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Derivational Complexity: TRS Innermost pair #487105908
details
property
value
status
complete
benchmark
gcd2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.657 seconds
cpu usage
1142.91
user time
1133.07
system time
9.83893
max virtual memory
3.81378E7
max residence set size
1.4926732E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 368 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 506 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), 140 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 1724 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: minus(s(x), y) -> if(gt(s(x), y), x, y) if(true, x, y) -> s(minus(x, y)) if(false, x, y) -> 0 gcd(x, y) -> if1(ge(x, y), x, y) if1(true, x, y) -> if2(gt(y, 0), x, y) if1(false, x, y) -> if3(gt(x, 0), x, y) if2(true, x, y) -> gcd(minus(x, y), y) if2(false, x, y) -> x if3(true, x, y) -> gcd(x, minus(y, x)) if3(false, x, y) -> y gt(0, y) -> false gt(s(x), 0) -> true gt(s(x), s(y)) -> gt(x, y) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(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(true) -> true encArg(false) -> false encArg(0) -> 0 encArg(cons_minus(x_1, x_2)) -> minus(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)) encArg(cons_gcd(x_1, x_2)) -> gcd(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)) encArg(cons_if3(x_1, x_2, x_3)) -> if3(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_0 -> 0 encode_gcd(x_1, x_2) -> gcd(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_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_if2(x_1, x_2, x_3) -> if2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_if3(x_1, x_2, x_3) -> if3(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: minus(s(x), y) -> if(gt(s(x), y), x, y) if(true, x, y) -> s(minus(x, y))
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