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Derivational Complexity: TRS pair #487101912
details
property
value
status
complete
benchmark
ExIntrod_GM01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
1.66288 seconds
cpu usage
3.84046
user time
3.67526
system time
0.165196
max virtual memory
1.8408912E7
max residence set size
246120.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 198 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) InfiniteLowerBoundProof [FINISHED, 0 ms] (8) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: incr(nil) -> nil incr(cons(X, L)) -> cons(s(X), incr(L)) adx(nil) -> nil adx(cons(X, L)) -> incr(cons(X, adx(L))) nats -> adx(zeros) zeros -> cons(0, zeros) head(cons(X, L)) -> X tail(cons(X, L)) -> L 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, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(cons_incr(x_1)) -> incr(encArg(x_1)) encArg(cons_adx(x_1)) -> adx(encArg(x_1)) encArg(cons_nats) -> nats encArg(cons_zeros) -> zeros encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encode_incr(x_1) -> incr(encArg(x_1)) encode_nil -> nil encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_adx(x_1) -> adx(encArg(x_1)) encode_nats -> nats encode_zeros -> zeros encode_0 -> 0 encode_head(x_1) -> head(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: incr(nil) -> nil incr(cons(X, L)) -> cons(s(X), incr(L)) adx(nil) -> nil adx(cons(X, L)) -> incr(cons(X, adx(L))) nats -> adx(zeros) zeros -> cons(0, zeros) head(cons(X, L)) -> X tail(cons(X, L)) -> L The (relative) TRS S consists of the following rules: encArg(nil) -> nil encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(cons_incr(x_1)) -> incr(encArg(x_1)) encArg(cons_adx(x_1)) -> adx(encArg(x_1)) encArg(cons_nats) -> nats encArg(cons_zeros) -> zeros encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encode_incr(x_1) -> incr(encArg(x_1)) encode_nil -> nil encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_adx(x_1) -> adx(encArg(x_1))
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