/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?, O(1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 21 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f54(A, B, B + A, D, E, F, G, H, I, J, K)) :|: A >= B
f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f54(A, B, B - A, D, E, F, G, H, I, J, K)) :|: B >= 1 + A
f38(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(L, B, C, D, E, D, D, H, I, J, K)) :|: D >= 1 + E
f38(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(L, B, C, D, E, D, D, M, I, J, K)) :|: E >= D
f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f38(1, 2, C, 1, 10, F, G, H, 10, 2, L)) :|: TRUE

The start-symbols are:[f0_11]


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(1) Koat Proof (FINISHED)
YES(?, 4)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    f11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f54(ar_0, ar_1, ar_1 + ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_0 >= ar_1 ]

		(Comp: ?, Cost: 1)    f11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f54(ar_0, ar_1, ar_1 - ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_1 >= ar_0 + 1 ]

		(Comp: ?, Cost: 1)    f38(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f11(l, ar_1, ar_2, ar_3, ar_4, ar_3, ar_3, ar_7, ar_8, ar_9, ar_10)) [ ar_3 >= ar_4 + 1 ]

		(Comp: ?, Cost: 1)    f38(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f11(l, ar_1, ar_2, ar_3, ar_4, ar_3, ar_3, m, ar_8, ar_9, ar_10)) [ ar_4 >= ar_3 ]

		(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) -> Com_1(f38(1, 2, ar_2, 1, 10, ar_5, ar_6, ar_7, 10, 2, l))

		(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) -> 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)) [ 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, ar_3, ar_4].

We thus obtain the following problem:

2:	T:

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_3, ar_4)) [ 0 <= 0 ]

		(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_3, ar_4) -> Com_1(f38(1, 2, 1, 10))

		(Comp: ?, Cost: 1)    f38(ar_0, ar_1, ar_3, ar_4) -> Com_1(f11(l, ar_1, ar_3, ar_4)) [ ar_4 >= ar_3 ]

		(Comp: ?, Cost: 1)    f38(ar_0, ar_1, ar_3, ar_4) -> Com_1(f11(l, ar_1, ar_3, ar_4)) [ ar_3 >= ar_4 + 1 ]

		(Comp: ?, Cost: 1)    f11(ar_0, ar_1, ar_3, ar_4) -> Com_1(f54(ar_0, ar_1, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]

		(Comp: ?, Cost: 1)    f11(ar_0, ar_1, ar_3, ar_4) -> Com_1(f54(ar_0, ar_1, ar_3, ar_4)) [ ar_0 >= ar_1 ]

	start location:	koat_start

	leaf cost:	0



Testing for reachability in the complexity graph removes the following transition from problem 2:

	f38(ar_0, ar_1, ar_3, ar_4) -> Com_1(f11(l, ar_1, ar_3, ar_4)) [ ar_3 >= ar_4 + 1 ]

We thus obtain the following problem:

3:	T:

		(Comp: ?, Cost: 1)    f11(ar_0, ar_1, ar_3, ar_4) -> Com_1(f54(ar_0, ar_1, ar_3, ar_4)) [ ar_0 >= ar_1 ]

		(Comp: ?, Cost: 1)    f11(ar_0, ar_1, ar_3, ar_4) -> Com_1(f54(ar_0, ar_1, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]

		(Comp: ?, Cost: 1)    f38(ar_0, ar_1, ar_3, ar_4) -> Com_1(f11(l, ar_1, ar_3, ar_4)) [ ar_4 >= ar_3 ]

		(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_3, ar_4) -> Com_1(f38(1, 2, 1, 10))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_3, ar_4)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 3 produces the following problem:

4:	T:

		(Comp: 1, Cost: 1)    f11(ar_0, ar_1, ar_3, ar_4) -> Com_1(f54(ar_0, ar_1, ar_3, ar_4)) [ ar_0 >= ar_1 ]

		(Comp: 1, Cost: 1)    f11(ar_0, ar_1, ar_3, ar_4) -> Com_1(f54(ar_0, ar_1, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]

		(Comp: 1, Cost: 1)    f38(ar_0, ar_1, ar_3, ar_4) -> Com_1(f11(l, ar_1, ar_3, ar_4)) [ ar_4 >= ar_3 ]

		(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_3, ar_4) -> Com_1(f38(1, 2, 1, 10))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_3, ar_4)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 4



Time: 0.026 sec (SMT: 0.024 sec)


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(2)
BOUNDS(1, 1)