MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            and(x,false()) -> false()
            and(x,true()) -> x
            f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,y,s(z))
            f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,s(y),z)
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {and/2,f/4,gt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,f,gt} and constructors {0,false,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          and#(x,false()) -> c_1()
          and#(x,true()) -> c_2()
          f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
          f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
          gt#(0(),v) -> c_5()
          gt#(s(u),0()) -> c_6()
          gt#(s(u),s(v)) -> c_7(gt#(u,v))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            and#(x,false()) -> c_1()
            and#(x,true()) -> c_2()
            f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
            f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
            gt#(0(),v) -> c_5()
            gt#(s(u),0()) -> c_6()
            gt#(s(u),s(v)) -> c_7(gt#(u,v))
        - Weak TRS:
            and(x,false()) -> false()
            and(x,true()) -> x
            f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,y,s(z))
            f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,s(y),z)
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {and/2,f/4,gt/2,and#/2,f#/4,gt#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/4,c_4/4,c_5/0,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,f#,gt#} and constructors {0,false,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          and(x,false()) -> false()
          and(x,true()) -> x
          gt(0(),v) -> false()
          gt(s(u),0()) -> true()
          gt(s(u),s(v)) -> gt(u,v)
          and#(x,false()) -> c_1()
          and#(x,true()) -> c_2()
          f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
          f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
          gt#(0(),v) -> c_5()
          gt#(s(u),0()) -> c_6()
          gt#(s(u),s(v)) -> c_7(gt#(u,v))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            and#(x,false()) -> c_1()
            and#(x,true()) -> c_2()
            f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
            f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
            gt#(0(),v) -> c_5()
            gt#(s(u),0()) -> c_6()
            gt#(s(u),s(v)) -> c_7(gt#(u,v))
        - Weak TRS:
            and(x,false()) -> false()
            and(x,true()) -> x
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {and/2,f/4,gt/2,and#/2,f#/4,gt#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/4,c_4/4,c_5/0,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,f#,gt#} 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}
        by application of
          Pre({1,2,5,6}) = {3,4,7}.
        Here rules are labelled as follows:
          1: and#(x,false()) -> c_1()
          2: and#(x,true()) -> c_2()
          3: f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
          4: f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
          5: gt#(0(),v) -> c_5()
          6: gt#(s(u),0()) -> c_6()
          7: gt#(s(u),s(v)) -> c_7(gt#(u,v))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
            f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
            gt#(s(u),s(v)) -> c_7(gt#(u,v))
        - Weak DPs:
            and#(x,false()) -> c_1()
            and#(x,true()) -> c_2()
            gt#(0(),v) -> c_5()
            gt#(s(u),0()) -> c_6()
        - Weak TRS:
            and(x,false()) -> false()
            and(x,true()) -> x
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {and/2,f/4,gt/2,and#/2,f#/4,gt#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/4,c_4/4,c_5/0,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,f#,gt#} and constructors {0,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
             -->_4 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
             -->_3 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
             -->_1 f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z)):2
             -->_4 gt#(s(u),0()) -> c_6():7
             -->_3 gt#(s(u),0()) -> c_6():7
             -->_4 gt#(0(),v) -> c_5():6
             -->_3 gt#(0(),v) -> c_5():6
             -->_2 and#(x,true()) -> c_2():5
             -->_2 and#(x,false()) -> c_1():4
             -->_1 f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z)):1
          
          2:S:f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
             -->_4 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
             -->_3 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
             -->_4 gt#(s(u),0()) -> c_6():7
             -->_3 gt#(s(u),0()) -> c_6():7
             -->_4 gt#(0(),v) -> c_5():6
             -->_3 gt#(0(),v) -> c_5():6
             -->_2 and#(x,true()) -> c_2():5
             -->_2 and#(x,false()) -> c_1():4
             -->_1 f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z)):2
             -->_1 f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z)):1
          
          3:S:gt#(s(u),s(v)) -> c_7(gt#(u,v))
             -->_1 gt#(s(u),0()) -> c_6():7
             -->_1 gt#(0(),v) -> c_5():6
             -->_1 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
          
          4:W:and#(x,false()) -> c_1()
             
          
          5:W:and#(x,true()) -> c_2()
             
          
          6:W:gt#(0(),v) -> c_5()
             
          
          7:W:gt#(s(u),0()) -> c_6()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: and#(x,false()) -> c_1()
          5: and#(x,true()) -> c_2()
          6: gt#(0(),v) -> c_5()
          7: gt#(s(u),0()) -> c_6()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
            f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
            gt#(s(u),s(v)) -> c_7(gt#(u,v))
        - Weak TRS:
            and(x,false()) -> false()
            and(x,true()) -> x
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {and/2,f/4,gt/2,and#/2,f#/4,gt#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/4,c_4/4,c_5/0,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,f#,gt#} and constructors {0,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
             -->_4 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
             -->_3 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
             -->_1 f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z)):2
             -->_1 f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z)):1
          
          2:S:f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z))
             -->_4 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
             -->_3 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
             -->_1 f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z)):2
             -->_1 f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),and#(gt(x,y),gt(x,z)),gt#(x,y),gt#(x,z)):1
          
          3:S:gt#(s(u),s(v)) -> c_7(gt#(u,v))
             -->_1 gt#(s(u),s(v)) -> c_7(gt#(u,v)):3
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),gt#(x,y),gt#(x,z))
          f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),gt#(x,y),gt#(x,z))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(true(),x,y,z) -> c_3(f#(and(gt(x,y),gt(x,z)),x,y,s(z)),gt#(x,y),gt#(x,z))
          f#(true(),x,y,z) -> c_4(f#(and(gt(x,y),gt(x,z)),x,s(y),z),gt#(x,y),gt#(x,z))
          gt#(s(u),s(v)) -> c_7(gt#(u,v))
      - Weak TRS:
          and(x,false()) -> false()
          and(x,true()) -> x
          gt(0(),v) -> false()
          gt(s(u),0()) -> true()
          gt(s(u),s(v)) -> gt(u,v)
      - Signature:
          {and/2,f/4,gt/2,and#/2,f#/4,gt#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/0,c_3/3,c_4/3,c_5/0,c_6/0,c_7/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {and#,f#,gt#} and constructors {0,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE