details

property	value
status	complete
benchmark	Ex2_Luc03b_L.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	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.521 seconds
cpu usage	316.787
user time	313.205
system time	3.58239
max virtual memory	1.9115376E7
max residence set size	5389920.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^1))

output

WORST_CASE(?, O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 199 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsTAProof [FINISHED, 182 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: fst(0, Z) -> nil fst(s, cons(Y)) -> cons(Y) from(X) -> cons(X) add(0, X) -> X add(s, Y) -> s len(nil) -> 0 len(cons(X)) -> s 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(nil) -> nil encArg(s) -> s encArg(cons(x_1)) -> cons(encArg(x_1)) encArg(cons_fst(x_1, x_2)) -> fst(encArg(x_1), encArg(x_2)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encArg(cons_len(x_1)) -> len(encArg(x_1)) encode_fst(x_1, x_2) -> fst(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_nil -> nil encode_s -> s encode_cons(x_1) -> cons(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) encode_len(x_1) -> len(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: fst(0, Z) -> nil fst(s, cons(Y)) -> cons(Y) from(X) -> cons(X) add(0, X) -> X add(s, Y) -> s len(nil) -> 0 len(cons(X)) -> s The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(nil) -> nil encArg(s) -> s encArg(cons(x_1)) -> cons(encArg(x_1)) encArg(cons_fst(x_1, x_2)) -> fst(encArg(x_1), encArg(x_2)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encArg(cons_len(x_1)) -> len(encArg(x_1)) encode_fst(x_1, x_2) -> fst(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_nil -> nil encode_s -> s encode_cons(x_1) -> cons(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) encode_len(x_1) -> len(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 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