*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(x,x) -> a()
        f(g(x),y) -> f(x,y)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/2} / {a/0,g/1}
      Obligation:
        Full
        basic terms: {f}/{a,g}
    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:
        f(x,x) -> a()
        f(g(x),y) -> f(x,y)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/2} / {a/0,g/1}
      Obligation:
        Innermost
        basic terms: {f}/{a,g}
    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() -> 1
        a_2() -> 1
        f_0(2,2) -> 1
        f_1(2,2) -> 1
        g_0(2) -> 2
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        f(x,x) -> a()
        f(g(x),y) -> f(x,y)
      Signature:
        {f/2} / {a/0,g/1}
      Obligation:
        Innermost
        basic terms: {f}/{a,g}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).