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Derivational Complexity: TRS Innermost pair #487108150
details
property
value
status
complete
benchmark
Ex4_DLMMU04_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
34.0939 seconds
cpu usage
127.226
user time
123.944
system time
3.28167
max virtual memory
3.8020128E7
max residence set size
5937468.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF).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), 601 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 37 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, 8607 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: and(tt, T) -> T isNatIList(IL) -> isNatList(activate(IL)) isNat(n__0) -> tt isNat(n__s(N)) -> isNat(activate(N)) isNat(n__length(L)) -> isNatList(activate(L)) isNatIList(n__zeros) -> tt isNatIList(n__cons(N, IL)) -> and(isNat(activate(N)), isNatIList(activate(IL))) isNatList(n__nil) -> tt isNatList(n__cons(N, L)) -> and(isNat(activate(N)), isNatList(activate(L))) isNatList(n__take(N, IL)) -> and(isNat(activate(N)), isNatIList(activate(IL))) zeros -> cons(0, n__zeros) take(0, IL) -> uTake1(isNatIList(IL)) uTake1(tt) -> nil take(s(M), cons(N, IL)) -> uTake2(and(isNat(M), and(isNat(N), isNatIList(activate(IL)))), M, N, activate(IL)) uTake2(tt, M, N, IL) -> cons(activate(N), n__take(activate(M), activate(IL))) length(cons(N, L)) -> uLength(and(isNat(N), isNatList(activate(L))), activate(L)) uLength(tt, L) -> s(length(activate(L))) 0 -> n__0 s(X) -> n__s(X) length(X) -> n__length(X) zeros -> n__zeros cons(X1, X2) -> n__cons(X1, X2) nil -> n__nil take(X1, X2) -> n__take(X1, X2) activate(n__0) -> 0 activate(n__s(X)) -> s(X) activate(n__length(X)) -> length(X) activate(n__zeros) -> zeros activate(n__cons(X1, X2)) -> cons(X1, X2) activate(n__nil) -> nil activate(n__take(X1, X2)) -> take(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(tt) -> tt encArg(n__0) -> n__0 encArg(n__s(x_1)) -> n__s(encArg(x_1)) encArg(n__length(x_1)) -> n__length(encArg(x_1)) encArg(n__zeros) -> n__zeros encArg(n__cons(x_1, x_2)) -> n__cons(encArg(x_1), encArg(x_2)) encArg(n__nil) -> n__nil encArg(n__take(x_1, x_2)) -> n__take(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNatIList(x_1)) -> isNatIList(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_isNatList(x_1)) -> isNatList(encArg(x_1)) encArg(cons_zeros) -> zeros encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_uTake1(x_1)) -> uTake1(encArg(x_1)) encArg(cons_uTake2(x_1, x_2, x_3, x_4)) -> uTake2(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_length(x_1)) -> length(encArg(x_1)) encArg(cons_uLength(x_1, x_2)) -> uLength(encArg(x_1), encArg(x_2)) encArg(cons_0) -> 0 encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_nil) -> nil encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_isNatIList(x_1) -> isNatIList(encArg(x_1)) encode_isNatList(x_1) -> isNatList(encArg(x_1))
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return to Derivational Complexity: TRS Innermost