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Derivational Complexity: TRS Innermost pair #487109134
details
property
value
status
complete
benchmark
Ex14_AEGL02_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
4.42841 seconds
cpu usage
14.3865
user time
13.2342
system time
1.15233
max virtual memory
1.8476724E7
max residence set size
3938188.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF).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), 314 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 3 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 (13) InfiniteLowerBoundProof [FINISHED, 1810 ms] (14) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: from(X) -> cons(X, n__from(n__s(X))) length(n__nil) -> 0 length(n__cons(X, Y)) -> s(length1(activate(Y))) length1(X) -> length(activate(X)) from(X) -> n__from(X) s(X) -> n__s(X) nil -> n__nil cons(X1, X2) -> n__cons(X1, X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__nil) -> nil activate(n__cons(X1, X2)) -> cons(activate(X1), X2) 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(n__from(x_1)) -> n__from(encArg(x_1)) encArg(n__s(x_1)) -> n__s(encArg(x_1)) encArg(n__nil) -> n__nil encArg(0) -> 0 encArg(n__cons(x_1, x_2)) -> n__cons(encArg(x_1), encArg(x_2)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_length(x_1)) -> length(encArg(x_1)) encArg(cons_length1(x_1)) -> length1(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_nil) -> nil encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_n__from(x_1) -> n__from(encArg(x_1)) encode_n__s(x_1) -> n__s(encArg(x_1)) encode_length(x_1) -> length(encArg(x_1)) encode_n__nil -> n__nil encode_0 -> 0 encode_n__cons(x_1, x_2) -> n__cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_length1(x_1) -> length1(encArg(x_1)) encode_activate(x_1) -> activate(encArg(x_1)) encode_nil -> nil ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: from(X) -> cons(X, n__from(n__s(X))) length(n__nil) -> 0 length(n__cons(X, Y)) -> s(length1(activate(Y))) length1(X) -> length(activate(X)) from(X) -> n__from(X) s(X) -> n__s(X) nil -> n__nil cons(X1, X2) -> n__cons(X1, X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__nil) -> nil
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