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Derivational Complexity: TRS Innermost pair #487105106
details
property
value
status
complete
benchmark
thiemann08.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
AProVE_07
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
293.98 seconds
cpu usage
1138.53
user time
1126.31
system time
12.2187
max virtual memory
3.7857112E7
max residence set size
1.511088E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 272 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 3 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 (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: empty(nil) -> true empty(cons(x, l)) -> false head(cons(x, l)) -> x tail(nil) -> nil tail(cons(x, l)) -> l rev(nil) -> nil rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l)) last(x, l) -> if(empty(l), x, l) if(true, x, l) -> x if(false, x, l) -> last(head(l), tail(l)) rev2(x, nil) -> nil rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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(true) -> true encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(false) -> false encArg(rev1(x_1, x_2)) -> rev1(encArg(x_1), encArg(x_2)) encArg(cons_empty(x_1)) -> empty(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_rev(x_1)) -> rev(encArg(x_1)) encArg(cons_last(x_1, x_2)) -> last(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_rev2(x_1, x_2)) -> rev2(encArg(x_1), encArg(x_2)) encode_empty(x_1) -> empty(encArg(x_1)) encode_nil -> nil encode_true -> true encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_false -> false encode_head(x_1) -> head(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_rev(x_1) -> rev(encArg(x_1)) encode_rev1(x_1, x_2) -> rev1(encArg(x_1), encArg(x_2)) encode_rev2(x_1, x_2) -> rev2(encArg(x_1), encArg(x_2)) encode_last(x_1, x_2) -> last(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: empty(nil) -> true empty(cons(x, l)) -> false head(cons(x, l)) -> x tail(nil) -> nil tail(cons(x, l)) -> l rev(nil) -> nil rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l)) last(x, l) -> if(empty(l), x, l) if(true, x, l) -> x if(false, x, l) -> last(head(l), tail(l)) rev2(x, nil) -> nil rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) The (relative) TRS S consists of the following rules:
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