MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> times(x,exp(x,y))
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            plus(0(),x) -> x
            plus(s(x),y) -> s(plus(p(s(x)),y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(p(s(x)),y))
            tower(x,y) -> towerIter(x,y,s(0()))
            towerIter(0(),y,z) -> z
            towerIter(s(x),y,z) -> towerIter(p(s(x)),y,exp(y,z))
        - Signature:
            {exp/2,p/1,plus/2,times/2,tower/2,towerIter/3} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {exp,p,plus,times,tower,towerIter} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          exp#(x,0()) -> c_1()
          exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
          p#(s(0())) -> c_3()
          p#(s(s(x))) -> c_4(p#(s(x)))
          plus#(0(),x) -> c_5()
          plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
          times#(0(),y) -> c_7()
          times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
          tower#(x,y) -> c_9(towerIter#(x,y,s(0())))
          towerIter#(0(),y,z) -> c_10()
          towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            exp#(x,0()) -> c_1()
            exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
            p#(s(0())) -> c_3()
            p#(s(s(x))) -> c_4(p#(s(x)))
            plus#(0(),x) -> c_5()
            plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
            times#(0(),y) -> c_7()
            times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
            tower#(x,y) -> c_9(towerIter#(x,y,s(0())))
            towerIter#(0(),y,z) -> c_10()
            towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
        - Weak TRS:
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> times(x,exp(x,y))
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            plus(0(),x) -> x
            plus(s(x),y) -> s(plus(p(s(x)),y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(p(s(x)),y))
            tower(x,y) -> towerIter(x,y,s(0()))
            towerIter(0(),y,z) -> z
            towerIter(s(x),y,z) -> towerIter(p(s(x)),y,exp(y,z))
        - Signature:
            {exp/2,p/1,plus/2,times/2,tower/2,towerIter/3,exp#/2,p#/1,plus#/2,times#/2,tower#/2,towerIter#/3} / {0/0,s/1
            ,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/2,c_7/0,c_8/3,c_9/1,c_10/0,c_11/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {exp#,p#,plus#,times#,tower#
            ,towerIter#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          exp(x,0()) -> s(0())
          exp(x,s(y)) -> times(x,exp(x,y))
          p(s(0())) -> 0()
          p(s(s(x))) -> s(p(s(x)))
          plus(0(),x) -> x
          plus(s(x),y) -> s(plus(p(s(x)),y))
          times(0(),y) -> 0()
          times(s(x),y) -> plus(y,times(p(s(x)),y))
          exp#(x,0()) -> c_1()
          exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
          p#(s(0())) -> c_3()
          p#(s(s(x))) -> c_4(p#(s(x)))
          plus#(0(),x) -> c_5()
          plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
          times#(0(),y) -> c_7()
          times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
          tower#(x,y) -> c_9(towerIter#(x,y,s(0())))
          towerIter#(0(),y,z) -> c_10()
          towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            exp#(x,0()) -> c_1()
            exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
            p#(s(0())) -> c_3()
            p#(s(s(x))) -> c_4(p#(s(x)))
            plus#(0(),x) -> c_5()
            plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
            times#(0(),y) -> c_7()
            times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
            tower#(x,y) -> c_9(towerIter#(x,y,s(0())))
            towerIter#(0(),y,z) -> c_10()
            towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
        - Weak TRS:
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> times(x,exp(x,y))
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            plus(0(),x) -> x
            plus(s(x),y) -> s(plus(p(s(x)),y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(p(s(x)),y))
        - Signature:
            {exp/2,p/1,plus/2,times/2,tower/2,towerIter/3,exp#/2,p#/1,plus#/2,times#/2,tower#/2,towerIter#/3} / {0/0,s/1
            ,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/2,c_7/0,c_8/3,c_9/1,c_10/0,c_11/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {exp#,p#,plus#,times#,tower#
            ,towerIter#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,5,7,10}
        by application of
          Pre({1,3,5,7,10}) = {2,4,6,8,9,11}.
        Here rules are labelled as follows:
          1: exp#(x,0()) -> c_1()
          2: exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
          3: p#(s(0())) -> c_3()
          4: p#(s(s(x))) -> c_4(p#(s(x)))
          5: plus#(0(),x) -> c_5()
          6: plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
          7: times#(0(),y) -> c_7()
          8: times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
          9: tower#(x,y) -> c_9(towerIter#(x,y,s(0())))
          10: towerIter#(0(),y,z) -> c_10()
          11: towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
            p#(s(s(x))) -> c_4(p#(s(x)))
            plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
            times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
            tower#(x,y) -> c_9(towerIter#(x,y,s(0())))
            towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
        - Weak DPs:
            exp#(x,0()) -> c_1()
            p#(s(0())) -> c_3()
            plus#(0(),x) -> c_5()
            times#(0(),y) -> c_7()
            towerIter#(0(),y,z) -> c_10()
        - Weak TRS:
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> times(x,exp(x,y))
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            plus(0(),x) -> x
            plus(s(x),y) -> s(plus(p(s(x)),y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(p(s(x)),y))
        - Signature:
            {exp/2,p/1,plus/2,times/2,tower/2,towerIter/3,exp#/2,p#/1,plus#/2,times#/2,tower#/2,towerIter#/3} / {0/0,s/1
            ,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/2,c_7/0,c_8/3,c_9/1,c_10/0,c_11/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {exp#,p#,plus#,times#,tower#
            ,towerIter#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
             -->_1 times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x))):4
             -->_1 times#(0(),y) -> c_7():10
             -->_2 exp#(x,0()) -> c_1():7
             -->_2 exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y)):1
          
