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Derivational Complexity: TRS Innermost pair #487105406
details
property
value
status
complete
benchmark
IJCAR_26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
292.417 seconds
cpu usage
1146.33
user time
1134.38
system time
11.9542
max virtual memory
3.7454188E7
max residence set size
1.4990552E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), ?)
output
WORST_CASE(Omega(n^3), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^3, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 464 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 3 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), 272 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), 108 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^3, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 92 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 110 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 6029 ms] (28) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^3, INF). The TRS R consists of the following rules: p(s(x)) -> x plus(x, 0) -> x plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(s(x), y) -> s(plus(p(s(x)), y)) plus(x, s(y)) -> s(plus(x, p(s(y)))) times(0, y) -> 0 times(s(0), y) -> y times(s(x), y) -> plus(y, times(x, y)) div(0, y) -> 0 div(x, y) -> quot(x, y, y) quot(0, s(y), z) -> 0 quot(s(x), s(y), z) -> quot(x, y, z) quot(x, 0, s(z)) -> s(div(x, s(z))) div(div(x, y), z) -> div(x, times(y, z)) eq(0, 0) -> true eq(s(x), 0) -> false eq(0, s(y)) -> false eq(s(x), s(y)) -> eq(x, y) divides(y, x) -> eq(x, times(div(x, y), y)) prime(s(s(x))) -> pr(s(s(x)), s(x)) pr(x, s(0)) -> true pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) if(true, x, y) -> false if(false, x, y) -> pr(x, 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_p(x_1)) -> p(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_times(x_1, x_2)) -> times(encArg(x_1), encArg(x_2)) encArg(cons_div(x_1, x_2)) -> div(encArg(x_1), encArg(x_2)) encArg(cons_quot(x_1, x_2, x_3)) -> quot(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) encArg(cons_divides(x_1, x_2)) -> divides(encArg(x_1), encArg(x_2)) encArg(cons_prime(x_1)) -> prime(encArg(x_1)) encArg(cons_pr(x_1, x_2)) -> pr(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_times(x_1, x_2) -> times(encArg(x_1), encArg(x_2)) encode_div(x_1, x_2) -> div(encArg(x_1), encArg(x_2))
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