details

property	value
status	complete
benchmark	4.57.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.70947 seconds
cpu usage	10.7679
user time	10.0764
system time	0.691513
max virtual memory	1.827736E7
max residence set size	2528508.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(1))

output

WORST_CASE(?, O(1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 10 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (6) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: f(x, y, z) -> g(<=(x, y), x, y, z) g(true, x, y, z) -> z g(false, x, y, z) -> f(f(p(x), y, z), f(p(y), z, x), f(p(z), x, y)) p(0) -> 0 p(s(x)) -> x S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: f(z0, z1, z2) -> g(<=(z0, z1), z0, z1, z2) g(true, z0, z1, z2) -> z2 g(false, z0, z1, z2) -> f(f(p(z0), z1, z2), f(p(z1), z2, z0), f(p(z2), z0, z1)) p(0) -> 0 p(s(z0)) -> z0 Tuples: F(z0, z1, z2) -> c(G(<=(z0, z1), z0, z1, z2)) G(true, z0, z1, z2) -> c1 G(false, z0, z1, z2) -> c2(F(f(p(z0), z1, z2), f(p(z1), z2, z0), f(p(z2), z0, z1)), F(p(z0), z1, z2), P(z0), F(p(z1), z2, z0), P(z1), F(p(z2), z0, z1), P(z2)) P(0) -> c3 P(s(z0)) -> c4 S tuples: F(z0, z1, z2) -> c(G(<=(z0, z1), z0, z1, z2)) G(true, z0, z1, z2) -> c1 G(false, z0, z1, z2) -> c2(F(f(p(z0), z1, z2), f(p(z1), z2, z0), f(p(z2), z0, z1)), F(p(z0), z1, z2), P(z0), F(p(z1), z2, z0), P(z1), F(p(z2), z0, z1), P(z2)) P(0) -> c3 P(s(z0)) -> c4 K tuples:none Defined Rule Symbols: f_3, g_4, p_1 Defined Pair Symbols: F_3, G_4, P_1 Compound Symbols: c_1, c1, c2_7, c3, c4 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: F(z0, z1, z2) -> c(G(<=(z0, z1), z0, z1, z2)) G(false, z0, z1, z2) -> c2(F(f(p(z0), z1, z2), f(p(z1), z2, z0), f(p(z2), z0, z1)), F(p(z0), z1, z2), P(z0), F(p(z1), z2, z0), P(z1), F(p(z2), z0, z1), P(z2)) P(s(z0)) -> c4 G(true, z0, z1, z2) -> c1 P(0) -> c3 ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: f(z0, z1, z2) -> g(<=(z0, z1), z0, z1, z2) g(true, z0, z1, z2) -> z2 g(false, z0, z1, z2) -> f(f(p(z0), z1, z2), f(p(z1), z2, z0), f(p(z2), z0, z1)) p(0) -> 0 p(s(z0)) -> z0 Tuples:none S tuples:none K tuples:none Defined Rule Symbols: f_3, g_4, p_1 Defined Pair Symbols:none Compound Symbols:none popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS Innermost