          2:S:p#(s(s(x))) -> c_4(p#(s(x)))
             -->_1 p#(s(0())) -> c_3():8
             -->_1 p#(s(s(x))) -> c_4(p#(s(x))):2
          
          3:S:plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
             -->_1 plus#(0(),x) -> c_5():9
             -->_2 p#(s(0())) -> c_3():8
             -->_1 plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x))):3
             -->_2 p#(s(s(x))) -> c_4(p#(s(x))):2
          
          4:S:times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
             -->_2 times#(0(),y) -> c_7():10
             -->_1 plus#(0(),x) -> c_5():9
             -->_3 p#(s(0())) -> c_3():8
             -->_2 times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x))):4
             -->_1 plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x))):3
             -->_3 p#(s(s(x))) -> c_4(p#(s(x))):2
          
          5:S:tower#(x,y) -> c_9(towerIter#(x,y,s(0())))
             -->_1 towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z)):6
             -->_1 towerIter#(0(),y,z) -> c_10():11
          
          6:S:towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
             -->_1 towerIter#(0(),y,z) -> c_10():11
             -->_2 p#(s(0())) -> c_3():8
             -->_3 exp#(x,0()) -> c_1():7
             -->_1 towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z)):6
             -->_2 p#(s(s(x))) -> c_4(p#(s(x))):2
             -->_3 exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y)):1
          
          7:W:exp#(x,0()) -> c_1()
             
          
          8:W:p#(s(0())) -> c_3()
             
          
          9:W:plus#(0(),x) -> c_5()
             
          
          10:W:times#(0(),y) -> c_7()
             
          
          11:W:towerIter#(0(),y,z) -> c_10()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          11: towerIter#(0(),y,z) -> c_10()
          7: exp#(x,0()) -> c_1()
          8: p#(s(0())) -> c_3()
          9: plus#(0(),x) -> c_5()
          10: times#(0(),y) -> c_7()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
            p#(s(s(x))) -> c_4(p#(s(x)))
            plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
            times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
            tower#(x,y) -> c_9(towerIter#(x,y,s(0())))
            towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
        - Weak TRS:
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> times(x,exp(x,y))
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            plus(0(),x) -> x
            plus(s(x),y) -> s(plus(p(s(x)),y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(p(s(x)),y))
        - Signature:
            {exp/2,p/1,plus/2,times/2,tower/2,towerIter/3,exp#/2,p#/1,plus#/2,times#/2,tower#/2,towerIter#/3} / {0/0,s/1
            ,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/2,c_7/0,c_8/3,c_9/1,c_10/0,c_11/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {exp#,p#,plus#,times#,tower#
            ,towerIter#} and constructors {0,s}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
           -->_1 times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x))):4
           -->_2 exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y)):1
        
        2:S:p#(s(s(x))) -> c_4(p#(s(x)))
           -->_1 p#(s(s(x))) -> c_4(p#(s(x))):2
        
        3:S:plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
           -->_1 plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x))):3
           -->_2 p#(s(s(x))) -> c_4(p#(s(x))):2
        
        4:S:times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
           -->_2 times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x))):4
           -->_1 plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x))):3
           -->_3 p#(s(s(x))) -> c_4(p#(s(x))):2
        
        5:S:tower#(x,y) -> c_9(towerIter#(x,y,s(0())))
           -->_1 towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z)):6
        
        6:S:towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
           -->_1 towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z)):6
           -->_2 p#(s(s(x))) -> c_4(p#(s(x))):2
           -->_3 exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y)):1
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(5,tower#(x,y) -> c_9(towerIter#(x,y,s(0()))))]
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          exp#(x,s(y)) -> c_2(times#(x,exp(x,y)),exp#(x,y))
          p#(s(s(x))) -> c_4(p#(s(x)))
          plus#(s(x),y) -> c_6(plus#(p(s(x)),y),p#(s(x)))
          times#(s(x),y) -> c_8(plus#(y,times(p(s(x)),y)),times#(p(s(x)),y),p#(s(x)))
          towerIter#(s(x),y,z) -> c_11(towerIter#(p(s(x)),y,exp(y,z)),p#(s(x)),exp#(y,z))
      - Weak TRS:
          exp(x,0()) -> s(0())
          exp(x,s(y)) -> times(x,exp(x,y))
          p(s(0())) -> 0()
          p(s(s(x))) -> s(p(s(x)))
          plus(0(),x) -> x
          plus(s(x),y) -> s(plus(p(s(x)),y))
          times(0(),y) -> 0()
          times(s(x),y) -> plus(y,times(p(s(x)),y))
      - Signature:
          {exp/2,p/1,plus/2,times/2,tower/2,towerIter/3,exp#/2,p#/1,plus#/2,times#/2,tower#/2,towerIter#/3} / {0/0,s/1
          ,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/2,c_7/0,c_8/3,c_9/1,c_10/0,c_11/3}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {exp#,p#,plus#,times#,tower#
          ,towerIter#} and constructors {0,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE