*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        activate(X) -> X
        and(tt(),X) -> activate(X)
        plus(N,0()) -> N
        plus(N,s(M)) -> s(plus(N,M))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
      Obligation:
        Full
        basic terms: {activate,and,plus}/{0,s,tt}
    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:
        activate(X) -> X
        and(tt(),X) -> activate(X)
        plus(N,0()) -> N
        plus(N,s(M)) -> s(plus(N,M))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
      Obligation:
        Innermost
        basic terms: {activate,and,plus}/{0,s,tt}
    Applied Processor:
      Bounds {initialAutomaton = perSymbol, 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_0() -> 3
        0_0() -> 4
        0_0() -> 7
        activate_0(1) -> 2
        activate_0(5) -> 2
        activate_0(6) -> 2
        activate_1(1) -> 3
        activate_1(5) -> 3
        activate_1(6) -> 3
        and_0(1,1) -> 3
        and_0(1,5) -> 3
        and_0(1,6) -> 3
        and_0(5,1) -> 3
        and_0(5,5) -> 3
        and_0(5,6) -> 3
        and_0(6,1) -> 3
        and_0(6,5) -> 3
        and_0(6,6) -> 3
        plus_0(1,1) -> 4
        plus_0(1,5) -> 4
        plus_0(1,6) -> 4
        plus_0(5,1) -> 4
        plus_0(5,5) -> 4
        plus_0(5,6) -> 4
        plus_0(6,1) -> 4
        plus_0(6,5) -> 4
        plus_0(6,6) -> 4
        plus_1(1,1) -> 7
        plus_1(1,5) -> 7
        plus_1(1,6) -> 7
        plus_1(5,1) -> 7
        plus_1(5,5) -> 7
        plus_1(5,6) -> 7
        plus_1(6,1) -> 7
        plus_1(6,5) -> 7
        plus_1(6,6) -> 7
        s_0(1) -> 2
        s_0(1) -> 3
        s_0(1) -> 4
        s_0(1) -> 5
        s_0(1) -> 7
        s_0(5) -> 2
        s_0(5) -> 3
        s_0(5) -> 4
        s_0(5) -> 5
        s_0(5) -> 7
        s_0(6) -> 2
        s_0(6) -> 3
        s_0(6) -> 4
        s_0(6) -> 5
        s_0(6) -> 7
        s_1(7) -> 4
        s_1(7) -> 7
        tt_0() -> 2
        tt_0() -> 3
        tt_0() -> 4
        tt_0() -> 6
        tt_0() -> 7
        1 -> 2
        1 -> 3
        1 -> 4
        1 -> 7
        5 -> 2
        5 -> 3
        5 -> 4
        5 -> 7
        6 -> 2
        6 -> 3
        6 -> 4
        6 -> 7
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        activate(X) -> X
        and(tt(),X) -> activate(X)
        plus(N,0()) -> N
        plus(N,s(M)) -> s(plus(N,M))
      Signature:
        {activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
      Obligation:
        Innermost
        basic terms: {activate,and,plus}/{0,s,tt}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).