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Derivational Complexity: TRS Innermost pair #487108632
details
property
value
status
complete
benchmark
Ex4_7_37_Bor03_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.542 seconds
cpu usage
1118.22
user time
1107.05
system time
11.1672
max virtual memory
3.7376868E7
max residence set size
1.491484E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 550 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 ---------------------------------------- (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: a__from(X) -> cons(mark(X), from(s(X))) a__sel(0, cons(X, XS)) -> mark(X) a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) a__minus(X, 0) -> 0 a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y)) a__quot(0, s(Y)) -> 0 a__quot(s(X), s(Y)) -> s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y)))) a__zWquot(XS, nil) -> nil a__zWquot(nil, XS) -> nil a__zWquot(cons(X, XS), cons(Y, YS)) -> cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS)) mark(from(X)) -> a__from(mark(X)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2)) mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2)) mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0) -> 0 mark(nil) -> nil a__from(X) -> from(X) a__sel(X1, X2) -> sel(X1, X2) a__minus(X1, X2) -> minus(X1, X2) a__quot(X1, X2) -> quot(X1, X2) a__zWquot(X1, X2) -> zWquot(X1, X2) 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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(from(x_1)) -> from(encArg(x_1)) encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(nil) -> nil encArg(zWquot(x_1, x_2)) -> zWquot(encArg(x_1), encArg(x_2)) encArg(sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encArg(cons_a__from(x_1)) -> a__from(encArg(x_1)) encArg(cons_a__sel(x_1, x_2)) -> a__sel(encArg(x_1), encArg(x_2)) encArg(cons_a__minus(x_1, x_2)) -> a__minus(encArg(x_1), encArg(x_2)) encArg(cons_a__quot(x_1, x_2)) -> a__quot(encArg(x_1), encArg(x_2)) encArg(cons_a__zWquot(x_1, x_2)) -> a__zWquot(encArg(x_1), encArg(x_2)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__from(x_1) -> a__from(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_mark(x_1) -> mark(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_a__sel(x_1, x_2) -> a__sel(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_a__minus(x_1, x_2) -> a__minus(encArg(x_1), encArg(x_2)) encode_a__quot(x_1, x_2) -> a__quot(encArg(x_1), encArg(x_2)) encode_a__zWquot(x_1, x_2) -> a__zWquot(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_zWquot(x_1, x_2) -> zWquot(encArg(x_1), encArg(x_2)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).
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