*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        +(0(),y) -> y
        +(s(x),y) -> +(x,s(y))
        +(s(x),y) -> s(+(x,y))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {+/2} / {0/0,s/1}
      Obligation:
        Full
        basic terms: {+}/{0,s}
    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:
        +(0(),y) -> y
        +(s(x),y) -> +(x,s(y))
        +(s(x),y) -> s(+(x,y))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {+/2} / {0/0,s/1}
      Obligation:
        Innermost
        basic terms: {+}/{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(2,2) -> 4
        +_1(2,3) -> 1
        +_1(2,3) -> 4
        0_0() -> 1
        0_0() -> 2
        0_0() -> 4
        s_0(2) -> 1
        s_0(2) -> 2
        s_0(2) -> 4
        s_1(1) -> 1
        s_1(2) -> 1
        s_1(2) -> 3
        s_1(2) -> 4
        s_1(3) -> 1
        s_1(3) -> 3
        s_1(3) -> 4
        s_1(4) -> 1
        s_1(4) -> 4
        2 -> 1
        2 -> 4
        3 -> 1
        3 -> 4
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        +(0(),y) -> y
        +(s(x),y) -> +(x,s(y))
        +(s(x),y) -> s(+(x,y))
      Signature:
        {+/2} / {0/0,s/1}
      Obligation:
        Innermost
        basic terms: {+}/{0,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).