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:
            -'(z0,0()) -> c()
            -'(s(z0),s(z1)) -> c1(-'(z0,z1))
            F(s(z0),s(z1)) -> c10(F(-(z0,min(z0,z1)),s(twice(min(z0,z1)))),TWICE(min(z0,z1)),MIN(z0,z1))
            F(s(z0),s(z1)) -> c7(F(-(z1,min(z0,z1)),s(twice(min(z0,z1)))),-'(z1,min(z0,z1)),MIN(z0,z1))
            F(s(z0),s(z1)) -> c8(F(-(z1,min(z0,z1)),s(twice(min(z0,z1)))),TWICE(min(z0,z1)),MIN(z0,z1))
            F(s(z0),s(z1)) -> c9(F(-(z0,min(z0,z1)),s(twice(min(z0,z1)))),-'(z0,min(z0,z1)),MIN(z0,z1))
            MIN(z0,0()) -> c2()
            MIN(0(),z0) -> c3()
            MIN(s(z0),s(z1)) -> c4(MIN(z0,z1))
            TWICE(0()) -> c5()
            TWICE(s(z0)) -> c6(TWICE(z0))
        - Weak TRS:
            -(z0,0()) -> z0
            -(s(z0),s(z1)) -> -(z0,z1)
            f(s(z0),s(z1)) -> f(-(z0,min(z0,z1)),s(twice(min(z0,z1))))
            f(s(z0),s(z1)) -> f(-(z1,min(z0,z1)),s(twice(min(z0,z1))))
            min(z0,0()) -> 0()
            min(0(),z0) -> 0()
            min(s(z0),s(z1)) -> s(min(z0,z1))
            twice(0()) -> 0()
            twice(s(z0)) -> s(s(twice(z0)))
        - Signature:
            {-/2,-'/2,F/2,MIN/2,TWICE/1,f/2,min/2,twice/1} / {0/0,c/0,c1/1,c10/3,c2/0,c3/0,c4/1,c5/0,c6/1,c7/3,c8/3,c9/3
            ,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,-',F,MIN,TWICE,f,min,twice} and constructors {0,c,c1
            ,c10,c2,c3,c4,c5,c6,c7,c8,c9,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            -'(z0,0()) -> c()
            -'(s(z0),s(z1)) -> c1(-'(z0,z1))
            F(s(z0),s(z1)) -> c10(F(-(z0,min(z0,z1)),s(twice(min(z0,z1)))),TWICE(min(z0,z1)),MIN(z0,z1))
            F(s(z0),s(z1)) -> c7(F(-(z1,min(z0,z1)),s(twice(min(z0,z1)))),-'(z1,min(z0,z1)),MIN(z0,z1))
            F(s(z0),s(z1)) -> c8(F(-(z1,min(z0,z1)),s(twice(min(z0,z1)))),TWICE(min(z0,z1)),MIN(z0,z1))
            F(s(z0),s(z1)) -> c9(F(-(z0,min(z0,z1)),s(twice(min(z0,z1)))),-'(z0,min(z0,z1)),MIN(z0,z1))
            MIN(z0,0()) -> c2()
            MIN(0(),z0) -> c3()
            MIN(s(z0),s(z1)) -> c4(MIN(z0,z1))
            TWICE(0()) -> c5()
            TWICE(s(z0)) -> c6(TWICE(z0))
        - Weak TRS:
            -(z0,0()) -> z0
            -(s(z0),s(z1)) -> -(z0,z1)
            f(s(z0),s(z1)) -> f(-(z0,min(z0,z1)),s(twice(min(z0,z1))))
            f(s(z0),s(z1)) -> f(-(z1,min(z0,z1)),s(twice(min(z0,z1))))
            min(z0,0()) -> 0()
            min(0(),z0) -> 0()
            min(s(z0),s(z1)) -> s(min(z0,z1))
            twice(0()) -> 0()
            twice(s(z0)) -> s(s(twice(z0)))
        - Signature:
            {-/2,-'/2,F/2,MIN/2,TWICE/1,f/2,min/2,twice/1} / {0/0,c/0,c1/1,c10/3,c2/0,c3/0,c4/1,c5/0,c6/1,c7/3,c8/3,c9/3
            ,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,-',F,MIN,TWICE,f,min,twice} and constructors {0,c,c1
            ,c10,c2,c3,c4,c5,c6,c7,c8,c9,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            -'(z0,0()) -> c()
            -'(s(z0),s(z1)) -> c1(-'(z0,z1))
            F(s(z0),s(z1)) -> c10(F(-(z0,min(z0,z1)),s(twice(min(z0,z1)))),TWICE(min(z0,z1)),MIN(z0,z1))
            F(s(z0),s(z1)) -> c7(F(-(z1,min(z0,z1)),s(twice(min(z0,z1)))),-'(z1,min(z0,z1)),MIN(z0,z1))
            F(s(z0),s(z1)) -> c8(F(-(z1,min(z0,z1)),s(twice(min(z0,z1)))),TWICE(min(z0,z1)),MIN(z0,z1))
            F(s(z0),s(z1)) -> c9(F(-(z0,min(z0,z1)),s(twice(min(z0,z1)))),-'(z0,min(z0,z1)),MIN(z0,z1))
            MIN(z0,0()) -> c2()
            MIN(0(),z0) -> c3()
            MIN(s(z0),s(z1)) -> c4(MIN(z0,z1))
            TWICE(0()) -> c5()
            TWICE(s(z0)) -> c6(TWICE(z0))
        - Weak TRS:
            -(z0,0()) -> z0
            -(s(z0),s(z1)) -> -(z0,z1)
            f(s(z0),s(z1)) -> f(-(z0,min(z0,z1)),s(twice(min(z0,z1))))
            f(s(z0),s(z1)) -> f(-(z1,min(z0,z1)),s(twice(min(z0,z1))))
            min(z0,0()) -> 0()
            min(0(),z0) -> 0()
            min(s(z0),s(z1)) -> s(min(z0,z1))
            twice(0()) -> 0()
            twice(s(z0)) -> s(s(twice(z0)))
        - Signature:
            {-/2,-'/2,F/2,MIN/2,TWICE/1,f/2,min/2,twice/1} / {0/0,c/0,c1/1,c10/3,c2/0,c3/0,c4/1,c5/0,c6/1,c7/3,c8/3,c9/3
            ,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,-',F,MIN,TWICE,f,min,twice} and constructors {0,c,c1
            ,c10,c2,c3,c4,c5,c6,c7,c8,c9,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          -'(x,y){x -> s(x),y -> s(y)} =
            -'(s(x),s(y)) ->^+ c1(-'(x,y))
              = C[-'(x,y) = -'(x,y){}]

WORST_CASE(Omega(n^1),?)