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Runtime Complexity: TRS pair #487109888
details
property
value
status
complete
benchmark
Ex26_Luc03b_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.60126 seconds
cpu usage
3.53747
user time
3.3862
system time
0.151268
max virtual memory
1.827736E7
max residence set size
227680.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
WORST_CASE(?, O(1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] (4) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(n__add(sqr(activate(X)), dbl(activate(X)))) dbl(0) -> 0 dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) add(0, X) -> X add(s(X), Y) -> s(n__add(activate(X), Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(activate(X), activate(Z))) terms(X) -> n__terms(X) add(X1, X2) -> n__add(X1, X2) s(X) -> n__s(X) dbl(X) -> n__dbl(X) first(X1, X2) -> n__first(X1, X2) activate(n__terms(X)) -> terms(X) activate(n__add(X1, X2)) -> add(X1, X2) activate(n__s(X)) -> s(X) activate(n__dbl(X)) -> dbl(X) activate(n__first(X1, X2)) -> first(X1, X2) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The TRS does not nest defined symbols. Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: sqr(s(X)) -> s(n__add(sqr(activate(X)), dbl(activate(X)))) dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) add(s(X), Y) -> s(n__add(activate(X), Y)) first(s(X), cons(Y, Z)) -> cons(Y, n__first(activate(X), activate(Z))) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 dbl(0) -> 0 add(0, X) -> X first(0, X) -> nil terms(X) -> n__terms(X) add(X1, X2) -> n__add(X1, X2) s(X) -> n__s(X) dbl(X) -> n__dbl(X) first(X1, X2) -> n__first(X1, X2) activate(n__terms(X)) -> terms(X) activate(n__add(X1, X2)) -> add(X1, X2) activate(n__s(X)) -> s(X) activate(n__dbl(X)) -> dbl(X) activate(n__first(X1, X2)) -> first(X1, X2) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) NarrowingOnBasicTermsTerminatesProof (FINISHED) Constant runtime complexity proven by termination of constructor-based narrowing. The maximal most general narrowing sequences give rise to the following rewrite sequences: activate(n__first(x0, x1)) ->^* n__first(x0, x1) activate(n__first(0, x0)) ->^* nil activate(n__dbl(x0)) ->^* n__dbl(x0) activate(n__dbl(0)) ->^* 0 activate(n__s(x0)) ->^* n__s(x0)
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