/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(?,O(n^1))
* Step 1: Sum.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {p} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  MAYBE
    + Considered Problem:
        - Strict TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {p} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {p} 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"(1)
          F (TrsFun "0") :: [] -(0)-> "A"(0)
          F (TrsFun "main") :: ["A"(0) x "A"(1) x "A"(1)] -(1)-> "A"(0)
          F (TrsFun "p") :: ["A"(0) x "A"(1) x "A"(1)] -(1)-> "A"(0)
          F (TrsFun "s") :: ["A"(1)] -(1)-> "A"(1)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          p(m,n,s(r)) -> p(m,r,n)
          p(m,0(),0()) -> m
          p(m,s(n),0()) -> p(0(),n,m)
          main(x1,x2,x3) -> p(x1,x2,x3)
        2. Weak:
          
        

** Step 1.b:1: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {p} and constructors {0,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          {p}
        TcT has computed the following interpretation:
          p(0) = [0]         
          p(p) = [2] x1 + [1]
          p(s) = [0]         
        
        Following rules are strictly oriented:
        p(m,0(),0()) = [2] m + [1]
                     > [1] m + [0]
                     = m          
        
        
        Following rules are (at-least) weakly oriented:
          p(m,n,s(r)) =  [2] m + [1]
                      >= [2] m + [1]
                      =  p(m,r,n)   
        
        p(m,s(n),0()) =  [2] m + [1]
                      >= [1]        
                      =  p(0(),n,m) 
        
** Step 1.b:2: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,s(n),0()) -> p(0(),n,m)
        - Weak TRS:
            p(m,0(),0()) -> m
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {p} and constructors {0,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          {p}
        TcT has computed the following interpretation:
          p(0) = [0]                           
          p(p) = [1] x1 + [1] x2 + [1] x3 + [0]
          p(s) = [1] x1 + [2]                  
        
        Following rules are strictly oriented:
          p(m,n,s(r)) = [1] m + [1] n + [1] r + [2]
                      > [1] m + [1] n + [1] r + [0]
                      = p(m,r,n)                   
        
        p(m,s(n),0()) = [1] m + [1] n + [2]        
                      > [1] m + [1] n + [0]        
                      = p(0(),n,m)                 
        
        
        Following rules are (at-least) weakly oriented:
        p(m,0(),0()) =  [1] m + [0]
                     >= [1] m + [0]
                     =  m          
        
** Step 1.b:3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {p} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))