WORST_CASE(?, O(1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19) -> Com_1(f6(0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19))
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19) -> Com_1(f6(Fresh_34, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19)) [ 63 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1, Fresh_17 + Fresh_18, Fresh_19, Fresh_20 + Fresh_21, Fresh_22, Fresh_23 + Fresh_24, Fresh_25, Fresh_26 + Fresh_27, Fresh_28, Fresh_17 + Fresh_18 + Fresh_26 + Fresh_27, Fresh_17 + Fresh_18 - Fresh_26 - Fresh_27, Fresh_20 + Fresh_21 + Fresh_23 + Fresh_24, Fresh_20 + Fresh_21 - Fresh_23 - Fresh_24, Fresh_29, Fresh_30, Fresh_31 + Fresh_32, Fresh_33 + Fresh_32, Fresh_32)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f57(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19) -> Com_1(f57(Ar_0, Ar_1, Ar_2 - 1, Fresh_0 + Fresh_1, Fresh_2, Fresh_3 + Fresh_4, Fresh_5, Fresh_6 + Fresh_7, Fresh_8, Fresh_9 + Fresh_10, Fresh_11, Fresh_0 + Fresh_1 + Fresh_9 + Fresh_10, Fresh_0 + Fresh_1 - Fresh_9 - Fresh_10, Fresh_3 + Fresh_4 + Fresh_6 + Fresh_7, Fresh_3 + Fresh_4 - Fresh_6 - Fresh_7, Fresh_12, Fresh_13, Fresh_14 + Fresh_15, Fresh_16 + Fresh_15, Fresh_15)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f57(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19) -> Com_1(f101(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19) -> Com_1(f57(Ar_0, Ar_1, 7, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19) -> Com_1(f14(Ar_0, Ar_1, 7, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19)) [ Ar_1 >= 64 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_1, Ar_2].
We thus obtain the following problem:
2:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_1, Ar_2) -> Com_1(f0(Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f6(Ar_1, Ar_2) -> Com_1(f14(Ar_1, 7)) [ Ar_1 >= 64 ]
		(Comp: ?, Cost: 1)    f14(Ar_1, Ar_2) -> Com_1(f57(Ar_1, 7)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f57(Ar_1, Ar_2) -> Com_1(f101(Ar_1, Ar_2)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f57(Ar_1, Ar_2) -> Com_1(f57(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f6(Ar_1, Ar_2) -> Com_1(f6(Ar_1 + 1, Ar_2)) [ 63 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f0(Ar_1, Ar_2) -> Com_1(f6(0, Ar_2))
	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_1, Ar_2) -> Com_1(f0(Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f6(Ar_1, Ar_2) -> Com_1(f14(Ar_1, 7)) [ Ar_1 >= 64 ]
		(Comp: ?, Cost: 1)    f14(Ar_1, Ar_2) -> Com_1(f57(Ar_1, 7)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f57(Ar_1, Ar_2) -> Com_1(f101(Ar_1, Ar_2)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f57(Ar_1, Ar_2) -> Com_1(f57(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f6(Ar_1, Ar_2) -> Com_1(f6(Ar_1 + 1, Ar_2)) [ 63 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f0(Ar_1, Ar_2) -> Com_1(f6(0, Ar_2))
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = 3
	Pol(f0) = 3
	Pol(f6) = 3
	Pol(f14) = 2
	Pol(f57) = 1
	Pol(f101) = 0
orients all transitions weakly and the transitions
	f6(Ar_1, Ar_2) -> Com_1(f14(Ar_1, 7)) [ Ar_1 >= 64 ]
	f57(Ar_1, Ar_2) -> Com_1(f101(Ar_1, Ar_2)) [ 0 >= Ar_2 + 1 ]
	f14(Ar_1, Ar_2) -> Com_1(f57(Ar_1, 7)) [ 0 >= Ar_2 + 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_1, Ar_2) -> Com_1(f0(Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 3, Cost: 1)    f6(Ar_1, Ar_2) -> Com_1(f14(Ar_1, 7)) [ Ar_1 >= 64 ]
		(Comp: 3, Cost: 1)    f14(Ar_1, Ar_2) -> Com_1(f57(Ar_1, 7)) [ 0 >= Ar_2 + 1 ]
		(Comp: 3, Cost: 1)    f57(Ar_1, Ar_2) -> Com_1(f101(Ar_1, Ar_2)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f57(Ar_1, Ar_2) -> Com_1(f57(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f6(Ar_1, Ar_2) -> Com_1(f6(Ar_1 + 1, Ar_2)) [ 63 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f0(Ar_1, Ar_2) -> Com_1(f6(0, Ar_2))
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = 64
	Pol(f0) = 64
	Pol(f6) = -V_1 + 64
	Pol(f14) = -V_1
	Pol(f57) = -V_1 + V_2 - 7
	Pol(f101) = -V_1 + V_2 - 7
orients all transitions weakly and the transition
