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Derivational Complexity: TRS Innermost pair #487107724
details
property
value
status
complete
benchmark
factorial2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.626 seconds
cpu usage
1139.33
user time
1127.94
system time
11.3863
max virtual memory
3.7776708E7
max residence set size
1.4905292E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^3, INF).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), 515 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 8 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 297 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), 103 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^2, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 633 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 324 ms] (26) BEST (27) proven lower bound (28) LowerBoundPropagationProof [FINISHED, 0 ms] (29) BOUNDS(n^3, INF) (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 1111 ms] (32) 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: plus(0, x) -> x plus(s(x), y) -> s(plus(x, y)) times(0, y) -> 0 times(s(x), y) -> plus(y, times(x, y)) p(s(x)) -> x p(0) -> 0 minus(x, 0) -> x minus(0, x) -> 0 minus(x, s(y)) -> p(minus(x, y)) isZero(0) -> true isZero(s(x)) -> false facIter(x, y) -> if(isZero(x), minus(x, s(0)), y, times(y, x)) if(true, x, y, z) -> y if(false, x, y, z) -> facIter(x, z) factorial(x) -> facIter(x, s(0)) 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(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false 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_p(x_1)) -> p(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_isZero(x_1)) -> isZero(encArg(x_1)) encArg(cons_facIter(x_1, x_2)) -> facIter(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3, x_4)) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_factorial(x_1)) -> factorial(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_times(x_1, x_2) -> times(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_isZero(x_1) -> isZero(encArg(x_1)) encode_true -> true encode_false -> false encode_facIter(x_1, x_2) -> facIter(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3, x_4) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_factorial(x_1) -> factorial(encArg(x_1))
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