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Derivational Complexity: TRS pair #487104214
details
property
value
status
complete
benchmark
Ex1_Luc04b_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.572 seconds
cpu usage
1121.19
user time
1106.6
system time
14.5845
max virtual memory
3.7837796E7
max residence set size
1.5216004E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 332 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (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__nats -> cons(0, incr(nats)) a__pairs -> cons(0, incr(odds)) a__odds -> a__incr(a__pairs) a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) a__head(cons(X, XS)) -> mark(X) a__tail(cons(X, XS)) -> mark(XS) mark(nats) -> a__nats mark(incr(X)) -> a__incr(mark(X)) mark(pairs) -> a__pairs mark(odds) -> a__odds mark(head(X)) -> a__head(mark(X)) mark(tail(X)) -> a__tail(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__nats -> nats a__incr(X) -> incr(X) a__pairs -> pairs a__odds -> odds a__head(X) -> head(X) a__tail(X) -> tail(X) 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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(incr(x_1)) -> incr(encArg(x_1)) encArg(nats) -> nats encArg(odds) -> odds encArg(s(x_1)) -> s(encArg(x_1)) encArg(pairs) -> pairs encArg(head(x_1)) -> head(encArg(x_1)) encArg(tail(x_1)) -> tail(encArg(x_1)) encArg(cons_a__nats) -> a__nats encArg(cons_a__pairs) -> a__pairs encArg(cons_a__odds) -> a__odds encArg(cons_a__incr(x_1)) -> a__incr(encArg(x_1)) encArg(cons_a__head(x_1)) -> a__head(encArg(x_1)) encArg(cons_a__tail(x_1)) -> a__tail(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__nats -> a__nats encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_incr(x_1) -> incr(encArg(x_1)) encode_nats -> nats encode_a__pairs -> a__pairs encode_odds -> odds encode_a__odds -> a__odds encode_a__incr(x_1) -> a__incr(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_a__head(x_1) -> a__head(encArg(x_1)) encode_a__tail(x_1) -> a__tail(encArg(x_1)) encode_pairs -> pairs 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(n^1, INF).
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