	f6(Ar_1, Ar_2) -> Com_1(f6(Ar_1 + 1, Ar_2)) [ 63 >= Ar_1 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 0)     koat_start(Ar_1, Ar_2) -> Com_1(f0(Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 3, Cost: 1)     f6(Ar_1, Ar_2) -> Com_1(f14(Ar_1, 7)) [ Ar_1 >= 64 ]
		(Comp: 3, Cost: 1)     f14(Ar_1, Ar_2) -> Com_1(f57(Ar_1, 7)) [ 0 >= Ar_2 + 1 ]
		(Comp: 3, Cost: 1)     f57(Ar_1, Ar_2) -> Com_1(f101(Ar_1, Ar_2)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)     f57(Ar_1, Ar_2) -> Com_1(f57(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)     f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: 64, Cost: 1)    f6(Ar_1, Ar_2) -> Com_1(f6(Ar_1 + 1, Ar_2)) [ 63 >= Ar_1 ]
		(Comp: 1, Cost: 1)     f0(Ar_1, Ar_2) -> Com_1(f6(0, Ar_2))
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = 8
	Pol(f0) = 8
	Pol(f6) = 8
	Pol(f14) = 8
	Pol(f57) = V_2 + 1
	Pol(f101) = V_2 + 1
orients all transitions weakly and the transition
	f57(Ar_1, Ar_2) -> Com_1(f57(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
strictly and produces the following problem:
6:	T:
		(Comp: 1, Cost: 0)     koat_start(Ar_1, Ar_2) -> Com_1(f0(Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 3, Cost: 1)     f6(Ar_1, Ar_2) -> Com_1(f14(Ar_1, 7)) [ Ar_1 >= 64 ]
		(Comp: 3, Cost: 1)     f14(Ar_1, Ar_2) -> Com_1(f57(Ar_1, 7)) [ 0 >= Ar_2 + 1 ]
		(Comp: 3, Cost: 1)     f57(Ar_1, Ar_2) -> Com_1(f101(Ar_1, Ar_2)) [ 0 >= Ar_2 + 1 ]
		(Comp: 8, Cost: 1)     f57(Ar_1, Ar_2) -> Com_1(f57(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)     f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: 64, Cost: 1)    f6(Ar_1, Ar_2) -> Com_1(f6(Ar_1 + 1, Ar_2)) [ 63 >= Ar_1 ]
		(Comp: 1, Cost: 1)     f0(Ar_1, Ar_2) -> Com_1(f6(0, Ar_2))
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f14) = V_2 + 1
and size complexities
	S("f0(Ar_1, Ar_2) -> Com_1(f6(0, Ar_2))", 0-0) = 0
	S("f0(Ar_1, Ar_2) -> Com_1(f6(0, Ar_2))", 0-1) = Ar_2
	S("f6(Ar_1, Ar_2) -> Com_1(f6(Ar_1 + 1, Ar_2)) [ 63 >= Ar_1 ]", 0-0) = 64
	S("f6(Ar_1, Ar_2) -> Com_1(f6(Ar_1 + 1, Ar_2)) [ 63 >= Ar_1 ]", 0-1) = Ar_2
	S("f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]", 0-0) = 64
	S("f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]", 0-1) = 7
	S("f57(Ar_1, Ar_2) -> Com_1(f57(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]", 0-0) = 64
	S("f57(Ar_1, Ar_2) -> Com_1(f57(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]", 0-1) = 7
	S("f57(Ar_1, Ar_2) -> Com_1(f101(Ar_1, Ar_2)) [ 0 >= Ar_2 + 1 ]", 0-0) = 64
	S("f57(Ar_1, Ar_2) -> Com_1(f101(Ar_1, Ar_2)) [ 0 >= Ar_2 + 1 ]", 0-1) = 7
	S("f14(Ar_1, Ar_2) -> Com_1(f57(Ar_1, 7)) [ 0 >= Ar_2 + 1 ]", 0-0) = 64
	S("f14(Ar_1, Ar_2) -> Com_1(f57(Ar_1, 7)) [ 0 >= Ar_2 + 1 ]", 0-1) = 7
	S("f6(Ar_1, Ar_2) -> Com_1(f14(Ar_1, 7)) [ Ar_1 >= 64 ]", 0-0) = 64
	S("f6(Ar_1, Ar_2) -> Com_1(f14(Ar_1, 7)) [ Ar_1 >= 64 ]", 0-1) = 7
	S("koat_start(Ar_1, Ar_2) -> Com_1(f0(Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_1
	S("koat_start(Ar_1, Ar_2) -> Com_1(f0(Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_2
orients the transitions
	f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
weakly and the transition
	f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
strictly and produces the following problem:
7:	T:
		(Comp: 1, Cost: 0)     koat_start(Ar_1, Ar_2) -> Com_1(f0(Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 3, Cost: 1)     f6(Ar_1, Ar_2) -> Com_1(f14(Ar_1, 7)) [ Ar_1 >= 64 ]
		(Comp: 3, Cost: 1)     f14(Ar_1, Ar_2) -> Com_1(f57(Ar_1, 7)) [ 0 >= Ar_2 + 1 ]
		(Comp: 3, Cost: 1)     f57(Ar_1, Ar_2) -> Com_1(f101(Ar_1, Ar_2)) [ 0 >= Ar_2 + 1 ]
		(Comp: 8, Cost: 1)     f57(Ar_1, Ar_2) -> Com_1(f57(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: 24, Cost: 1)    f14(Ar_1, Ar_2) -> Com_1(f14(Ar_1, Ar_2 - 1)) [ Ar_2 >= 0 ]
		(Comp: 64, Cost: 1)    f6(Ar_1, Ar_2) -> Com_1(f6(Ar_1 + 1, Ar_2)) [ 63 >= Ar_1 ]
		(Comp: 1, Cost: 1)     f0(Ar_1, Ar_2) -> Com_1(f6(0, Ar_2))
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 106

Time: 1.012 sec (SMT: 0.974 sec)