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


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            a__f(X) -> f(X)
            a__f(X) -> g(h(f(X)))
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(X)
            mark(h(X)) -> h(mark(X))
        - Signature:
            {a__f/1,mark/1} / {f/1,g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g,h}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__f(X) -> f(X)
            a__f(X) -> g(h(f(X)))
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(X)
            mark(h(X)) -> h(mark(X))
        - Signature:
            {a__f/1,mark/1} / {f/1,g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g,h}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__f(X) -> f(X)
            a__f(X) -> g(h(f(X)))
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(X)
            mark(h(X)) -> h(mark(X))
        - Signature:
            {a__f/1,mark/1} / {f/1,g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g,h}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> f(x)} =
            mark(f(x)) ->^+ a__f(mark(x))
              = C[mark(x) = mark(x){}]

** Step 1.b:1: Ara.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a__f(X) -> f(X)
            a__f(X) -> g(h(f(X)))
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(X)
            mark(h(X)) -> h(mark(X))
        - Signature:
            {a__f/1,mark/1} / {f/1,g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g,h}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 1, araTimeout = 8, araRuleShifting = Just 1, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "a__f") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "f") :: ["A"(2)] -(2)-> "A"(2)
          F (TrsFun "f") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "g") :: ["A"(2)] -(2)-> "A"(2)
          F (TrsFun "g") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "h") :: ["A"(2)] -(2)-> "A"(2)
          F (TrsFun "h") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "mark") :: ["A"(2)] -(0)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          a__f(X) -> f(X)
          a__f(X) -> g(h(f(X)))
          mark(f(X)) -> a__f(mark(X))
          mark(g(X)) -> g(X)
          mark(h(X)) -> h(mark(X))
        2. Weak:
          
        

WORST_CASE(Omega(n^1),O(n^1))