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
            minus(x,y) -> cond(gt(x,y),x,y)
        - Signature:
            {cond/3,gt/2,minus/2,cond#/3,gt#/2,minus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,gt#,minus#} and constructors {0,false,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          gt(0(),v) -> false()
          gt(s(u),0()) -> true()
          gt(s(u),s(v)) -> gt(u,v)
          cond#(false(),x,y) -> c_1()
          cond#(true(),x,y) -> c_2(minus#(x,s(y)))
          gt#(0(),v) -> c_3()
          gt#(s(u),0()) -> c_4()
          gt#(s(u),s(v)) -> c_5(gt#(u,v))
          minus#(x,y) -> c_6(cond#(gt(x,y),x,y),gt#(x,y))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(false(),x,y) -> c_1()
            cond#(true(),x,y) -> c_2(minus#(x,s(y)))
            gt#(0(),v) -> c_3()
            gt#(s(u),0()) -> c_4()
            gt#(s(u),s(v)) -> c_5(gt#(u,v))
            minus#(x,y) -> c_6(cond#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {cond/3,gt/2,minus/2,cond#/3,gt#/2,minus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,gt#,minus#} and constructors {0,false,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,4}
        by application of
          Pre({1,3,4}) = {5,6}.
        Here rules are labelled as follows:
          1: cond#(false(),x,y) -> c_1()
          2: cond#(true(),x,y) -> c_2(minus#(x,s(y)))
          3: gt#(0(),v) -> c_3()
          4: gt#(s(u),0()) -> c_4()
          5: gt#(s(u),s(v)) -> c_5(gt#(u,v))
          6: minus#(x,y) -> c_6(cond#(gt(x,y),x,y),gt#(x,y))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(true(),x,y) -> c_2(minus#(x,s(y)))
            gt#(s(u),s(v)) -> c_5(gt#(u,v))
            minus#(x,y) -> c_6(cond#(gt(x,y),x,y),gt#(x,y))
        - Weak DPs:
            cond#(false(),x,y) -> c_1()
            gt#(0(),v) -> c_3()
            gt#(s(u),0()) -> c_4()
        - Weak TRS:
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {cond/3,gt/2,minus/2,cond#/3,gt#/2,minus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,gt#,minus#} and constructors {0,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:cond#(true(),x,y) -> c_2(minus#(x,s(y)))
             -->_1 minus#(x,y) -> c_6(cond#(gt(x,y),x,y),gt#(x,y)):3
          
          2:S:gt#(s(u),s(v)) -> c_5(gt#(u,v))
             -->_1 gt#(s(u),0()) -> c_4():6
             -->_1 gt#(0(),v) -> c_3():5
             -->_1 gt#(s(u),s(v)) -> c_5(gt#(u,v)):2
          
          3:S:minus#(x,y) -> c_6(cond#(gt(x,y),x,y),gt#(x,y))
             -->_2 gt#(s(u),0()) -> c_4():6
             -->_2 gt#(0(),v) -> c_3():5
             -->_1 cond#(false(),x,y) -> c_1():4
             -->_2 gt#(s(u),s(v)) -> c_5(gt#(u,v)):2
             -->_1 cond#(true(),x,y) -> c_2(minus#(x,s(y))):1
          
          4:W:cond#(false(),x,y) -> c_1()
             
          
          5:W:gt#(0(),v) -> c_3()
             
          
          6:W:gt#(s(u),0()) -> c_4()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: cond#(false(),x,y) -> c_1()
          5: gt#(0(),v) -> c_3()
          6: gt#(s(u),0()) -> c_4()
* Step 5: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(true(),x,y) -> c_2(minus#(x,s(y)))
            gt#(s(u),s(v)) -> c_5(gt#(u,v))
            minus#(x,y) -> c_6(cond#(gt(x,y),x,y),gt#(x,y))
        - Weak TRS:
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {cond/3,gt/2,minus/2,cond#/3,gt#/2,minus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,gt#,minus#} and constructors {0,false,s,true}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            uargs(cond#) = {1},
            uargs(c_2) = {1},
            uargs(c_5) = {1},
            uargs(c_6) = {1,2}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                 p(0) = [0]                  
              p(cond) = [0]                  
             p(false) = [0]                  
                p(gt) = [4]                  
             p(minus) = [0]                  
                 p(s) = [0]                  
              p(true) = [0]                  
             p(cond#) = [1] x1 + [2] x2 + [4]
               p(gt#) = [12]                 
            p(minus#) = [2] x1 + [8] x2 + [3]
               p(c_1) = [0]                  
               p(c_2) = [1] x1 + [0]         
               p(c_3) = [0]                  
               p(c_4) = [0]                  
               p(c_5) = [1] x1 + [2]         
               p(c_6) = [1] x1 + [1] x2 + [8]
          
          Following rules are strictly oriented:
          cond#(true(),x,y) = [2] x + [4]        
                            > [2] x + [3]        
                            = c_2(minus#(x,s(y)))
          
          
          Following rules are (at-least) weakly oriented:
          gt#(s(u),s(v)) =  [12]                            
                         >= [14]                            
                         =  c_5(gt#(u,v))                   
          
             minus#(x,y) =  [2] x + [8] y + [3]             
                         >= [2] x + [28]                    
                         =  c_6(cond#(gt(x,y),x,y),gt#(x,y))
          
               gt(0(),v) =  [4]                             
                         >= [0]                             
                         =  false()                         
          
            gt(s(u),0()) =  [4]                             
                         >= [0]                             
                         =  true()                          
          
           gt(s(u),s(v)) =  [4]                             
                         >= [4]                             
                         =  gt(u,v)                         
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          gt#(s(u),s(v)) -> c_5(gt#(u,v))
          minus#(x,y) -> c_6(cond#(gt(x,y),x,y),gt#(x,y))
      - Weak DPs:
          cond#(true(),x,y) -> c_2(minus#(x,s(y)))
      - Weak TRS:
          gt(0(),v) -> false()
          gt(s(u),0()) -> true()
          gt(s(u),s(v)) -> gt(u,v)
      - Signature:
          {cond/3,gt/2,minus/2,cond#/3,gt#/2,minus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {cond#,gt#,minus#} and constructors {0,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE