/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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:
            dbl(0(),y) -> y
            dbl(S(0()),S(0())) -> S(S(S(S(0()))))
            unsafe(0()) -> 0()
            unsafe(S(x)) -> dbl(unsafe(x),0())
        - Signature:
            {dbl/2,unsafe/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,unsafe} and constructors {0,S}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dbl(0(),y) -> y
            dbl(S(0()),S(0())) -> S(S(S(S(0()))))
            unsafe(0()) -> 0()
            unsafe(S(x)) -> dbl(unsafe(x),0())
        - Signature:
            {dbl/2,unsafe/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,unsafe} and constructors {0,S}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
*** Step 1.a:1.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            dbl(0(),y) -> y
            dbl(S(0()),S(0())) -> S(S(S(S(0()))))
            unsafe(0()) -> 0()
            unsafe(S(x)) -> dbl(unsafe(x),0())
        - Signature:
            {dbl/2,unsafe/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,unsafe} 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 "S") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "S") :: ["A"(1)] -(1)-> "A"(1)
          F (TrsFun "dbl") :: ["A"(0) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "main") :: ["A"(1)] -(1)-> "A"(0)
          F (TrsFun "unsafe") :: ["A"(1)] -(1)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          dbl(0(),y) -> y
          dbl(S(0()),S(0())) -> S(S(S(S(0()))))
          unsafe(0()) -> 0()
          unsafe(S(x)) -> dbl(unsafe(x),0())
          main(x1) -> unsafe(x1)
        2. Weak:
          
        

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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            dbl(0(),y) -> y
            dbl(S(0()),S(0())) -> S(S(S(S(0()))))
            unsafe(0()) -> 0()
            unsafe(S(x)) -> dbl(unsafe(x),0())
        - Signature:
            {dbl/2,unsafe/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,unsafe} and constructors {0,S}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_0() -> 3
          0_1() -> 4
          0_1() -> 8
          0_1() -> 9
          S_0(1) -> 2
          S_0(1) -> 3
          S_0(2) -> 2
          S_0(2) -> 3
          S_1(5) -> 3
          S_1(6) -> 5
          S_1(7) -> 6
          S_1(8) -> 7
          dbl_0(1,1) -> 3
          dbl_0(1,2) -> 3
          dbl_0(2,1) -> 3
          dbl_0(2,2) -> 3
          dbl_1(9,8) -> 4
          dbl_1(9,9) -> 9
          unsafe_0(1) -> 4
          unsafe_0(2) -> 4
          unsafe_1(1) -> 9
          unsafe_1(2) -> 9
          1 -> 3
          2 -> 3
          8 -> 4
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            dbl(0(),y) -> y
            dbl(S(0()),S(0())) -> S(S(S(S(0()))))
            unsafe(0()) -> 0()
            unsafe(S(x)) -> dbl(unsafe(x),0())
        - Signature:
            {dbl/2,unsafe/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,unsafe} and constructors {0,S}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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