/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),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,XS)
            from(X) -> cons(X,from(s(X)))
        - Signature:
            {after/2,from/1} / {0/0,cons/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {after,from} and constructors {0,cons,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,XS)
            from(X) -> cons(X,from(s(X)))
        - Signature:
            {after/2,from/1} / {0/0,cons/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {after,from} and constructors {0,cons,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 2.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,XS)
            from(X) -> cons(X,from(s(X)))
        - Signature:
            {after/2,from/1} / {0/0,cons/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {after,from} and constructors {0,cons,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, 0, 0)
          F (TrsFun "after") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "cons") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "from") :: ["A"(1, 1, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "main") :: ["A"(0, 0, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(2, 2, 1)] -(1)-> "A"(1, 1, 1)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          after(0(),XS) -> XS
          from(X) -> cons(X,from(s(X)))
          main(x1) -> from(x1)
        2. Weak:
          after(s(N),cons(X,XS)) -> after(N,XS)
        
** Step 2.a:2: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            after(s(N),cons(X,XS)) -> after(N,XS)
        - Weak TRS:
            after(0(),XS) -> XS
            from(X) -> cons(X,from(s(X)))
        - Signature:
            {after/2,from/1} / {0/0,cons/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {after,from} and constructors {0,cons,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"(1)
          F (TrsFun "after") :: ["A"(1) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "from") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "main") :: ["A"(1) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "s") :: ["A"(1)] -(1)-> "A"(1)
          F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          after(s(N),cons(X,XS)) -> after(N,XS)
          main(x1,x2) -> after(x1,x2)
        2. Weak:
          
        

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

WORST_CASE(Omega(n^1),?)