/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(?, O(1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 19 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f7(8, 0, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T)) :|: TRUE
f7(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f7(A, B + 1, U + V, W, X + Y, Z, A1 + B1, C1, D1 + E1, F1, U + V + D1 + E1, U + V - D1 - E1, X + Y + A1 + B1, X + Y - A1 - B1, -(3196), G1, H1, I1 + J1, K1 + J1, J1)) :|: 7 >= B
f62(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f62(A, B + 1, U + V, W, X + Y, Z, A1 + B1, C1, D1 + E1, F1, U + V + D1 + E1, U + V - D1 - E1, X + Y + A1 + B1, X + Y - A1 - B1, -(3196), G1, H1, I1 + J1, K1 + J1, J1)) :|: 7 >= B
f62(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f118(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T)) :|: B >= 8
f7(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f62(A, 0, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T)) :|: B >= 8

The start-symbols are:[f0_20]


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(1) Koat Proof (FINISHED)
YES(?, 21)



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(f7(8, 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)    f7(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(f7(Ar_0, Ar_1 + 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, -3196, Fresh_29, Fresh_30, Fresh_31 + Fresh_32, Fresh_33 + Fresh_32, Fresh_32)) [ 7 >= Ar_1 ]

		(Comp: ?, Cost: 1)    f62(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(f62(Ar_0, Ar_1 + 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, -3196, Fresh_12, Fresh_13, Fresh_14 + Fresh_15, Fresh_16 + Fresh_15, Fresh_15)) [ 7 >= Ar_1 ]

		(Comp: ?, Cost: 1)    f62(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(f118(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)) [ Ar_1 >= 8 ]

		(Comp: ?, Cost: 1)    f7(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(f62(Ar_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)) [ Ar_1 >= 8 ]

		(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].

We thus obtain the following problem:

2:	T:

		(Comp: 1, Cost: 0)    koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ]

		(Comp: ?, Cost: 1)    f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ]

		(Comp: ?, Cost: 1)    f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ]

		(Comp: ?, Cost: 1)    f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: ?, Cost: 1)    f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: ?, Cost: 1)    f0(Ar_1) -> Com_1(f7(0))

	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) -> Com_1(f0(Ar_1)) [ 0 <= 0 ]

		(Comp: ?, Cost: 1)    f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ]

		(Comp: ?, Cost: 1)    f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ]

		(Comp: ?, Cost: 1)    f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: ?, Cost: 1)    f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: 1, Cost: 1)    f0(Ar_1) -> Com_1(f7(0))

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(koat_start) = 2

	Pol(f0) = 2

	Pol(f7) = 2

	Pol(f62) = 1

	Pol(f118) = 0

orients all transitions weakly and the transitions

	f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ]

	f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ]

strictly and produces the following problem:

4:	T:

		(Comp: 1, Cost: 0)    koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)    f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ]

		(Comp: 2, Cost: 1)    f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ]

		(Comp: ?, Cost: 1)    f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: ?, Cost: 1)    f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: 1, Cost: 1)    f0(Ar_1) -> Com_1(f7(0))

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(koat_start) = 8

	Pol(f0) = 8

	Pol(f7) = 8

	Pol(f62) = -V_1 + 8

	Pol(f118) = -V_1

orients all transitions weakly and the transition

	f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ]

strictly and produces the following problem:

5:	T:

		(Comp: 1, Cost: 0)    koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)    f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ]

		(Comp: 2, Cost: 1)    f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ]

		(Comp: 8, Cost: 1)    f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: ?, Cost: 1)    f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: 1, Cost: 1)    f0(Ar_1) -> Com_1(f7(0))

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(f7) = -V_1 + 8

and size complexities

	S("f0(Ar_1) -> Com_1(f7(0))", 0-0) = 0

	S("f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ]", 0-0) = 8

	S("f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ]", 0-0) = 8

	S("f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ]", 0-0) = 8

	S("f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ]", 0-0) = 0

	S("koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_1

orients the transitions

	f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ]

weakly and the transition

	f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ]

strictly and produces the following problem:

6:	T:

		(Comp: 1, Cost: 0)    koat_start(Ar_1) -> Com_1(f0(Ar_1)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)    f7(Ar_1) -> Com_1(f62(0)) [ Ar_1 >= 8 ]

		(Comp: 2, Cost: 1)    f62(Ar_1) -> Com_1(f118(Ar_1)) [ Ar_1 >= 8 ]

		(Comp: 8, Cost: 1)    f62(Ar_1) -> Com_1(f62(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: 8, Cost: 1)    f7(Ar_1) -> Com_1(f7(Ar_1 + 1)) [ 7 >= Ar_1 ]

		(Comp: 1, Cost: 1)    f0(Ar_1) -> Com_1(f7(0))

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 21



Time: 0.056 sec (SMT: 0.050 sec)


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(2)
BOUNDS(1, 1)