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

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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a(),a()) -> f(a(),b())
            f(a(),b()) -> f(s(a()),c())
            f(c(),c()) -> f(a(),a())
            f(s(X),c()) -> f(X,c())
        - Signature:
            {f/2} / {a/0,b/0,c/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 4.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 2
          a_1() -> 3
          a_2() -> 7
          a_3() -> 10
          b_0() -> 2
          b_1() -> 4
          b_2() -> 9
          c_0() -> 2
          c_1() -> 4
          c_2() -> 6
          c_3() -> 8
          c_4() -> 11
          f_0(2,2) -> 1
          f_1(2,4) -> 1
          f_1(3,3) -> 1
          f_1(3,4) -> 1
          f_2(3,6) -> 1
          f_2(5,6) -> 1
          f_2(7,9) -> 1
          f_3(7,8) -> 1
          f_4(10,11) -> 1
          s_0(2) -> 2
          s_1(3) -> 3
          s_2(7) -> 5
          s_3(10) -> 7
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(a(),a()) -> f(a(),b())
            f(a(),b()) -> f(s(a()),c())
            f(c(),c()) -> f(a(),a())
            f(s(X),c()) -> f(X,c())
        - Signature:
            {f/2} / {a/0,b/0,c/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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