/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),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
*** Step 1.a:1.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "Cons") :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "Nil") :: [] -(0)-> "A"(1)
          F (TrsFun "Nil") :: [] -(0)-> "A"(0)
          F (TrsFun "anchored") :: ["A"(1) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "goal") :: ["A"(1) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "main") :: ["A"(1) x "A"(0)] -(1)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
          anchored(Nil(),y) -> y
          goal(x,y) -> anchored(x,y)
          main(x1,x2) -> goal(x1,x2)
        2. Weak:
          
        

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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          Cons_0(1,1) -> 1
          Cons_0(1,1) -> 3
          Cons_0(1,1) -> 4
          Cons_0(1,2) -> 1
          Cons_0(1,2) -> 3
          Cons_0(1,2) -> 4
          Cons_0(2,1) -> 1
          Cons_0(2,1) -> 3
          Cons_0(2,1) -> 4
          Cons_0(2,2) -> 1
          Cons_0(2,2) -> 3
          Cons_0(2,2) -> 4
          Cons_1(6,1) -> 3
          Cons_1(6,1) -> 4
          Cons_1(6,1) -> 5
          Cons_1(6,2) -> 3
          Cons_1(6,2) -> 4
          Cons_1(6,2) -> 5
          Cons_1(6,5) -> 3
          Cons_1(6,5) -> 4
          Cons_1(6,5) -> 5
          Cons_1(7,8) -> 6
          Nil_0() -> 2
          Nil_0() -> 3
          Nil_0() -> 4
          Nil_1() -> 7
          Nil_1() -> 8
          anchored_0(1,1) -> 3
          anchored_0(1,2) -> 3
          anchored_0(2,1) -> 3
          anchored_0(2,2) -> 3
          anchored_1(1,1) -> 4
          anchored_1(1,2) -> 4
          anchored_1(1,5) -> 3
          anchored_1(1,5) -> 4
          anchored_1(2,1) -> 4
          anchored_1(2,2) -> 4
          anchored_1(2,5) -> 3
          anchored_1(2,5) -> 4
          goal_0(1,1) -> 4
          goal_0(1,2) -> 4
          goal_0(2,1) -> 4
          goal_0(2,2) -> 4
          1 -> 3
          1 -> 4
          2 -> 3
          2 -> 4
          5 -> 3
          5 -> 4
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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