*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        a(b(x)) -> b(a(x))
        a(c(x)) -> x
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a/1} / {b/1,c/1}
      Obligation:
        Full
        basic terms: {a}/{b,c}
    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:
        a(b(x)) -> b(a(x))
        a(c(x)) -> x
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a/1} / {b/1,c/1}
      Obligation:
        Innermost
        basic terms: {a}/{b,c}
    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
        a_1(2) -> 3
        b_0(2) -> 1
        b_0(2) -> 2
        b_0(2) -> 3
        b_1(3) -> 1
        b_1(3) -> 3
        c_0(2) -> 1
        c_0(2) -> 2
        c_0(2) -> 3
        2 -> 1
        2 -> 3
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        a(b(x)) -> b(a(x))
        a(c(x)) -> x
      Signature:
        {a/1} / {b/1,c/1}
      Obligation:
        Innermost
        basic terms: {a}/{b,c}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).