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:
            ANY(z0) -> c12()
            ANY(s(z0)) -> c11(ANY(z0))
            GCD(s(z0),s(z1)) -> c10(GCD(minus(max(z0,z1),min(z0,z1)),s(min(z0,z1))),MIN(z0,z1))
            GCD(s(z0),s(z1)) -> c8(GCD(minus(max(z0,z1),min(z0,z1)),s(min(z0,z1)))
                                  ,MINUS(max(z0,z1),min(z0,z1))
                                  ,MAX(z0,z1))
            GCD(s(z0),s(z1)) -> c9(GCD(minus(max(z0,z1),min(z0,z1)),s(min(z0,z1)))
                                  ,MINUS(max(z0,z1),min(z0,z1))
                                  ,MIN(z0,z1))
            MAX(z0,0()) -> c3()
            MAX(0(),z0) -> c4()
            MAX(s(z0),s(z1)) -> c5(MAX(z0,z1))
            MIN(z0,0()) -> c()
            MIN(0(),z0) -> c1()
            MIN(s(z0),s(z1)) -> c2(MIN(z0,z1))
            MINUS(z0,0()) -> c6()
            MINUS(s(z0),s(z1)) -> c7(MINUS(z0,any(z1)),ANY(z1))
        - Weak TRS:
            any(z0) -> z0
            any(s(z0)) -> s(s(any(z0)))
            gcd(s(z0),s(z1)) -> gcd(minus(max(z0,z1),min(z0,z1)),s(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))
            minus(z0,0()) -> z0
            minus(s(z0),s(z1)) -> s(minus(z0,any(z1)))
        - Signature:
            {ANY/1,GCD/2,MAX/2,MIN/2,MINUS/2,any/1,gcd/2,max/2,min/2,minus/2} / {0/0,c/0,c1/0,c10/2,c11/1,c12/0,c2/1
            ,c3/0,c4/0,c5/1,c6/0,c7/2,c8/3,c9/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ANY,GCD,MAX,MIN,MINUS,any,gcd,max,min
            ,minus} and constructors {0,c,c1,c10,c11,c12,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:
            ANY(z0) -> c12()
            ANY(s(z0)) -> c11(ANY(z0))
            GCD(s(z0),s(z1)) -> c10(GCD(minus(max(z0,z1),min(z0,z1)),s(min(z0,z1))),MIN(z0,z1))
            GCD(s(z0),s(z1)) -> c8(GCD(minus(max(z0,z1),min(z0,z1)),s(min(z0,z1)))
                                  ,MINUS(max(z0,z1),min(z0,z1))
                                  ,MAX(z0,z1))
            GCD(s(z0),s(z1)) -> c9(GCD(minus(max(z0,z1),min(z0,z1)),s(min(z0,z1)))
                                  ,MINUS(max(z0,z1),min(z0,z1))
                                  ,MIN(z0,z1))
            MAX(z0,0()) -> c3()
            MAX(0(),z0) -> c4()
            MAX(s(z0),s(z1)) -> c5(MAX(z0,z1))
            MIN(z0,0()) -> c()
            MIN(0(),z0) -> c1()
            MIN(s(z0),s(z1)) -> c2(MIN(z0,z1))
            MINUS(z0,0()) -> c6()
            MINUS(s(z0),s(z1)) -> c7(MINUS(z0,any(z1)),ANY(z1))
        - Weak TRS:
            any(z0) -> z0
            any(s(z0)) -> s(s(any(z0)))
            gcd(s(z0),s(z1)) -> gcd(minus(max(z0,z1),min(z0,z1)),s(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))
            minus(z0,0()) -> z0
            minus(s(z0),s(z1)) -> s(minus(z0,any(z1)))
        - Signature:
            {ANY/1,GCD/2,MAX/2,MIN/2,MINUS/2,any/1,gcd/2,max/2,min/2,minus/2} / {0/0,c/0,c1/0,c10/2,c11/1,c12/0,c2/1
            ,c3/0,c4/0,c5/1,c6/0,c7/2,c8/3,c9/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ANY,GCD,MAX,MIN,MINUS,any,gcd,max,min
            ,minus} and constructors {0,c,c1,c10,c11,c12,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:
            ANY(z0) -> c12()
            ANY(s(z0)) -> c11(ANY(z0))
            GCD(s(z0),s(z1)) -> c10(GCD(minus(max(z0,z1),min(z0,z1)),s(min(z0,z1))),MIN(z0,z1))
            GCD(s(z0),s(z1)) -> c8(GCD(minus(max(z0,z1),min(z0,z1)),s(min(z0,z1)))
                                  ,MINUS(max(z0,z1),min(z0,z1))
                                  ,MAX(z0,z1))
            GCD(s(z0),s(z1)) -> c9(GCD(minus(max(z0,z1),min(z0,z1)),s(min(z0,z1)))
                                  ,MINUS(max(z0,z1),min(z0,z1))
                                  ,MIN(z0,z1))
            MAX(z0,0()) -> c3()
            MAX(0(),z0) -> c4()
            MAX(s(z0),s(z1)) -> c5(MAX(z0,z1))
            MIN(z0,0()) -> c()
            MIN(0(),z0) -> c1()
            MIN(s(z0),s(z1)) -> c2(MIN(z0,z1))
            MINUS(z0,0()) -> c6()
            MINUS(s(z0),s(z1)) -> c7(MINUS(z0,any(z1)),ANY(z1))
        - Weak TRS:
            any(z0) -> z0
            any(s(z0)) -> s(s(any(z0)))
            gcd(s(z0),s(z1)) -> gcd(minus(max(z0,z1),min(z0,z1)),s(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))
            minus(z0,0()) -> z0
            minus(s(z0),s(z1)) -> s(minus(z0,any(z1)))
        - Signature:
            {ANY/1,GCD/2,MAX/2,MIN/2,MINUS/2,any/1,gcd/2,max/2,min/2,minus/2} / {0/0,c/0,c1/0,c10/2,c11/1,c12/0,c2/1
            ,c3/0,c4/0,c5/1,c6/0,c7/2,c8/3,c9/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ANY,GCD,MAX,MIN,MINUS,any,gcd,max,min
            ,minus} and constructors {0,c,c1,c10,c11,c12,c2,c3,c4,c5,c6,c7,c8,c9,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ANY(x){x -> s(x)} =
            ANY(s(x)) ->^+ c11(ANY(x))
              = C[ANY(x) = ANY(x){}]

WORST_CASE(Omega(n^1),?)