*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        eq0(0(),0()) -> S(0())
        eq0(0(),S(x)) -> 0()
        eq0(S(x),0()) -> 0()
        eq0(S(x'),S(x)) -> eq0(x',x)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {eq0/2} / {0/0,S/1}
      Obligation:
        Innermost
        basic terms: {eq0}/{0,S}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with follwoing automaton.
        0_0() -> 2
        0_1() -> 1
        0_1() -> 3
        S_0(2) -> 2
        S_1(3) -> 1
        eq0_0(2,2) -> 1
        eq0_1(2,2) -> 1
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        eq0(0(),0()) -> S(0())
        eq0(0(),S(x)) -> 0()
        eq0(S(x),0()) -> 0()
        eq0(S(x'),S(x)) -> eq0(x',x)
      Signature:
        {eq0/2} / {0/0,S/1}
      Obligation:
        Innermost
        basic terms: {eq0}/{0,S}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).