tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ACTIVATE(z0) -> c12()
            ACTIVATE(n__add(z0,z1)) -> c10(ADD(activate(z0),activate(z1)),ACTIVATE(z0))
            ACTIVATE(n__add(z0,z1)) -> c11(ADD(activate(z0),activate(z1)),ACTIVATE(z1))
            ACTIVATE(n__fib1(z0,z1)) -> c8(FIB1(activate(z0),activate(z1)),ACTIVATE(z0))
            ACTIVATE(n__fib1(z0,z1)) -> c9(FIB1(activate(z0),activate(z1)),ACTIVATE(z1))
            ADD(z0,z1) -> c5()
            ADD(0(),z0) -> c3()
            ADD(s(z0),z1) -> c4(ADD(z0,z1))
            FIB(z0) -> c(SEL(z0,fib1(s(0()),s(0()))),FIB1(s(0()),s(0())))
            FIB1(z0,z1) -> c1()
            FIB1(z0,z1) -> c2()
            SEL(0(),cons(z0,z1)) -> c6()
            SEL(s(z0),cons(z1,z2)) -> c7(SEL(z0,activate(z2)),ACTIVATE(z2))
        - Weak TRS:
            activate(z0) -> z0
            activate(n__add(z0,z1)) -> add(activate(z0),activate(z1))
            activate(n__fib1(z0,z1)) -> fib1(activate(z0),activate(z1))
            add(z0,z1) -> n__add(z0,z1)
            add(0(),z0) -> z0
            add(s(z0),z1) -> s(add(z0,z1))
            fib(z0) -> sel(z0,fib1(s(0()),s(0())))
            fib1(z0,z1) -> cons(z0,n__fib1(z1,n__add(z0,z1)))
            fib1(z0,z1) -> n__fib1(z0,z1)
            sel(0(),cons(z0,z1)) -> z0
            sel(s(z0),cons(z1,z2)) -> sel(z0,activate(z2))
        - Signature:
            {ACTIVATE/1,ADD/2,FIB/1,FIB1/2,SEL/2,activate/1,add/2,fib/1,fib1/2,sel/2} / {0/0,c/2,c1/0,c10/2,c11/2,c12/0
            ,c2/0,c3/0,c4/1,c5/0,c6/0,c7/2,c8/2,c9/2,cons/2,n__add/2,n__fib1/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ACTIVATE,ADD,FIB,FIB1,SEL,activate,add,fib,fib1
            ,sel} and constructors {0,c,c1,c10,c11,c12,c2,c3,c4,c5,c6,c7,c8,c9,cons,n__add,n__fib1,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ACTIVATE(z0) -> c12()
            ACTIVATE(n__add(z0,z1)) -> c10(ADD(activate(z0),activate(z1)),ACTIVATE(z0))
            ACTIVATE(n__add(z0,z1)) -> c11(ADD(activate(z0),activate(z1)),ACTIVATE(z1))
            ACTIVATE(n__fib1(z0,z1)) -> c8(FIB1(activate(z0),activate(z1)),ACTIVATE(z0))
            ACTIVATE(n__fib1(z0,z1)) -> c9(FIB1(activate(z0),activate(z1)),ACTIVATE(z1))
            ADD(z0,z1) -> c5()
            ADD(0(),z0) -> c3()
            ADD(s(z0),z1) -> c4(ADD(z0,z1))
            FIB(z0) -> c(SEL(z0,fib1(s(0()),s(0()))),FIB1(s(0()),s(0())))
            FIB1(z0,z1) -> c1()
            FIB1(z0,z1) -> c2()
            SEL(0(),cons(z0,z1)) -> c6()
            SEL(s(z0),cons(z1,z2)) -> c7(SEL(z0,activate(z2)),ACTIVATE(z2))
        - Weak TRS:
            activate(z0) -> z0
            activate(n__add(z0,z1)) -> add(activate(z0),activate(z1))
            activate(n__fib1(z0,z1)) -> fib1(activate(z0),activate(z1))
            add(z0,z1) -> n__add(z0,z1)
