*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        dbl(0(),y) -> y
        dbl(S(0()),S(0())) -> S(S(S(S(0()))))
        unsafe(0()) -> 0()
        unsafe(S(x)) -> dbl(unsafe(x),0())
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {dbl/2,unsafe/1} / {0/0,S/1}
      Obligation:
        Innermost
        basic terms: {dbl,unsafe}/{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() -> 1
        0_0() -> 2
        0_1() -> 1
        0_1() -> 6
        0_1() -> 7
        S_0(2) -> 1
        S_0(2) -> 2
        S_1(3) -> 1
        S_1(4) -> 3
        S_1(5) -> 4
        S_1(6) -> 5
        dbl_0(2,2) -> 1
        dbl_1(7,6) -> 1
        dbl_1(7,7) -> 7
        unsafe_0(2) -> 1
        unsafe_1(2) -> 7
        2 -> 1
        6 -> 1
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        dbl(0(),y) -> y
        dbl(S(0()),S(0())) -> S(S(S(S(0()))))
        unsafe(0()) -> 0()
        unsafe(S(x)) -> dbl(unsafe(x),0())
      Signature:
        {dbl/2,unsafe/1} / {0/0,S/1}
      Obligation:
        Innermost
        basic terms: {dbl,unsafe}/{0,S}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).