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Runti Compl Full Rewri 10127 pair #381903351
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
n073.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.58535790443 seconds
cpu usage
3.457509715
max memory
2.1909504E8
stage attributes
key
value
output-size
3631
starexec-result
WORST_CASE(?, O(1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).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, 10 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
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