            add(0(),z0) -> z0
            add(s(z0),z1) -> s(add(z0,z1))
            fib(z0) -> sel(z0,fib1(s(0()),s(0())))
            fib1(z0,z1) -> cons(z0,n__fib1(z1,n__add(z0,z1)))
            fib1(z0,z1) -> n__fib1(z0,z1)
            sel(0(),cons(z0,z1)) -> z0
            sel(s(z0),cons(z1,z2)) -> sel(z0,activate(z2))
        - Signature:
            {ACTIVATE/1,ADD/2,FIB/1,FIB1/2,SEL/2,activate/1,add/2,fib/1,fib1/2,sel/2} / {0/0,c/2,c1/0,c10/2,c11/2,c12/0
            ,c2/0,c3/0,c4/1,c5/0,c6/0,c7/2,c8/2,c9/2,cons/2,n__add/2,n__fib1/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ACTIVATE,ADD,FIB,FIB1,SEL,activate,add,fib,fib1
            ,sel} and constructors {0,c,c1,c10,c11,c12,c2,c3,c4,c5,c6,c7,c8,c9,cons,n__add,n__fib1,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ACTIVATE(z0) -> c12()
            ACTIVATE(n__add(z0,z1)) -> c10(ADD(activate(z0),activate(z1)),ACTIVATE(z0))
            ACTIVATE(n__add(z0,z1)) -> c11(ADD(activate(z0),activate(z1)),ACTIVATE(z1))
            ACTIVATE(n__fib1(z0,z1)) -> c8(FIB1(activate(z0),activate(z1)),ACTIVATE(z0))
            ACTIVATE(n__fib1(z0,z1)) -> c9(FIB1(activate(z0),activate(z1)),ACTIVATE(z1))
            ADD(z0,z1) -> c5()
            ADD(0(),z0) -> c3()
            ADD(s(z0),z1) -> c4(ADD(z0,z1))
            FIB(z0) -> c(SEL(z0,fib1(s(0()),s(0()))),FIB1(s(0()),s(0())))
            FIB1(z0,z1) -> c1()
            FIB1(z0,z1) -> c2()
            SEL(0(),cons(z0,z1)) -> c6()
            SEL(s(z0),cons(z1,z2)) -> c7(SEL(z0,activate(z2)),ACTIVATE(z2))
        - Weak TRS:
            activate(z0) -> z0
            activate(n__add(z0,z1)) -> add(activate(z0),activate(z1))
            activate(n__fib1(z0,z1)) -> fib1(activate(z0),activate(z1))
            add(z0,z1) -> n__add(z0,z1)
            add(0(),z0) -> z0
            add(s(z0),z1) -> s(add(z0,z1))
            fib(z0) -> sel(z0,fib1(s(0()),s(0())))
            fib1(z0,z1) -> cons(z0,n__fib1(z1,n__add(z0,z1)))
            fib1(z0,z1) -> n__fib1(z0,z1)
            sel(0(),cons(z0,z1)) -> z0
            sel(s(z0),cons(z1,z2)) -> sel(z0,activate(z2))
        - Signature:
            {ACTIVATE/1,ADD/2,FIB/1,FIB1/2,SEL/2,activate/1,add/2,fib/1,fib1/2,sel/2} / {0/0,c/2,c1/0,c10/2,c11/2,c12/0
            ,c2/0,c3/0,c4/1,c5/0,c6/0,c7/2,c8/2,c9/2,cons/2,n__add/2,n__fib1/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ACTIVATE,ADD,FIB,FIB1,SEL,activate,add,fib,fib1
            ,sel} and constructors {0,c,c1,c10,c11,c12,c2,c3,c4,c5,c6,c7,c8,c9,cons,n__add,n__fib1,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ACTIVATE(x){x -> n__add(x,y)} =
            ACTIVATE(n__add(x,y)) ->^+ c10(ADD(activate(x),activate(y)),ACTIVATE(x))
              = C[ACTIVATE(x) = ACTIVATE(x){}]

WORST_CASE(Omega(n^1),?)