*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
        f(a(x),a(y)) -> a(f(x,y))
        f(b(x),b(y)) -> b(f(x,y))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a/1,f/2} / {b/1}
      Obligation:
        Innermost
        basic terms: {a,f}/{b}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with follwoing automaton.
        a_0(2) -> 1
        b_0(2) -> 2
        b_1(3) -> 1
        b_1(3) -> 3
        f_0(2,2) -> 1
        f_1(2,2) -> 3
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
        f(a(x),a(y)) -> a(f(x,y))
        f(b(x),b(y)) -> b(f(x,y))
      Signature:
        {a/1,f/2} / {b/1}
      Obligation:
        Innermost
        basic terms: {a,f}/{b}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).