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