/bin/sh: line 1: 55799 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP55648-90 > /tmp/SMTS55648-91
/bin/sh: line 1: 55832 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP55648-88 > /tmp/SMTS55648-89
/bin/sh: line 1: 55838 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP55648-76 > /tmp/SMTS55648-77
/bin/sh: line 1: 55806 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP55648-47 > /tmp/SMTS55648-49
WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            sqr(x) -> *(x,x)
            sum(0()) -> 0()
            sum(s(x)) -> +(*(s(x),s(x)),sum(x))
            sum(s(x)) -> +(sqr(s(x)),sum(x))
        - Signature:
            {sqr/1,sum/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {sqr,sum} and constructors {*,+,0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            sqr(x) -> *(x,x)
            sum(0()) -> 0()
            sum(s(x)) -> +(*(s(x),s(x)),sum(x))
            sum(s(x)) -> +(sqr(s(x)),sum(x))
        - Signature:
            {sqr/1,sum/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {sqr,sum} and constructors {*,+,0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
*** Step 1.a:1.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            sqr(x) -> *(x,x)
            sum(0()) -> 0()
            sum(s(x)) -> +(*(s(x),s(x)),sum(x))
            sum(s(x)) -> +(sqr(s(x)),sum(x))
        - Signature:
            {sqr/1,sum/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {sqr,sum} and constructors {*,+,0,s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "*") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "+") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "0") :: [] -(0)-> "A"(1)
          F (TrsFun "0") :: [] -(0)-> "A"(0)
          F (TrsFun "main") :: ["A"(1)] -(1)-> "A"(0)
          F (TrsFun "s") :: ["A"(1)] -(1)-> "A"(1)
          F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "sqr") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "sum") :: ["A"(1)] -(1)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          sqr(x) -> *(x,x)
          sum(0()) -> 0()
          sum(s(x)) -> +(*(s(x),s(x)),sum(x))
          sum(s(x)) -> +(sqr(s(x)),sum(x))
          main(x1) -> sum(x1)
        2. Weak:
          
        

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

** Step 1.b:1: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            sqr(x) -> *(x,x)
            sum(0()) -> 0()
            sum(s(x)) -> +(*(s(x),s(x)),sum(x))
            sum(s(x)) -> +(sqr(s(x)),sum(x))
        - Signature:
            {sqr/1,sum/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {sqr,sum} and constructors {*,+,0,s}
    + 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(+) = {1,2}
        
        Following symbols are considered usable:
          {sqr,sum}
        TcT has computed the following interpretation:
            p(*) = [0]                  
            p(+) = [1] x1 + [1] x2 + [0]
            p(0) = [0]                  
            p(s) = [1] x1 + [14]        
          p(sqr) = [0]                  
          p(sum) = [1] x1 + [9]         
        
        Following rules are strictly oriented:
         sum(0()) = [9]                   
                  > [0]                   
                  = 0()                   
        
        sum(s(x)) = [1] x + [23]          
                  > [1] x + [9]           
                  = +(*(s(x),s(x)),sum(x))
        
        sum(s(x)) = [1] x + [23]          
                  > [1] x + [9]           
                  = +(sqr(s(x)),sum(x))   
        
        
        Following rules are (at-least) weakly oriented:
        sqr(x) =  [0]   
               >= [0]   
               =  *(x,x)
        
** Step 1.b:2: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            sqr(x) -> *(x,x)
        - Weak TRS:
            sum(0()) -> 0()
            sum(s(x)) -> +(*(s(x),s(x)),sum(x))
            sum(s(x)) -> +(sqr(s(x)),sum(x))
        - Signature:
            {sqr/1,sum/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {sqr,sum} and constructors {*,+,0,s}
    + 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(+) = {1,2}
        
        Following symbols are considered usable:
          {sqr,sum}
        TcT has computed the following interpretation:
            p(*) = [0]                  
            p(+) = [1] x1 + [1] x2 + [0]
            p(0) = [11]                 
            p(s) = [1] x1 + [2]         
          p(sqr) = [1]                  
          p(sum) = [1] x1 + [6]         
        
        Following rules are strictly oriented:
        sqr(x) = [1]   
               > [0]   
               = *(x,x)
        
        
        Following rules are (at-least) weakly oriented:
         sum(0()) =  [17]                  
                  >= [11]                  
                  =  0()                   
        
        sum(s(x)) =  [1] x + [8]           
                  >= [1] x + [6]           
                  =  +(*(s(x),s(x)),sum(x))
        
        sum(s(x)) =  [1] x + [8]           
                  >= [1] x + [7]           
                  =  +(sqr(s(x)),sum(x))   
        
** Step 1.b:3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            sqr(x) -> *(x,x)
            sum(0()) -> 0()
            sum(s(x)) -> +(*(s(x),s(x)),sum(x))
            sum(s(x)) -> +(sqr(s(x)),sum(x))
        - Signature:
            {sqr/1,sum/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {sqr,sum} and constructors {*,+,0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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