MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x)))
            f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x))))
            p(s(x)) -> x
        - Signature:
            {-/2,f/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,f,p} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          -#(x,0()) -> c_1()
          -#(s(x),s(y)) -> c_2(-#(x,y))
          f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x))
          f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x)))
          p#(s(x)) -> c_5()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            -#(x,0()) -> c_1()
            -#(s(x),s(y)) -> c_2(-#(x,y))
            f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x))
            f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x)))
            p#(s(x)) -> c_5()
        - Weak TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x)))
            f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x))))
            p(s(x)) -> x
        - Signature:
            {-/2,f/2,p/1,-#/2,f#/2,p#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/5,c_4/5,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-#,f#,p#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          -(x,0()) -> x
          -(s(x),s(y)) -> -(x,y)
          p(s(x)) -> x
          -#(x,0()) -> c_1()
          -#(s(x),s(y)) -> c_2(-#(x,y))
          f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x))
          f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x)))
          p#(s(x)) -> c_5()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            -#(x,0()) -> c_1()
            -#(s(x),s(y)) -> c_2(-#(x,y))
            f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x))
            f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x)))
            p#(s(x)) -> c_5()
        - Weak TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            p(s(x)) -> x
        - Signature:
            {-/2,f/2,p/1,-#/2,f#/2,p#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/5,c_4/5,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-#,f#,p#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,5}
        by application of
          Pre({1,5}) = {2,3,4}.
        Here rules are labelled as follows:
          1: -#(x,0()) -> c_1()
          2: -#(s(x),s(y)) -> c_2(-#(x,y))
          3: f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x))
          4: f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x)))
          5: p#(s(x)) -> c_5()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_2(-#(x,y))
            f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x))
            f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x)))
        - Weak DPs:
            -#(x,0()) -> c_1()
            p#(s(x)) -> c_5()
        - Weak TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            p(s(x)) -> x
        - Signature:
            {-/2,f/2,p/1,-#/2,f#/2,p#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/5,c_4/5,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-#,f#,p#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:-#(s(x),s(y)) -> c_2(-#(x,y))
             -->_1 -#(x,0()) -> c_1():4
             -->_1 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
          2:S:f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x))
             -->_1 f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x))))
                                    ,p#(-(s(x),y))
                                    ,-#(s(x),y)
                                    ,p#(-(y,s(x)))
                                    ,-#(y,s(x))):3
             -->_4 p#(s(x)) -> c_5():5
             -->_2 p#(s(x)) -> c_5():5
             -->_5 -#(x,0()) -> c_1():4
             -->_1 f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x)):2
             -->_5 -#(s(x),s(y)) -> c_2(-#(x,y)):1
             -->_3 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
          3:S:f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x)))
             -->_4 p#(s(x)) -> c_5():5
             -->_2 p#(s(x)) -> c_5():5
             -->_3 -#(x,0()) -> c_1():4
             -->_1 f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x))):3
             -->_1 f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x)):2
             -->_5 -#(s(x),s(y)) -> c_2(-#(x,y)):1
             -->_3 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
          4:W:-#(x,0()) -> c_1()
             
          
          5:W:p#(s(x)) -> c_5()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          5: p#(s(x)) -> c_5()
          4: -#(x,0()) -> c_1()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_2(-#(x,y))
            f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x))
            f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x)))
        - Weak TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            p(s(x)) -> x
        - Signature:
            {-/2,f/2,p/1,-#/2,f#/2,p#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/5,c_4/5,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-#,f#,p#} and constructors {0,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:-#(s(x),s(y)) -> c_2(-#(x,y))
             -->_1 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
          2:S:f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x))
             -->_1 f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x))))
                                    ,p#(-(s(x),y))
                                    ,-#(s(x),y)
                                    ,p#(-(y,s(x)))
                                    ,-#(y,s(x))):3
             -->_1 f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x)):2
             -->_5 -#(s(x),s(y)) -> c_2(-#(x,y)):1
             -->_3 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
          3:S:f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),p#(-(s(x),y)),-#(s(x),y),p#(-(y,s(x))),-#(y,s(x)))
             -->_1 f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x))))
                                    ,p#(-(s(x),y))
                                    ,-#(s(x),y)
                                    ,p#(-(y,s(x)))
                                    ,-#(y,s(x))):3
             -->_1 f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),p#(-(x,s(y))),-#(x,s(y)),p#(-(s(y),x)),-#(s(y),x)):2
             -->_5 -#(s(x),s(y)) -> c_2(-#(x,y)):1
             -->_3 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),-#(x,s(y)),-#(s(y),x))
          f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),-#(s(x),y),-#(y,s(x)))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          -#(s(x),s(y)) -> c_2(-#(x,y))
          f#(x,s(y)) -> c_3(f#(p(-(x,s(y))),p(-(s(y),x))),-#(x,s(y)),-#(s(y),x))
          f#(s(x),y) -> c_4(f#(p(-(s(x),y)),p(-(y,s(x)))),-#(s(x),y),-#(y,s(x)))
      - Weak TRS:
          -(x,0()) -> x
          -(s(x),s(y)) -> -(x,y)
          p(s(x)) -> x
      - Signature:
          {-/2,f/2,p/1,-#/2,f#/2,p#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/3,c_4/3,c_5/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {-#,f#,p#} and constructors {0,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE