*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        +(x,0()) -> x
        +(x,s(y)) -> s(+(x,y))
        +(s(x),y) -> s(+(x,y))
        not(false()) -> true()
        not(true()) -> false()
        odd(0()) -> false()
        odd(s(x)) -> not(odd(x))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {+/2,not/1,odd/1} / {0/0,false/0,s/1,true/0}
      Obligation:
        Full
        basic terms: {+,not,odd}/{0,false,s,true}
    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:
        +(x,0()) -> x
        +(x,s(y)) -> s(+(x,y))
        +(s(x),y) -> s(+(x,y))
        not(false()) -> true()
        not(true()) -> false()
        odd(0()) -> false()
        odd(s(x)) -> not(odd(x))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {+/2,not/1,odd/1} / {0/0,false/0,s/1,true/0}
      Obligation:
        Innermost
        basic terms: {+,not,odd}/{0,false,s,true}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        +_0(2,2) -> 1
        +_1(2,2) -> 3
        0_0() -> 1
        0_0() -> 2
        0_0() -> 3
        false_0() -> 1
        false_0() -> 2
        false_0() -> 3
        false_1() -> 1
        false_1() -> 4
        false_2() -> 1
        false_2() -> 4
        not_0(2) -> 1
        not_1(4) -> 1
        not_1(4) -> 4
        odd_0(2) -> 1
        odd_1(2) -> 4
        s_0(2) -> 1
        s_0(2) -> 2
        s_0(2) -> 3
        s_1(3) -> 1
        s_1(3) -> 3
        true_0() -> 1
        true_0() -> 2
        true_0() -> 3
        true_1() -> 1
        true_2() -> 1
        true_2() -> 4
        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:
        +(x,0()) -> x
        +(x,s(y)) -> s(+(x,y))
        +(s(x),y) -> s(+(x,y))
        not(false()) -> true()
        not(true()) -> false()
        odd(0()) -> false()
        odd(s(x)) -> not(odd(x))
      Signature:
        {+/2,not/1,odd/1} / {0/0,false/0,s/1,true/0}
      Obligation:
        Innermost
        basic terms: {+,not,odd}/{0,false,s,true}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).