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Derivational Complexity: TRS pair #487104216
details
property
value
status
complete
benchmark
Ex1_Luc04b_Z.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
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
1.68191 seconds
cpu usage
3.85599
user time
3.69167
system time
0.164319
max virtual memory
1.8475704E7
max residence set size
244988.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 257 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) InfiniteLowerBoundProof [FINISHED, 1 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: nats -> cons(0, n__incr(nats)) pairs -> cons(0, n__incr(odds)) odds -> incr(pairs) incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS))) head(cons(X, XS)) -> X tail(cons(X, XS)) -> activate(XS) incr(X) -> n__incr(X) activate(n__incr(X)) -> incr(X) activate(X) -> 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(n__incr(x_1)) -> n__incr(encArg(x_1)) encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_nats) -> nats encArg(cons_pairs) -> pairs encArg(cons_odds) -> odds encArg(cons_incr(x_1)) -> incr(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_nats -> nats encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_n__incr(x_1) -> n__incr(encArg(x_1)) encode_pairs -> pairs encode_odds -> odds encode_incr(x_1) -> incr(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_activate(x_1) -> activate(encArg(x_1)) 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: nats -> cons(0, n__incr(nats)) pairs -> cons(0, n__incr(odds)) odds -> incr(pairs) incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS))) head(cons(X, XS)) -> X tail(cons(X, XS)) -> activate(XS) incr(X) -> n__incr(X) activate(n__incr(X)) -> incr(X) activate(X) -> X The (relative) TRS S consists of the following rules: encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(n__incr(x_1)) -> n__incr(encArg(x_1)) encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_nats) -> nats encArg(cons_pairs) -> pairs encArg(cons_odds) -> odds encArg(cons_incr(x_1)) -> incr(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_activate(x_1)) -> activate(encArg(x_1))
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