*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        add0(0(),x2) -> x2
        add0(S(x),x2) -> +(S(0()),add0(x2,x))
      Weak DP Rules:
        
      Weak TRS Rules:
        +(x,S(0())) -> S(x)
        +(S(0()),y) -> S(y)
      Signature:
        {+/2,add0/2} / {0/0,S/1}
      Obligation:
        Innermost
        basic terms: {+,add0}/{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(2,2) -> 1
        +_1(3,4) -> 1
        +_1(3,4) -> 4
        0_0() -> 1
        0_0() -> 2
        0_0() -> 4
        0_1() -> 5
        S_0(2) -> 1
        S_0(2) -> 2
        S_0(2) -> 4
        S_1(3) -> 1
        S_1(3) -> 4
        S_1(4) -> 1
        S_1(4) -> 4
        S_1(5) -> 3
        add0_0(2,2) -> 1
        add0_1(2,2) -> 4
        2 -> 1
        2 -> 4
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        +(x,S(0())) -> S(x)
        +(S(0()),y) -> S(y)
        add0(0(),x2) -> x2
        add0(S(x),x2) -> +(S(0()),add0(x2,x))
      Signature:
        {+/2,add0/2} / {0/0,S/1}
      Obligation:
        Innermost
        basic terms: {+,add0}/{0,S}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).