/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),O(n^2))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^2))
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(x,s(y)) -> if(le(x,s(y)),0(),p(minus(x,p(s(y)))))
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {if/3,le/2,minus/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if,le,minus,p} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(x,s(y)) -> if(le(x,s(y)),0(),p(minus(x,p(s(y)))))
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {if/3,le/2,minus/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if,le,minus,p} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(x,s(y)) -> if(le(x,s(y)),0(),p(minus(x,p(s(y)))))
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {if/3,le/2,minus/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if,le,minus,p} 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(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(x,s(y)) -> if(le(x,s(y)),0(),p(minus(x,p(s(y)))))
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {if/3,le/2,minus/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if,le,minus,p} and constructors {0,false,s,true}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "0") :: [] -(0)-> "A"(0, 0)
          F (TrsFun "0") :: [] -(0)-> "A"(1, 0)
          F (TrsFun "0") :: [] -(0)-> "A"(12, 6)
          F (TrsFun "0") :: [] -(0)-> "A"(6, 6)
          F (TrsFun "false") :: [] -(0)-> "A"(0, 0)
          F (TrsFun "if") :: ["A"(0, 0) x "A"(6, 6) x "A"(6, 6)] -(1)-> "A"(6, 6)
          F (TrsFun "le") :: ["A"(0, 0) x "A"(1, 0)] -(1)-> "A"(0, 0)
          F (TrsFun "minus") :: ["A"(6, 6) x "A"(12, 6)] -(1)-> "A"(6, 6)
          F (TrsFun "p") :: ["A"(6, 6)] -(1)-> "A"(12, 6)
          F (TrsFun "s") :: ["A"(0, 0)] -(0)-> "A"(0, 0)
          F (TrsFun "s") :: ["A"(1, 0)] -(1)-> "A"(1, 0)
          F (TrsFun "s") :: ["A"(18, 6)] -(12)-> "A"(12, 6)
          F (TrsFun "s") :: ["A"(12, 6)] -(6)-> "A"(6, 6)
          F (TrsFun "true") :: [] -(0)-> "A"(0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        

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