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Derivational Complexity: TRS Innermost pair #487105228
details
property
value
status
complete
benchmark
kabasci05.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)
291.954 seconds
cpu usage
1132.87
user time
1121.47
system time
11.4001
max virtual memory
3.790938E7
max residence set size
1.489462E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 286 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), 325 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), 84 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 70 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 174 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 238 ms] (24) 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: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) minus(x, 0) -> x minus(s(x), s(y)) -> s(minus(x, y)) gcd(s(x), s(y)) -> gcd(minus(max(x, y), min(x, transform(y))), s(min(x, y))) transform(x) -> s(s(x)) transform(cons(x, y)) -> cons(cons(x, x), x) transform(cons(x, y)) -> y transform(s(x)) -> s(s(transform(x))) cons(x, y) -> y cons(x, cons(y, s(z))) -> cons(y, x) cons(cons(x, z), s(y)) -> transform(x) 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(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encArg(cons_transform(x_1)) -> transform(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) encode_transform(x_1) -> transform(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) ---------------------------------------- (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: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y))
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