details

property	value
status	complete
benchmark	z29.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.675 seconds
cpu usage	1058.21
user time	1047.3
system time	10.9155
max virtual memory	1.9936204E7
max residence set size	1.4997168E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 199 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), 313 ms] (12) proven lower bound (13) LowerBoundPropagationProof [FINISHED, 0 ms] (14) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a(lambda(x), y) -> lambda(a(x, 1)) a(lambda(x), y) -> lambda(a(x, a(y, t))) a(a(x, y), z) -> a(x, a(y, z)) lambda(x) -> x a(x, y) -> x a(x, y) -> y S is empty. Rewrite Strategy: FULL ---------------------------------------- (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(1) -> 1 encArg(t) -> t encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(cons_lambda(x_1)) -> lambda(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_lambda(x_1) -> lambda(encArg(x_1)) encode_1 -> 1 encode_t -> t ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a(lambda(x), y) -> lambda(a(x, 1)) a(lambda(x), y) -> lambda(a(x, a(y, t))) a(a(x, y), z) -> a(x, a(y, z)) lambda(x) -> x a(x, y) -> x a(x, y) -> y The (relative) TRS S consists of the following rules: encArg(1) -> 1 encArg(t) -> t encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(cons_lambda(x_1)) -> lambda(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_lambda(x_1) -> lambda(encArg(x_1)) encode_1 -> 1 encode_t -> t Rewrite Strategy: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a(lambda(x), y) -> lambda(a(x, 1)) a(lambda(x), y) -> lambda(a(x, a(y, t))) popout

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all output return to Derivational Complexity: TRS