/bin/sh: line 1: 45366 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP45290-24 > /tmp/SMTS45290-25
WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,revapp} 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:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,revapp} and constructors {Cons,Nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
*** Step 1.a:1.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,revapp} 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 "goal") :: ["A"(1) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "main") :: ["A"(1) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "revapp") :: ["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:
          goal(xs,ys) -> revapp(xs,ys)
          revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
          revapp(Nil(),rest) -> rest
          main(x1,x2) -> revapp(x1,x2)
        2. Weak:
          
        

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

** Step 1.b:1: DependencyPairs.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,revapp} and constructors {Cons,Nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          goal#(xs,ys) -> c_1(revapp#(xs,ys))
          revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
          revapp#(Nil(),rest) -> c_3()
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            goal#(xs,ys) -> c_1(revapp#(xs,ys))
            revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
            revapp#(Nil(),rest) -> c_3()
        - Weak TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2,goal#/2,revapp#/2} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,revapp#} and constructors {Cons,Nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3}
        by application of
          Pre({3}) = {1,2}.
        Here rules are labelled as follows:
          1: goal#(xs,ys) -> c_1(revapp#(xs,ys))
          2: revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
          3: revapp#(Nil(),rest) -> c_3()
** Step 1.b:3: RemoveWeakSuffixes.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            goal#(xs,ys) -> c_1(revapp#(xs,ys))
            revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
        - Weak DPs:
            revapp#(Nil(),rest) -> c_3()
        - Weak TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2,goal#/2,revapp#/2} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,revapp#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:goal#(xs,ys) -> c_1(revapp#(xs,ys))
             -->_1 revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest))):2
             -->_1 revapp#(Nil(),rest) -> c_3():3
          
          2:S:revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
             -->_1 revapp#(Nil(),rest) -> c_3():3
             -->_1 revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest))):2
          
          3:W:revapp#(Nil(),rest) -> c_3()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: revapp#(Nil(),rest) -> c_3()
** Step 1.b:4: RemoveHeads.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            goal#(xs,ys) -> c_1(revapp#(xs,ys))
            revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
        - Weak TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2,goal#/2,revapp#/2} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,revapp#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:goal#(xs,ys) -> c_1(revapp#(xs,ys))
           -->_1 revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest))):2
        
        2:S:revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
           -->_1 revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest))):2
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(1,goal#(xs,ys) -> c_1(revapp#(xs,ys)))]
** Step 1.b:5: UsableRules.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
        - Weak TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2,goal#/2,revapp#/2} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,revapp#} and constructors {Cons,Nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
** Step 1.b:6: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
        - Signature:
            {goal/2,revapp/2,goal#/2,revapp#/2} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,revapp#} and constructors {Cons,Nil}
    + 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:
          uargs(c_2) = {1}
        
        Following symbols are considered usable:
          {goal#,revapp#}
        TcT has computed the following interpretation:
             p(Cons) = [1] x2 + [4]         
              p(Nil) = [2]                  
             p(goal) = [2] x2 + [1]         
           p(revapp) = [4] x1 + [2] x2 + [2]
            p(goal#) = [1] x1 + [4] x2 + [0]
          p(revapp#) = [4] x1 + [4]         
              p(c_1) = [0]                  
              p(c_2) = [1] x1 + [15]        
              p(c_3) = [0]                  
        
        Following rules are strictly oriented:
        revapp#(Cons(x,xs),rest) = [4] xs + [20]                
                                 > [4] xs + [19]                
                                 = c_2(revapp#(xs,Cons(x,rest)))
        
        
        Following rules are (at-least) weakly oriented:
        
** Step 1.b:7: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            revapp#(Cons(x,xs),rest) -> c_2(revapp#(xs,Cons(x,rest)))
        - Signature:
            {goal/2,revapp/2,goal#/2,revapp#/2} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,revapp#} 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))