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:
            COND1(true(),z0,z1,z2) -> c(COND2(gr(z1,z2),z0,z1,z2),GR(z1,z2))
            COND2(false(),z0,z1,z2) -> c3(COND1(gr(z0,z2),p(z0),z1,z2),GR(z0,z2))
            COND2(false(),z0,z1,z2) -> c4(COND1(gr(z0,z2),p(z0),z1,z2),P(z0))
            COND2(true(),z0,z1,z2) -> c1(COND2(gr(z1,z2),z0,p(z1),z2),GR(z1,z2))
            COND2(true(),z0,z1,z2) -> c2(COND2(gr(z1,z2),z0,p(z1),z2),P(z1))
            GR(0(),z0) -> c5()
            GR(s(z0),0()) -> c6()
            GR(s(z0),s(z1)) -> c7(GR(z0,z1))
            P(0()) -> c8()
            P(s(z0)) -> c9()
        - Weak TRS:
            cond1(true(),z0,z1,z2) -> cond2(gr(z1,z2),z0,z1,z2)
            cond2(false(),z0,z1,z2) -> cond1(gr(z0,z2),p(z0),z1,z2)
            cond2(true(),z0,z1,z2) -> cond2(gr(z1,z2),z0,p(z1),z2)
            gr(0(),z0) -> false()
            gr(s(z0),0()) -> true()
            gr(s(z0),s(z1)) -> gr(z0,z1)
            p(0()) -> 0()
            p(s(z0)) -> z0
        - Signature:
            {COND1/4,COND2/4,GR/2,P/1,cond1/4,cond2/4,gr/2,p/1} / {0/0,c/2,c1/2,c2/2,c3/2,c4/2,c5/0,c6/0,c7/1,c8/0,c9/0
            ,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {COND1,COND2,GR,P,cond1,cond2,gr,p} and constructors {0,c
            ,c1,c2,c3,c4,c5,c6,c7,c8,c9,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            COND1(true(),z0,z1,z2) -> c(COND2(gr(z1,z2),z0,z1,z2),GR(z1,z2))
            COND2(false(),z0,z1,z2) -> c3(COND1(gr(z0,z2),p(z0),z1,z2),GR(z0,z2))
            COND2(false(),z0,z1,z2) -> c4(COND1(gr(z0,z2),p(z0),z1,z2),P(z0))
            COND2(true(),z0,z1,z2) -> c1(COND2(gr(z1,z2),z0,p(z1),z2),GR(z1,z2))
            COND2(true(),z0,z1,z2) -> c2(COND2(gr(z1,z2),z0,p(z1),z2),P(z1))
            GR(0(),z0) -> c5()
            GR(s(z0),0()) -> c6()
            GR(s(z0),s(z1)) -> c7(GR(z0,z1))
            P(0()) -> c8()
            P(s(z0)) -> c9()
        - Weak TRS:
            cond1(true(),z0,z1,z2) -> cond2(gr(z1,z2),z0,z1,z2)
            cond2(false(),z0,z1,z2) -> cond1(gr(z0,z2),p(z0),z1,z2)
            cond2(true(),z0,z1,z2) -> cond2(gr(z1,z2),z0,p(z1),z2)
            gr(0(),z0) -> false()
            gr(s(z0),0()) -> true()
            gr(s(z0),s(z1)) -> gr(z0,z1)
            p(0()) -> 0()
            p(s(z0)) -> z0
        - Signature:
            {COND1/4,COND2/4,GR/2,P/1,cond1/4,cond2/4,gr/2,p/1} / {0/0,c/2,c1/2,c2/2,c3/2,c4/2,c5/0,c6/0,c7/1,c8/0,c9/0
            ,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {COND1,COND2,GR,P,cond1,cond2,gr,p} and constructors {0,c
            ,c1,c2,c3,c4,c5,c6,c7,c8,c9,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            COND1(true(),z0,z1,z2) -> c(COND2(gr(z1,z2),z0,z1,z2),GR(z1,z2))
            COND2(false(),z0,z1,z2) -> c3(COND1(gr(z0,z2),p(z0),z1,z2),GR(z0,z2))
            COND2(false(),z0,z1,z2) -> c4(COND1(gr(z0,z2),p(z0),z1,z2),P(z0))
            COND2(true(),z0,z1,z2) -> c1(COND2(gr(z1,z2),z0,p(z1),z2),GR(z1,z2))
            COND2(true(),z0,z1,z2) -> c2(COND2(gr(z1,z2),z0,p(z1),z2),P(z1))
            GR(0(),z0) -> c5()
            GR(s(z0),0()) -> c6()
            GR(s(z0),s(z1)) -> c7(GR(z0,z1))
            P(0()) -> c8()
            P(s(z0)) -> c9()
        - Weak TRS:
            cond1(true(),z0,z1,z2) -> cond2(gr(z1,z2),z0,z1,z2)
            cond2(false(),z0,z1,z2) -> cond1(gr(z0,z2),p(z0),z1,z2)
            cond2(true(),z0,z1,z2) -> cond2(gr(z1,z2),z0,p(z1),z2)
            gr(0(),z0) -> false()
            gr(s(z0),0()) -> true()
            gr(s(z0),s(z1)) -> gr(z0,z1)
            p(0()) -> 0()
            p(s(z0)) -> z0
        - Signature:
            {COND1/4,COND2/4,GR/2,P/1,cond1/4,cond2/4,gr/2,p/1} / {0/0,c/2,c1/2,c2/2,c3/2,c4/2,c5/0,c6/0,c7/1,c8/0,c9/0
            ,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {COND1,COND2,GR,P,cond1,cond2,gr,p} and constructors {0,c
            ,c1,c2,c3,c4,c5,c6,c7,c8,c9,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          GR(x,y){x -> s(x),y -> s(y)} =
            GR(s(x),s(y)) ->^+ c7(GR(x,y))
              = C[GR(x,y) = GR(x,y){}]

WORST_CASE(Omega(n^1),?)