details

property	value
status	complete
benchmark	thiemann05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	292.6 seconds
cpu usage	1149.56
user time	1138.73
system time	10.8296
max virtual memory	3.8562744E7
max residence set size	1.489968E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 353 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), 304 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), 338 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 731 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: isLeaf(leaf) -> true isLeaf(cons(u, v)) -> false left(cons(u, v)) -> u right(cons(u, v)) -> v concat(leaf, y) -> y concat(cons(u, v), y) -> cons(u, concat(v, y)) less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) if1(b, true, u, v) -> false if1(b, false, u, v) -> if2(b, u, v) if2(true, u, v) -> true if2(false, u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v))) 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(leaf) -> leaf encArg(true) -> true encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(false) -> false encArg(cons_isLeaf(x_1)) -> isLeaf(encArg(x_1)) encArg(cons_left(x_1)) -> left(encArg(x_1)) encArg(cons_right(x_1)) -> right(encArg(x_1)) encArg(cons_concat(x_1, x_2)) -> concat(encArg(x_1), encArg(x_2)) encArg(cons_less_leaves(x_1, x_2)) -> less_leaves(encArg(x_1), encArg(x_2)) encArg(cons_if1(x_1, x_2, x_3, x_4)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_if2(x_1, x_2, x_3)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isLeaf(x_1) -> isLeaf(encArg(x_1)) encode_leaf -> leaf encode_true -> true encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_false -> false encode_left(x_1) -> left(encArg(x_1)) encode_right(x_1) -> right(encArg(x_1)) encode_concat(x_1, x_2) -> concat(encArg(x_1), encArg(x_2)) encode_less_leaves(x_1, x_2) -> less_leaves(encArg(x_1), encArg(x_2)) encode_if1(x_1, x_2, x_3, x_4) -> if1(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) 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: isLeaf(leaf) -> true isLeaf(cons(u, v)) -> false left(cons(u, v)) -> u right(cons(u, v)) -> v concat(leaf, y) -> y concat(cons(u, v), y) -> cons(u, concat(v, y)) less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) if1(b, true, u, v) -> false if1(b, false, u, v) -> if2(b, u, v) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Derivational Complexity: TRS Innermost