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()) -> c8()
            -'(s(z0),s(z1)) -> c9(-'(z0,z1))
            F(s(z0),s(z1)) -> c11(F(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
                                 ,-'(max(s(z0),s(z1)),min(s(z0),s(z1)))
                                 ,MAX(s(z0),s(z1)))
            F(s(z0),s(z1)) -> c12(F(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
                                 ,-'(max(s(z0),s(z1)),min(s(z0),s(z1)))
                                 ,MIN(s(z0),s(z1)))
            F(s(z0),s(z1)) -> c13(F(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
                                 ,P(twice(min(z0,z1)))
                                 ,TWICE(min(z0,z1))
                                 ,MIN(z0,z1))
            MAX(z0,0()) -> c4()
            MAX(0(),z0) -> c3()
            MAX(s(z0),s(z1)) -> c5(MAX(z0,z1))
            MIN(z0,0()) -> c1()
            MIN(0(),z0) -> c()
            MIN(s(z0),s(z1)) -> c2(MIN(z0,z1))
            P(s(z0)) -> c10()
            TWICE(0()) -> c6()
            TWICE(s(z0)) -> c7(TWICE(z0))
        - Weak TRS:
            -(z0,0()) -> z0
            -(s(z0),s(z1)) -> -(z0,z1)
            f(s(z0),s(z1)) -> f(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
            max(z0,0()) -> z0
            max(0(),z0) -> z0
            max(s(z0),s(z1)) -> s(max(z0,z1))
            min(z0,0()) -> 0()
            min(0(),z0) -> 0()
            min(s(z0),s(z1)) -> s(min(z0,z1))
            p(s(z0)) -> z0
            twice(0()) -> 0()
            twice(s(z0)) -> s(s(twice(z0)))
        - Signature:
            {-/2,-'/2,F/2,MAX/2,MIN/2,P/1,TWICE/1,f/2,max/2,min/2,p/1,twice/1} / {0/0,c/0,c1/0,c10/0,c11/3,c12/3,c13/4
            ,c2/1,c3/0,c4/0,c5/1,c6/0,c7/1,c8/0,c9/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,-',F,MAX,MIN,P,TWICE,f,max,min,p
            ,twice} and constructors {0,c,c1,c10,c11,c12,c13,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()) -> c8()
            -'(s(z0),s(z1)) -> c9(-'(z0,z1))
            F(s(z0),s(z1)) -> c11(F(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
                                 ,-'(max(s(z0),s(z1)),min(s(z0),s(z1)))
                                 ,MAX(s(z0),s(z1)))
            F(s(z0),s(z1)) -> c12(F(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
                                 ,-'(max(s(z0),s(z1)),min(s(z0),s(z1)))
                                 ,MIN(s(z0),s(z1)))
            F(s(z0),s(z1)) -> c13(F(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
                                 ,P(twice(min(z0,z1)))
                                 ,TWICE(min(z0,z1))
                                 ,MIN(z0,z1))
            MAX(z0,0()) -> c4()
            MAX(0(),z0) -> c3()
            MAX(s(z0),s(z1)) -> c5(MAX(z0,z1))
            MIN(z0,0()) -> c1()
            MIN(0(),z0) -> c()
            MIN(s(z0),s(z1)) -> c2(MIN(z0,z1))
            P(s(z0)) -> c10()
            TWICE(0()) -> c6()
            TWICE(s(z0)) -> c7(TWICE(z0))
        - Weak TRS:
            -(z0,0()) -> z0
            -(s(z0),s(z1)) -> -(z0,z1)
            f(s(z0),s(z1)) -> f(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
            max(z0,0()) -> z0
            max(0(),z0) -> z0
            max(s(z0),s(z1)) -> s(max(z0,z1))
            min(z0,0()) -> 0()
            min(0(),z0) -> 0()
            min(s(z0),s(z1)) -> s(min(z0,z1))
            p(s(z0)) -> z0
            twice(0()) -> 0()
            twice(s(z0)) -> s(s(twice(z0)))
        - Signature:
            {-/2,-'/2,F/2,MAX/2,MIN/2,P/1,TWICE/1,f/2,max/2,min/2,p/1,twice/1} / {0/0,c/0,c1/0,c10/0,c11/3,c12/3,c13/4
            ,c2/1,c3/0,c4/0,c5/1,c6/0,c7/1,c8/0,c9/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,-',F,MAX,MIN,P,TWICE,f,max,min,p
            ,twice} and constructors {0,c,c1,c10,c11,c12,c13,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()) -> c8()
            -'(s(z0),s(z1)) -> c9(-'(z0,z1))
            F(s(z0),s(z1)) -> c11(F(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
                                 ,-'(max(s(z0),s(z1)),min(s(z0),s(z1)))
                                 ,MAX(s(z0),s(z1)))
            F(s(z0),s(z1)) -> c12(F(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
                                 ,-'(max(s(z0),s(z1)),min(s(z0),s(z1)))
                                 ,MIN(s(z0),s(z1)))
            F(s(z0),s(z1)) -> c13(F(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
                                 ,P(twice(min(z0,z1)))
                                 ,TWICE(min(z0,z1))
                                 ,MIN(z0,z1))
            MAX(z0,0()) -> c4()
            MAX(0(),z0) -> c3()
            MAX(s(z0),s(z1)) -> c5(MAX(z0,z1))
            MIN(z0,0()) -> c1()
            MIN(0(),z0) -> c()
            MIN(s(z0),s(z1)) -> c2(MIN(z0,z1))
            P(s(z0)) -> c10()
            TWICE(0()) -> c6()
            TWICE(s(z0)) -> c7(TWICE(z0))
        - Weak TRS:
            -(z0,0()) -> z0
            -(s(z0),s(z1)) -> -(z0,z1)
            f(s(z0),s(z1)) -> f(-(max(s(z0),s(z1)),min(s(z0),s(z1))),p(twice(min(z0,z1))))
            max(z0,0()) -> z0
            max(0(),z0) -> z0
            max(s(z0),s(z1)) -> s(max(z0,z1))
            min(z0,0()) -> 0()
            min(0(),z0) -> 0()
            min(s(z0),s(z1)) -> s(min(z0,z1))
            p(s(z0)) -> z0
            twice(0()) -> 0()
            twice(s(z0)) -> s(s(twice(z0)))
        - Signature:
            {-/2,-'/2,F/2,MAX/2,MIN/2,P/1,TWICE/1,f/2,max/2,min/2,p/1,twice/1} / {0/0,c/0,c1/0,c10/0,c11/3,c12/3,c13/4
            ,c2/1,c3/0,c4/0,c5/1,c6/0,c7/1,c8/0,c9/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,-',F,MAX,MIN,P,TWICE,f,max,min,p
            ,twice} and constructors {0,c,c1,c10,c11,c12,c13,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)) ->^+ c9(-'(x,y))
              = C[-'(x,y) = -'(x,y){}]

WORST_CASE(Omega(n^1),?)