/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(0()) -> s(0())
            f(s(x)) -> minus(s(x),g(f(x)))
            g(0()) -> 0()
            g(s(x)) -> minus(s(x),f(g(x)))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {f/1,g/1,minus/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,minus} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(0()) -> s(0())
            f(s(x)) -> minus(s(x),g(f(x)))
            g(0()) -> 0()
            g(s(x)) -> minus(s(x),f(g(x)))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {f/1,g/1,minus/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,minus} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 2.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            f(0()) -> s(0())
            f(s(x)) -> minus(s(x),g(f(x)))
            g(0()) -> 0()
            g(s(x)) -> minus(s(x),f(g(x)))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {f/1,g/1,minus/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,minus} and constructors {0,s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "0") :: [] -(0)-> "A"(0)
          F (TrsFun "0") :: [] -(0)-> "A"(1)
          F (TrsFun "f") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "g") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "main") :: ["A"(0) x "A"(1)] -(1)-> "A"(0)
          F (TrsFun "minus") :: ["A"(0) x "A"(1)] -(1)-> "A"(0)
          F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "s") :: ["A"(1)] -(1)-> "A"(1)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          f(0()) -> s(0())
          f(s(x)) -> minus(s(x),g(f(x)))
          g(0()) -> 0()
          g(s(x)) -> minus(s(x),f(g(x)))
          minus(x,0()) -> x
          minus(s(x),s(y)) -> minus(x,y)
          main(x1,x2) -> minus(x1,x2)
        2. Weak:
          
        

** Step 2.b:1: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(0()) -> s(0())
            f(s(x)) -> minus(s(x),g(f(x)))
            g(0()) -> 0()
            g(s(x)) -> minus(s(x),f(g(x)))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {f/1,g/1,minus/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,minus} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(x){x -> s(x)} =
            f(s(x)) ->^+ minus(s(x),g(f(x)))
              = C[f(x) = f(x){}]

WORST_CASE(Omega(n^1),?)