/bin/sh: line 1:   990 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-30 > /tmp/SMTS809-31
/bin/sh: line 1:  1055 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-78 > /tmp/SMTS809-79
/bin/sh: line 1:  1074 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-74 > /tmp/SMTS809-75
/bin/sh: line 1:  1051 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-50 > /tmp/SMTS809-51
/bin/sh: line 1:  1076 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-28 > /tmp/SMTS809-29
/bin/sh: line 1:  1067 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-76 > /tmp/SMTS809-77
/bin/sh: line 1:  1061 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-43 > /tmp/SMTS809-45
/bin/sh: line 1:  1026 Quit                    (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-53 > /tmp/SMTS809-54
WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(c(X,s(Y))) -> f(c(s(X),Y))
            g(c(s(X),Y)) -> f(c(X,s(Y)))
        - Signature:
            {f/1,g/1} / {c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(c(X,s(Y))) -> f(c(s(X),Y))
            g(c(s(X),Y)) -> f(c(X,s(Y)))
        - Signature:
            {f/1,g/1} / {c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
*** Step 1.a:1.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            f(c(X,s(Y))) -> f(c(s(X),Y))
            g(c(s(X),Y)) -> f(c(X,s(Y)))
        - Signature:
            {f/1,g/1} / {c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "c") :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          F (TrsFun "f") :: ["A"(1)] -(0)-> "A"(0)
          F (TrsFun "g") :: ["A"(1)] -(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)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          f(c(X,s(Y))) -> f(c(s(X),Y))
          g(c(s(X),Y)) -> f(c(X,s(Y)))
          main(x1) -> g(x1)
        2. Weak:
          
        

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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(c(X,s(Y))) -> f(c(s(X),Y))
            g(c(s(X),Y)) -> f(c(X,s(Y)))
        - Signature:
            {f/1,g/1} / {c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          c_0(1,1) -> 1
          c_0(1,4) -> 1
          c_0(4,1) -> 1
          c_0(4,4) -> 1
          c_1(1,6) -> 7
          c_1(4,6) -> 7
          c_1(6,1) -> 5
          c_1(6,4) -> 5
          c_1(10,1) -> 7
          c_1(10,4) -> 7
          c_2(9,1) -> 8
          c_2(9,4) -> 8
          c_2(9,6) -> 8
          f_0(1) -> 2
          f_0(4) -> 2
          f_1(5) -> 2
          f_1(7) -> 3
          f_2(8) -> 3
          g_0(1) -> 3
          g_0(4) -> 3
          s_0(1) -> 4
          s_0(4) -> 4
          s_1(1) -> 6
          s_1(4) -> 6
          s_1(6) -> 6
          s_1(9) -> 10
          s_1(10) -> 10
          s_2(1) -> 9
          s_2(4) -> 9
          s_2(9) -> 9
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(c(X,s(Y))) -> f(c(s(X),Y))
            g(c(s(X),Y)) -> f(c(X,s(Y)))
        - Signature:
            {f/1,g/1} / {c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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