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Runti Compl Inner Rewri 22807 pair #381904387
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
n050.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.00237202644 seconds
cpu usage
10.826776858
max memory
2.175492096E9
stage attributes
key
value
output-size
3190
starexec-result
WORST_CASE(?, O(1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).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), 0 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 P(0) -> c3 G(true, z0, z1, z2) -> c1 ---------------------------------------- (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
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