*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        h(f(x,y)) -> f(y,f(h(h(x)),a()))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {h/1} / {a/0,f/2}
      Obligation:
        Full
        basic terms: {h}/{a,f}
    Applied Processor:
      ToInnermost
    Proof:
      switch to innermost, as the system is overlay and right linear and does not contain weak rules
*** 1.1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        h(f(x,y)) -> f(y,f(h(h(x)),a()))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {h/1} / {a/0,f/2}
      Obligation:
        Innermost
        basic terms: {h}/{a,f}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        a_0() -> 2
        a_1() -> 5
        a_2() -> 9
        f_0(2,2) -> 2
        f_1(2,3) -> 1
        f_1(2,3) -> 6
        f_1(2,3) -> 10
        f_1(4,5) -> 3
        f_2(3,7) -> 4
        f_2(3,7) -> 8
        f_2(8,9) -> 7
        h_0(2) -> 1
        h_1(2) -> 6
        h_1(6) -> 4
        h_2(2) -> 10
        h_2(10) -> 8
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        h(f(x,y)) -> f(y,f(h(h(x)),a()))
      Signature:
        {h/1} / {a/0,f/2}
      Obligation:
        Innermost
        basic terms: {h}/{a,f}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).