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

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

WORST_CASE(Omega(n^1),?)