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Derivational Complexity: TRS Innermost pair #487108200
details
property
value
status
complete
benchmark
LengthOfFiniteLists_complete_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
296.683 seconds
cpu usage
1164.94
user time
1153.59
system time
11.3538
max virtual memory
2.0188004E7
max residence set size
1.4712984E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 1032 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 173 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: zeros -> cons(0, n__zeros) U11(tt, V1) -> U12(isNatList(activate(V1))) U12(tt) -> tt U21(tt, V1) -> U22(isNat(activate(V1))) U22(tt) -> tt U31(tt, V) -> U32(isNatList(activate(V))) U32(tt) -> tt U41(tt, V1, V2) -> U42(isNat(activate(V1)), activate(V2)) U42(tt, V2) -> U43(isNatIList(activate(V2))) U43(tt) -> tt U51(tt, V1, V2) -> U52(isNat(activate(V1)), activate(V2)) U52(tt, V2) -> U53(isNatList(activate(V2))) U53(tt) -> tt U61(tt, L) -> s(length(activate(L))) and(tt, X) -> activate(X) isNat(n__0) -> tt isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) isNatIList(n__zeros) -> tt isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) isNatIListKind(n__nil) -> tt isNatIListKind(n__zeros) -> tt isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) isNatKind(n__0) -> tt isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatList(n__nil) -> tt isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) length(nil) -> 0 length(cons(N, L)) -> U61(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(isNat(N), n__isNatKind(N))), activate(L)) zeros -> n__zeros 0 -> n__0 length(X) -> n__length(X) s(X) -> n__s(X) cons(X1, X2) -> n__cons(X1, X2) isNatIListKind(X) -> n__isNatIListKind(X) nil -> n__nil and(X1, X2) -> n__and(X1, X2) isNatKind(X) -> n__isNatKind(X) activate(n__zeros) -> zeros activate(n__0) -> 0 activate(n__length(X)) -> length(X) activate(n__s(X)) -> s(X) activate(n__cons(X1, X2)) -> cons(X1, X2) activate(n__isNatIListKind(X)) -> isNatIListKind(X) activate(n__nil) -> nil activate(n__and(X1, X2)) -> and(X1, X2) activate(n__isNatKind(X)) -> isNatKind(X) 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__zeros) -> n__zeros encArg(tt) -> tt encArg(n__0) -> n__0 encArg(n__length(x_1)) -> n__length(encArg(x_1)) encArg(n__s(x_1)) -> n__s(encArg(x_1)) encArg(n__cons(x_1, x_2)) -> n__cons(encArg(x_1), encArg(x_2)) encArg(n__isNatIListKind(x_1)) -> n__isNatIListKind(encArg(x_1)) encArg(n__nil) -> n__nil encArg(n__and(x_1, x_2)) -> n__and(encArg(x_1), encArg(x_2)) encArg(n__isNatKind(x_1)) -> n__isNatKind(encArg(x_1)) encArg(cons_zeros) -> zeros
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