/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^2))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^2))
    + Considered Problem:
        - Strict TRS:
            if_mod(false(),s(x),s(y)) -> s(x)
            if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            mod(0(),y) -> 0()
            mod(s(x),0()) -> 0()
            mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
        - Signature:
            {if_mod/3,le/2,minus/2,mod/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if_mod,le,minus,mod} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if_mod(false(),s(x),s(y)) -> s(x)
            if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            mod(0(),y) -> 0()
            mod(s(x),0()) -> 0()
            mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
        - Signature:
            {if_mod/3,le/2,minus/2,mod/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if_mod,le,minus,mod} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          le(x,y){x -> s(x),y -> s(y)} =
            le(s(x),s(y)) ->^+ le(x,y)
              = C[le(x,y) = le(x,y){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            if_mod(false(),s(x),s(y)) -> s(x)
            if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            mod(0(),y) -> 0()
            mod(s(x),0()) -> 0()
            mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
        - Signature:
            {if_mod/3,le/2,minus/2,mod/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if_mod,le,minus,mod} and constructors {0,false,s,true}
    + Applied Processor:
        Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(0, 0)
          0 :: [] -(0)-> "A"(1, 0)
          0 :: [] -(0)-> "A"(4, 4)
          false :: [] -(0)-> "A"(0, 0)
          if_mod :: ["A"(0, 0) x "A"(0, 4) x "A"(0, 0)] -(3)-> "A"(0, 0)
          le :: ["A"(0, 0) x "A"(1, 0)] -(1)-> "A"(0, 0)
          minus :: ["A"(4, 4) x "A"(0, 0)] -(1)-> "A"(4, 4)
          mod :: ["A"(4, 4) x "A"(0, 0)] -(1)-> "A"(0, 0)
          s :: ["A"(4, 4)] -(0)-> "A"(0, 4)
          s :: ["A"(0, 0)] -(0)-> "A"(0, 0)
          s :: ["A"(1, 0)] -(1)-> "A"(1, 0)
          s :: ["A"(8, 4)] -(4)-> "A"(4, 4)
          true :: [] -(0)-> "A"(0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "0_A" :: [] -(0)-> "A"(0)
          "false_A" :: [] -(0)-> "A"(0)
          "s_A" :: ["A"(0)] -(0)-> "A"(0)
          "true_A" :: [] -(0)-> "A"(0)
        

WORST_CASE(Omega(n^1),O(n^2))