MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            cond(false(),x,y) -> 0()
            cond(true(),x,y) -> s(minus(x,s(y)))
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            minus(x,y) -> cond(ge(x,s(y)),x,y)
        - Signature:
            {cond/3,ge/2,minus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond,ge,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)))
          ge#(u,0()) -> c_3()
          ge#(0(),s(v)) -> c_4()
          ge#(s(u),s(v)) -> c_5(ge#(u,v))
          minus#(x,y) -> c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(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)))
            ge#(u,0()) -> c_3()
            ge#(0(),s(v)) -> c_4()
            ge#(s(u),s(v)) -> c_5(ge#(u,v))
            minus#(x,y) -> c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(y)))
        - Weak TRS:
            cond(false(),x,y) -> 0()
            cond(true(),x,y) -> s(minus(x,s(y)))
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            minus(x,y) -> cond(ge(x,s(y)),x,y)
        - Signature:
            {cond/3,ge/2,minus/2,cond#/3,ge#/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#,ge#,minus#} and constructors {0,false,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          ge(u,0()) -> true()
          ge(0(),s(v)) -> false()
          ge(s(u),s(v)) -> ge(u,v)
          cond#(false(),x,y) -> c_1()
          cond#(true(),x,y) -> c_2(minus#(x,s(y)))
          ge#(u,0()) -> c_3()
          ge#(0(),s(v)) -> c_4()
          ge#(s(u),s(v)) -> c_5(ge#(u,v))
          minus#(x,y) -> c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(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)))
            ge#(u,0()) -> c_3()
            ge#(0(),s(v)) -> c_4()
            ge#(s(u),s(v)) -> c_5(ge#(u,v))
            minus#(x,y) -> c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(y)))
        - Weak TRS:
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
        - Signature:
            {cond/3,ge/2,minus/2,cond#/3,ge#/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#,ge#,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: ge#(u,0()) -> c_3()
          4: ge#(0(),s(v)) -> c_4()
          5: ge#(s(u),s(v)) -> c_5(ge#(u,v))
          6: minus#(x,y) -> c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(y)))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(true(),x,y) -> c_2(minus#(x,s(y)))
            ge#(s(u),s(v)) -> c_5(ge#(u,v))
            minus#(x,y) -> c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(y)))
        - Weak DPs:
            cond#(false(),x,y) -> c_1()
            ge#(u,0()) -> c_3()
            ge#(0(),s(v)) -> c_4()
        - Weak TRS:
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
        - Signature:
            {cond/3,ge/2,minus/2,cond#/3,ge#/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#,ge#,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#(ge(x,s(y)),x,y),ge#(x,s(y))):3
          
          2:S:ge#(s(u),s(v)) -> c_5(ge#(u,v))
             -->_1 ge#(0(),s(v)) -> c_4():6
             -->_1 ge#(u,0()) -> c_3():5
             -->_1 ge#(s(u),s(v)) -> c_5(ge#(u,v)):2
          
          3:S:minus#(x,y) -> c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(y)))
             -->_2 ge#(0(),s(v)) -> c_4():6
             -->_1 cond#(false(),x,y) -> c_1():4
             -->_2 ge#(s(u),s(v)) -> c_5(ge#(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:ge#(u,0()) -> c_3()
             
          
          6:W:ge#(0(),s(v)) -> c_4()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          5: ge#(u,0()) -> c_3()
          4: cond#(false(),x,y) -> c_1()
          6: ge#(0(),s(v)) -> c_4()
* Step 5: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(true(),x,y) -> c_2(minus#(x,s(y)))
            ge#(s(u),s(v)) -> c_5(ge#(u,v))
            minus#(x,y) -> c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(y)))
        - Weak TRS:
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
        - Signature:
            {cond/3,ge/2,minus/2,cond#/3,ge#/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#,ge#,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) = [1] x2 + [0]         
             p(false) = [1]                  
                p(ge) = [1]                  
             p(minus) = [0]                  
                 p(s) = [0]                  
              p(true) = [1]                  
             p(cond#) = [1] x1 + [5] x2 + [9]
               p(ge#) = [0]                  
            p(minus#) = [5] x1 + [11]        
               p(c_1) = [0]                  
               p(c_2) = [1] x1 + [0]         
               p(c_3) = [0]                  
               p(c_4) = [0]                  
               p(c_5) = [1] x1 + [0]         
               p(c_6) = [1] x1 + [1] x2 + [0]
          
          Following rules are strictly oriented:
          minus#(x,y) = [5] x + [11]                          
                      > [5] x + [10]                          
                      = c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(y)))
          
          
          Following rules are (at-least) weakly oriented:
          cond#(true(),x,y) =  [5] x + [10]       
                            >= [5] x + [11]       
                            =  c_2(minus#(x,s(y)))
          
             ge#(s(u),s(v)) =  [0]                
                            >= [0]                
                            =  c_5(ge#(u,v))      
          
                  ge(u,0()) =  [1]                
                            >= [1]                
                            =  true()             
          
               ge(0(),s(v)) =  [1]                
                            >= [1]                
                            =  false()            
          
              ge(s(u),s(v)) =  [1]                
                            >= [1]                
                            =  ge(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:
          cond#(true(),x,y) -> c_2(minus#(x,s(y)))
          ge#(s(u),s(v)) -> c_5(ge#(u,v))
      - Weak DPs:
          minus#(x,y) -> c_6(cond#(ge(x,s(y)),x,y),ge#(x,s(y)))
      - Weak TRS:
          ge(u,0()) -> true()
          ge(0(),s(v)) -> false()
          ge(s(u),s(v)) -> ge(u,v)
      - Signature:
          {cond/3,ge/2,minus/2,cond#/3,ge#/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#,ge#,minus#} and constructors {0,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE