*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        -(x,0()) -> x
        -(s(x),s(y)) -> -(x,y)
        double(0()) -> 0()
        double(s(x)) -> s(s(double(x)))
        half(0()) -> 0()
        half(double(x)) -> x
        half(s(0())) -> 0()
        half(s(s(x))) -> s(half(x))
        if(0(),y,z) -> y
        if(s(x),y,z) -> z
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {-/2,double/1,half/1,if/3} / {0/0,s/1}
      Obligation:
        Innermost
        basic terms: {-,double,half,if}/{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) -> 1
        0_0() -> 1
        0_0() -> 2
        0_1() -> 1
        0_1() -> 3
        0_1() -> 4
        double_0(2) -> 1
        double_1(2) -> 4
        half_0(2) -> 1
        half_1(2) -> 3
        if_0(2,2,2) -> 1
        s_0(2) -> 1
        s_0(2) -> 2
        s_1(3) -> 1
        s_1(3) -> 3
        s_1(3) -> 4
        s_1(4) -> 3
        2 -> 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
        -(s(x),s(y)) -> -(x,y)
        double(0()) -> 0()
        double(s(x)) -> s(s(double(x)))
        half(0()) -> 0()
        half(double(x)) -> x
        half(s(0())) -> 0()
        half(s(s(x))) -> s(half(x))
        if(0(),y,z) -> y
        if(s(x),y,z) -> z
      Signature:
        {-/2,double/1,half/1,if/3} / {0/0,s/1}
      Obligation:
        Innermost
        basic terms: {-,double,half,if}/{0,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).