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Derivational Complexity: TRS pair #487104064
details
property
value
status
complete
benchmark
Ex3_3_25_Bor03_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)
291.49 seconds
cpu usage
314.965
user time
312.072
system time
2.89257
max virtual memory
1.9113056E7
max residence set size
5197664.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
WORST_CASE(?, O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 233 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsTAProof [FINISHED, 205 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: app(nil, YS) -> YS app(cons(X), YS) -> cons(X) from(X) -> cons(X) zWadr(nil, YS) -> nil zWadr(XS, nil) -> nil zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X))) prefix(L) -> cons(nil) 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(nil) -> nil encArg(cons(x_1)) -> cons(encArg(x_1)) encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_zWadr(x_1, x_2)) -> zWadr(encArg(x_1), encArg(x_2)) encArg(cons_prefix(x_1)) -> prefix(encArg(x_1)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_cons(x_1) -> cons(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_zWadr(x_1, x_2) -> zWadr(encArg(x_1), encArg(x_2)) encode_prefix(x_1) -> prefix(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: app(nil, YS) -> YS app(cons(X), YS) -> cons(X) from(X) -> cons(X) zWadr(nil, YS) -> nil zWadr(XS, nil) -> nil zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X))) prefix(L) -> cons(nil) The (relative) TRS S consists of the following rules: encArg(nil) -> nil encArg(cons(x_1)) -> cons(encArg(x_1)) encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_zWadr(x_1, x_2)) -> zWadr(encArg(x_1), encArg(x_2)) encArg(cons_prefix(x_1)) -> prefix(encArg(x_1)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_cons(x_1) -> cons(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_zWadr(x_1, x_2) -> zWadr(encArg(x_1), encArg(x_2)) encode_prefix(x_1) -> prefix(encArg(x_1)) 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(1, n^1).
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