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()) -> c4()
            *'(z0,s(z1)) -> c5(+'(z0,*(z0,z1)),*'(z0,z1))
            +'(0(),z0) -> c2()
            +'(s(z0),z1) -> c3(+'(z0,z1))
            -'(z0,0()) -> c()
            -'(s(z0),s(z1)) -> c1(-'(z0,z1))
            F(s(z0)) -> c7(F(-(p(*(s(z0),s(z0))),*(s(z0),s(z0))))
                          ,-'(p(*(s(z0),s(z0))),*(s(z0),s(z0)))
                          ,P(*(s(z0),s(z0)))
                          ,*'(s(z0),s(z0)))
            F(s(z0)) -> c8(F(-(p(*(s(z0),s(z0))),*(s(z0),s(z0)))),-'(p(*(s(z0),s(z0))),*(s(z0),s(z0))),*'(s(z0),s(z0)))
            P(s(z0)) -> c6()
        - Weak TRS:
            *(z0,0()) -> 0()
            *(z0,s(z1)) -> +(z0,*(z0,z1))
            +(0(),z0) -> z0
            +(s(z0),z1) -> s(+(z0,z1))
            -(z0,0()) -> z0
            -(s(z0),s(z1)) -> -(z0,z1)
            f(s(z0)) -> f(-(p(*(s(z0),s(z0))),*(s(z0),s(z0))))
            p(s(z0)) -> z0
        - Signature:
            {*/2,*'/2,+/2,+'/2,-/2,-'/2,F/1,P/1,f/1,p/1} / {0/0,c/0,c1/1,c2/0,c3/1,c4/0,c5/2,c6/0,c7/4,c8/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,*',+,+',-,-',F,P,f,p} and constructors {0,c,c1,c2,c3,c4
            ,c5,c6,c7,c8,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            *'(z0,0()) -> c4()
            *'(z0,s(z1)) -> c5(+'(z0,*(z0,z1)),*'(z0,z1))
            +'(0(),z0) -> c2()
            +'(s(z0),z1) -> c3(+'(z0,z1))
            -'(z0,0()) -> c()
            -'(s(z0),s(z1)) -> c1(-'(z0,z1))
            F(s(z0)) -> c7(F(-(p(*(s(z0),s(z0))),*(s(z0),s(z0))))
                          ,-'(p(*(s(z0),s(z0))),*(s(z0),s(z0)))
                          ,P(*(s(z0),s(z0)))
                          ,*'(s(z0),s(z0)))
            F(s(z0)) -> c8(F(-(p(*(s(z0),s(z0))),*(s(z0),s(z0)))),-'(p(*(s(z0),s(z0))),*(s(z0),s(z0))),*'(s(z0),s(z0)))
            P(s(z0)) -> c6()
        - Weak TRS:
            *(z0,0()) -> 0()
            *(z0,s(z1)) -> +(z0,*(z0,z1))
            +(0(),z0) -> z0
            +(s(z0),z1) -> s(+(z0,z1))
            -(z0,0()) -> z0
            -(s(z0),s(z1)) -> -(z0,z1)
            f(s(z0)) -> f(-(p(*(s(z0),s(z0))),*(s(z0),s(z0))))
            p(s(z0)) -> z0
        - Signature:
            {*/2,*'/2,+/2,+'/2,-/2,-'/2,F/1,P/1,f/1,p/1} / {0/0,c/0,c1/1,c2/0,c3/1,c4/0,c5/2,c6/0,c7/4,c8/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,*',+,+',-,-',F,P,f,p} and constructors {0,c,c1,c2,c3,c4
            ,c5,c6,c7,c8,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            *'(z0,0()) -> c4()
            *'(z0,s(z1)) -> c5(+'(z0,*(z0,z1)),*'(z0,z1))
            +'(0(),z0) -> c2()
            +'(s(z0),z1) -> c3(+'(z0,z1))
            -'(z0,0()) -> c()
            -'(s(z0),s(z1)) -> c1(-'(z0,z1))
            F(s(z0)) -> c7(F(-(p(*(s(z0),s(z0))),*(s(z0),s(z0))))
                          ,-'(p(*(s(z0),s(z0))),*(s(z0),s(z0)))
                          ,P(*(s(z0),s(z0)))
                          ,*'(s(z0),s(z0)))
            F(s(z0)) -> c8(F(-(p(*(s(z0),s(z0))),*(s(z0),s(z0)))),-'(p(*(s(z0),s(z0))),*(s(z0),s(z0))),*'(s(z0),s(z0)))
            P(s(z0)) -> c6()
        - Weak TRS:
            *(z0,0()) -> 0()
            *(z0,s(z1)) -> +(z0,*(z0,z1))
            +(0(),z0) -> z0
            +(s(z0),z1) -> s(+(z0,z1))
            -(z0,0()) -> z0
            -(s(z0),s(z1)) -> -(z0,z1)
            f(s(z0)) -> f(-(p(*(s(z0),s(z0))),*(s(z0),s(z0))))
            p(s(z0)) -> z0
        - Signature:
            {*/2,*'/2,+/2,+'/2,-/2,-'/2,F/1,P/1,f/1,p/1} / {0/0,c/0,c1/1,c2/0,c3/1,c4/0,c5/2,c6/0,c7/4,c8/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,*',+,+',-,-',F,P,f,p} and constructors {0,c,c1,c2,c3,c4
            ,c5,c6,c7,c8,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          *'(x,y){y -> s(y)} =
            *'(x,s(y)) ->^+ c5(+'(x,*(x,y)),*'(x,y))
              = C[*'(x,y) = *'(x,y){}]

WORST_CASE(Omega(n^1),?)