Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Derivational Complexity: TRS pair #487100832
details
property
value
status
complete
benchmark
4.11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.528 seconds
cpu usage
314.972
user time
312.482
system time
2.49087
max virtual memory
5.6010152E7
max residence set size
5094092.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 149 ms] (4) CpxRelTRS (5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (6) CpxRelTRS (7) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxWeightedTrs (11) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxWeightedTrs (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTypedWeightedTrs (15) CompletionProof [UPPER BOUND(ID), 0 ms] (16) CpxTypedWeightedCompleteTrs (17) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) CompleteCoflocoProof [FINISHED, 1186 ms] (20) BOUNDS(1, n^3) (21) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxRelTRS (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (24) typed CpxTrs (25) OrderProof [LOWER BOUND(ID), 0 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 227 ms] (28) proven lower bound (29) LowerBoundPropagationProof [FINISHED, 0 ms] (30) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: +(x, 0) -> x +(x, s(y)) -> s(+(x, y)) +(0, s(y)) -> s(y) s(+(0, y)) -> s(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(0) -> 0 encArg(cons_+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encode_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: +(x, 0) -> x +(x, s(y)) -> s(+(x, y)) +(0, s(y)) -> s(y) s(+(0, y)) -> s(y) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(cons_+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encode_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Derivational Complexity: TRS