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Derivational Complexity: TRS Innermost pair #487108424
details
property
value
status
complete
benchmark
PALINDROME_nokinds_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
292.501 seconds
cpu usage
1146.68
user time
1135.54
system time
11.138
max virtual memory
1.971942E7
max residence set size
1.512458E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 530 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 3 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 1498 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs ---------------------------------------- (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: __(__(X, Y), Z) -> __(X, __(Y, Z)) __(X, nil) -> X __(nil, X) -> X and(tt, X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil) -> tt isList(n____(V1, V2)) -> and(isList(activate(V1)), n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1, V2)) -> and(isList(activate(V1)), n__isNeList(activate(V2))) isNeList(n____(V1, V2)) -> and(isNeList(activate(V1)), n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I, n____(P, I))) -> and(isQid(activate(I)), n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil) -> tt isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil __(X1, X2) -> n____(X1, X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a -> n__a e -> n__e i -> n__i o -> n__o u -> n__u activate(n__nil) -> nil activate(n____(X1, X2)) -> __(activate(X1), activate(X2)) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__o) -> o activate(n__u) -> u activate(X) -> X 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(tt) -> tt encArg(n__nil) -> n__nil encArg(n____(x_1, x_2)) -> n____(encArg(x_1), encArg(x_2)) encArg(n__isList(x_1)) -> n__isList(encArg(x_1)) encArg(n__isNeList(x_1)) -> n__isNeList(encArg(x_1)) encArg(n__isPal(x_1)) -> n__isPal(encArg(x_1)) encArg(n__a) -> n__a encArg(n__e) -> n__e encArg(n__i) -> n__i encArg(n__o) -> n__o encArg(n__u) -> n__u encArg(cons___(x_1, x_2)) -> __(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isList(x_1)) -> isList(encArg(x_1)) encArg(cons_isNeList(x_1)) -> isNeList(encArg(x_1)) encArg(cons_isNePal(x_1)) -> isNePal(encArg(x_1)) encArg(cons_isPal(x_1)) -> isPal(encArg(x_1))
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return to Derivational Complexity: TRS Innermost