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