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:
            GCD(z0,0()) -> c7()
            GCD(0(),s(z0)) -> c8()
            GCD(s(z0),s(z1)) -> c10(GCD(mod(s(z0),s(z1)),mod(s(z1),s(z0))),MOD(s(z1),s(z0)))
            GCD(s(z0),s(z1)) -> c9(GCD(mod(s(z0),s(z1)),mod(s(z1),s(z0))),MOD(s(z0),s(z1)))
            IF(false(),z0,z1) -> c6(MOD(minus(z0,z1),z1),MINUS(z0,z1))
            IF(true(),z0,z1) -> c5()
            LT(z0,0()) -> c11()
            LT(0(),s(z0)) -> c12()
            LT(s(z0),s(z1)) -> c13(LT(z0,z1))
            MINUS(0(),z0) -> c()
            MINUS(s(z0),0()) -> c1()
            MINUS(s(z0),s(z1)) -> c2(MINUS(z0,z1))
            MOD(z0,0()) -> c3()
            MOD(z0,s(z1)) -> c4(IF(lt(z0,s(z1)),z0,s(z1)),LT(z0,s(z1)))
        - Weak TRS:
            gcd(z0,0()) -> z0
            gcd(0(),s(z0)) -> s(z0)
            gcd(s(z0),s(z1)) -> gcd(mod(s(z0),s(z1)),mod(s(z1),s(z0)))
            if(false(),z0,z1) -> mod(minus(z0,z1),z1)
            if(true(),z0,z1) -> z0
            lt(z0,0()) -> false()
            lt(0(),s(z0)) -> true()
            lt(s(z0),s(z1)) -> lt(z0,z1)
            minus(0(),z0) -> 0()
            minus(s(z0),0()) -> s(z0)
            minus(s(z0),s(z1)) -> minus(z0,z1)
            mod(z0,0()) -> 0()
            mod(z0,s(z1)) -> if(lt(z0,s(z1)),z0,s(z1))
        - Signature:
            {GCD/2,IF/3,LT/2,MINUS/2,MOD/2,gcd/2,if/3,lt/2,minus/2,mod/2} / {0/0,c/0,c1/0,c10/2,c11/0,c12/0,c13/1,c2/1
            ,c3/0,c4/2,c5/0,c6/2,c7/0,c8/0,c9/2,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {GCD,IF,LT,MINUS,MOD,gcd,if,lt,minus
            ,mod} and constructors {0,c,c1,c10,c11,c12,c13,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:
            GCD(z0,0()) -> c7()
            GCD(0(),s(z0)) -> c8()
            GCD(s(z0),s(z1)) -> c10(GCD(mod(s(z0),s(z1)),mod(s(z1),s(z0))),MOD(s(z1),s(z0)))
            GCD(s(z0),s(z1)) -> c9(GCD(mod(s(z0),s(z1)),mod(s(z1),s(z0))),MOD(s(z0),s(z1)))
            IF(false(),z0,z1) -> c6(MOD(minus(z0,z1),z1),MINUS(z0,z1))
            IF(true(),z0,z1) -> c5()
            LT(z0,0()) -> c11()
            LT(0(),s(z0)) -> c12()
            LT(s(z0),s(z1)) -> c13(LT(z0,z1))
            MINUS(0(),z0) -> c()
            MINUS(s(z0),0()) -> c1()
            MINUS(s(z0),s(z1)) -> c2(MINUS(z0,z1))
            MOD(z0,0()) -> c3()
            MOD(z0,s(z1)) -> c4(IF(lt(z0,s(z1)),z0,s(z1)),LT(z0,s(z1)))
        - Weak TRS:
            gcd(z0,0()) -> z0
            gcd(0(),s(z0)) -> s(z0)
            gcd(s(z0),s(z1)) -> gcd(mod(s(z0),s(z1)),mod(s(z1),s(z0)))
            if(false(),z0,z1) -> mod(minus(z0,z1),z1)
            if(true(),z0,z1) -> z0
            lt(z0,0()) -> false()
            lt(0(),s(z0)) -> true()
            lt(s(z0),s(z1)) -> lt(z0,z1)
            minus(0(),z0) -> 0()
            minus(s(z0),0()) -> s(z0)
            minus(s(z0),s(z1)) -> minus(z0,z1)
            mod(z0,0()) -> 0()
            mod(z0,s(z1)) -> if(lt(z0,s(z1)),z0,s(z1))
        - Signature:
            {GCD/2,IF/3,LT/2,MINUS/2,MOD/2,gcd/2,if/3,lt/2,minus/2,mod/2} / {0/0,c/0,c1/0,c10/2,c11/0,c12/0,c13/1,c2/1
            ,c3/0,c4/2,c5/0,c6/2,c7/0,c8/0,c9/2,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {GCD,IF,LT,MINUS,MOD,gcd,if,lt,minus
            ,mod} and constructors {0,c,c1,c10,c11,c12,c13,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:
            GCD(z0,0()) -> c7()
            GCD(0(),s(z0)) -> c8()
            GCD(s(z0),s(z1)) -> c10(GCD(mod(s(z0),s(z1)),mod(s(z1),s(z0))),MOD(s(z1),s(z0)))
            GCD(s(z0),s(z1)) -> c9(GCD(mod(s(z0),s(z1)),mod(s(z1),s(z0))),MOD(s(z0),s(z1)))
            IF(false(),z0,z1) -> c6(MOD(minus(z0,z1),z1),MINUS(z0,z1))
            IF(true(),z0,z1) -> c5()
            LT(z0,0()) -> c11()
            LT(0(),s(z0)) -> c12()
            LT(s(z0),s(z1)) -> c13(LT(z0,z1))
            MINUS(0(),z0) -> c()
            MINUS(s(z0),0()) -> c1()
            MINUS(s(z0),s(z1)) -> c2(MINUS(z0,z1))
            MOD(z0,0()) -> c3()
            MOD(z0,s(z1)) -> c4(IF(lt(z0,s(z1)),z0,s(z1)),LT(z0,s(z1)))
        - Weak TRS:
            gcd(z0,0()) -> z0
            gcd(0(),s(z0)) -> s(z0)
            gcd(s(z0),s(z1)) -> gcd(mod(s(z0),s(z1)),mod(s(z1),s(z0)))
            if(false(),z0,z1) -> mod(minus(z0,z1),z1)
            if(true(),z0,z1) -> z0
            lt(z0,0()) -> false()
            lt(0(),s(z0)) -> true()
            lt(s(z0),s(z1)) -> lt(z0,z1)
            minus(0(),z0) -> 0()
            minus(s(z0),0()) -> s(z0)
            minus(s(z0),s(z1)) -> minus(z0,z1)
            mod(z0,0()) -> 0()
            mod(z0,s(z1)) -> if(lt(z0,s(z1)),z0,s(z1))
        - Signature:
            {GCD/2,IF/3,LT/2,MINUS/2,MOD/2,gcd/2,if/3,lt/2,minus/2,mod/2} / {0/0,c/0,c1/0,c10/2,c11/0,c12/0,c13/1,c2/1
            ,c3/0,c4/2,c5/0,c6/2,c7/0,c8/0,c9/2,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {GCD,IF,LT,MINUS,MOD,gcd,if,lt,minus
            ,mod} and constructors {0,c,c1,c10,c11,c12,c13,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:
          LT(x,y){x -> s(x),y -> s(y)} =
            LT(s(x),s(y)) ->^+ c13(LT(x,y))
              = C[LT(x,y) = LT(x,y){}]

WORST_CASE(Omega(n^1),?)