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Derivational Complexity: TRS Innermost pair #487105114
details
property
value
status
complete
benchmark
thiemann34.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.686 seconds
cpu usage
1143.69
user time
1132.45
system time
11.2328
max virtual memory
3.8283572E7
max residence set size
1.501974E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 369 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 268 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 138 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 1264 ms] (20) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: gt(s(x), 0) -> true gt(0, y) -> false gt(s(x), s(y)) -> gt(x, y) divides(x, y) -> div(x, y, y) div(0, 0, z) -> true div(0, s(x), z) -> false div(s(x), 0, s(z)) -> div(s(x), s(z), s(z)) div(s(x), s(y), z) -> div(x, y, z) prime(x) -> test(x, s(s(0))) test(x, y) -> if1(gt(x, y), x, y) if1(true, x, y) -> if2(divides(x, y), x, y) if1(false, x, y) -> true if2(true, x, y) -> false if2(false, x, y) -> test(x, s(y)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(true) -> true encArg(false) -> false encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encArg(cons_divides(x_1, x_2)) -> divides(encArg(x_1), encArg(x_2)) encArg(cons_div(x_1, x_2, x_3)) -> div(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_prime(x_1)) -> prime(encArg(x_1)) encArg(cons_test(x_1, x_2)) -> test(encArg(x_1), encArg(x_2)) encArg(cons_if1(x_1, x_2, x_3)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_true -> true encode_false -> false encode_divides(x_1, x_2) -> divides(encArg(x_1), encArg(x_2)) encode_div(x_1, x_2, x_3) -> div(encArg(x_1), encArg(x_2), encArg(x_3)) encode_prime(x_1) -> prime(encArg(x_1)) encode_test(x_1, x_2) -> test(encArg(x_1), encArg(x_2)) encode_if1(x_1, x_2, x_3) -> if1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: gt(s(x), 0) -> true gt(0, y) -> false gt(s(x), s(y)) -> gt(x, y) divides(x, y) -> div(x, y, y) div(0, 0, z) -> true div(0, s(x), z) -> false
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