/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:
            ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
            u21(ackout(X),Y) -> u22(ackin(Y,X))
        - Signature:
            {ackin/2,u21/2} / {ackout/1,s/1,u22/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
            u21(ackout(X),Y) -> u22(ackin(Y,X))
        - Signature:
            {ackin/2,u21/2} / {ackout/1,s/1,u22/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
*** Step 1.a:1.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
            u21(ackout(X),Y) -> u22(ackin(Y,X))
        - Signature:
            {ackin/2,u21/2} / {ackout/1,s/1,u22/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "ackin") :: ["A"(1, 1, 1) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "ackout") :: ["A"(0, 0, 0)] -(0)-> "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"(2, 2, 1)] -(1)-> "A"(1, 1, 1)
          F (TrsFun "s") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(1, 1, 1)] -(1)-> "A"(1, 0, 1)
          F (TrsFun "u21") :: ["A"(0, 0, 0) x "A"(1, 1, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "u22") :: ["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:
          ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
          u21(ackout(X),Y) -> u22(ackin(Y,X))
          main(x1,x2) -> u21(x1,x2)
        2. Weak:
          
        

*** Step 1.a:1.b:1: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
            u21(ackout(X),Y) -> u22(ackin(Y,X))
        - Signature:
            {ackin/2,u21/2} / {ackout/1,s/1,u22/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ackin(s(x),y){y -> s(y)} =
            ackin(s(x),s(y)) ->^+ u21(ackin(s(x),y),x)
              = C[ackin(s(x),y) = ackin(s(x),y){}]

** Step 1.b:1: Ara.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
            u21(ackout(X),Y) -> u22(ackin(Y,X))
        - Signature:
            {ackin/2,u21/2} / {ackout/1,s/1,u22/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 1, araTimeout = 8, araRuleShifting = Just 1, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "ackin") :: ["A"(0) x "A"(2)] -(0)-> "A"(2)
          F (TrsFun "ackout") :: ["A"(2)] -(2)-> "A"(2)
          F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "s") :: ["A"(2)] -(2)-> "A"(2)
          F (TrsFun "u21") :: ["A"(2) x "A"(0)] -(1)-> "A"(2)
          F (TrsFun "u22") :: ["A"(2)] -(2)-> "A"(2)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
          u21(ackout(X),Y) -> u22(ackin(Y,X))
        2. Weak:
          
        

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