*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        +(0(),y) -> y
        +(s(x),y) -> s(+(x,y))
        -(x,0()) -> x
        -(0(),y) -> 0()
        -(s(x),s(y)) -> -(x,y)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {+/2,-/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) -> s(+(x,y))
        -(x,0()) -> x
        -(0(),y) -> 0()
        -(s(x),s(y)) -> -(x,y)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {+/2,-/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) -> 3
        -_0(2,2) -> 1
        -_1(2,2) -> 1
        0_0() -> 1
        0_0() -> 2
        0_0() -> 3
        0_1() -> 1
        s_0(2) -> 1
        s_0(2) -> 2
        s_0(2) -> 3
        s_1(3) -> 1
        s_1(3) -> 3
        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:
        +(0(),y) -> y
        +(s(x),y) -> s(+(x,y))
        -(x,0()) -> x
        -(0(),y) -> 0()
        -(s(x),s(y)) -> -(x,y)
      Signature:
        {+/2,-/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).