WORST_CASE(?, O(1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f31(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f39(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f31(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f24(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(10, 0, 10, Fresh_0, 10, Fresh_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_1].
We thus obtain the following problem:
2:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = 3
	Pol(f0) = 3
	Pol(f18) = 3
	Pol(f24) = 2
	Pol(f31) = 1
	Pol(f39) = 0
orients all transitions weakly and the transitions
	f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
	f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
	f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))
		(Comp: 3, Cost: 1)    f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: 3, Cost: 1)    f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: 3, Cost: 1)    f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = 10
	Pol(f0) = 10
	Pol(f18) = V_1
	Pol(f24) = V_1
	Pol(f31) = V_1 - V_2
	Pol(f39) = V_1 - V_2
orients all transitions weakly and the transition
	f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))
		(Comp: 3, Cost: 1)     f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: 3, Cost: 1)     f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: 3, Cost: 1)     f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: 10, Cost: 1)    f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)     f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)     f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f24) = -V_2
	Pol(f18) = V_1 - V_2
and size complexities
	S("f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 10
	S("f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ?
	S("f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 10
	S("f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ?
	S("f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 10
	S("f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = 10
	S("f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-0) = 10
	S("f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-1) = 10
	S("f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]", 0-0) = 10
	S("f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]", 0-1) = 0
	S("f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]", 0-0) = 10
	S("f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]", 0-1) = 0
	S("f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))", 0-0) = 10
	S("f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))", 0-1) = 0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
orients the transitions
	f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
	f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
weakly and the transition
	f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
6:	T:
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))
		(Comp: 3, Cost: 1)     f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: 3, Cost: 1)     f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: 3, Cost: 1)     f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: 10, Cost: 1)    f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)     f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 10, Cost: 1)    f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f24) = V_1 - V_2
and size complexities
	S("f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 10
	S("f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = 10
	S("f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 10
	S("f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ?
	S("f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 10
	S("f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = 10
	S("f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-0) = 10
	S("f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-1) = 10
	S("f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]", 0-0) = 10
	S("f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]", 0-1) = 0
	S("f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]", 0-0) = 10
	S("f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]", 0-1) = 0
	S("f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))", 0-0) = 10
	S("f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))", 0-1) = 0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
orients the transitions
	f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
weakly and the transition
	f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
7:	T:
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1) -> Com_1(f18(10, 0))
		(Comp: 3, Cost: 1)     f18(Ar_0, Ar_1) -> Com_1(f24(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: 3, Cost: 1)     f24(Ar_0, Ar_1) -> Com_1(f31(Ar_0, 0)) [ Ar_1 >= Ar_0 ]
		(Comp: 3, Cost: 1)     f31(Ar_0, Ar_1) -> Com_1(f39(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: 10, Cost: 1)    f31(Ar_0, Ar_1) -> Com_1(f31(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 30, Cost: 1)    f24(Ar_0, Ar_1) -> Com_1(f24(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 10, Cost: 1)    f18(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 60

Time: 0.801 sec (SMT: 0.763 sec)