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Derivational Complexity: TRS pair #487104098
details
property
value
status
complete
benchmark
ExIntrod_GM04_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
26.8839 seconds
cpu usage
96.3215
user time
93.8312
system time
2.49031
max virtual memory
1.9448988E7
max residence set size
5299724.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(INF, INF).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), 390 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 6 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, 14.8 s] (14) 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 -> adx(zeros) zeros -> cons(n__0, n__zeros) incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) hd(cons(X, Y)) -> activate(X) tl(cons(X, Y)) -> activate(Y) 0 -> n__0 zeros -> n__zeros s(X) -> n__s(X) incr(X) -> n__incr(X) adx(X) -> n__adx(X) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(X)) -> s(X) activate(n__incr(X)) -> incr(activate(X)) activate(n__adx(X)) -> adx(activate(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(n__0) -> n__0 encArg(n__zeros) -> n__zeros encArg(n__s(x_1)) -> n__s(encArg(x_1)) encArg(n__incr(x_1)) -> n__incr(encArg(x_1)) encArg(n__adx(x_1)) -> n__adx(encArg(x_1)) encArg(cons_nats) -> nats encArg(cons_zeros) -> zeros encArg(cons_incr(x_1)) -> incr(encArg(x_1)) encArg(cons_adx(x_1)) -> adx(encArg(x_1)) encArg(cons_hd(x_1)) -> hd(encArg(x_1)) encArg(cons_tl(x_1)) -> tl(encArg(x_1)) encArg(cons_0) -> 0 encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_nats -> nats encode_adx(x_1) -> adx(encArg(x_1)) encode_zeros -> zeros encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_n__0 -> n__0 encode_n__zeros -> n__zeros encode_incr(x_1) -> incr(encArg(x_1)) encode_n__s(x_1) -> n__s(encArg(x_1)) encode_activate(x_1) -> activate(encArg(x_1)) encode_n__incr(x_1) -> n__incr(encArg(x_1)) encode_n__adx(x_1) -> n__adx(encArg(x_1)) encode_hd(x_1) -> hd(encArg(x_1)) encode_tl(x_1) -> tl(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(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 -> adx(zeros)
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