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Runti Compl Inner Rewri 22807 pair #381904370
details
property
value
status
complete
benchmark
fold.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.50772094727 seconds
cpu usage
14.153916158
max memory
3.978129408E9
stage attributes
key
value
output-size
11344
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 54 ms] (10) CdtProblem (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (12) BOUNDS(1, 1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: foldl(x, Cons(S(0), xs)) -> foldl(S(x), xs) foldl(S(0), Cons(x, xs)) -> foldl(S(x), xs) foldr(a, Cons(x, xs)) -> op(x, foldr(a, xs)) foldr(a, Nil) -> a foldl(a, Nil) -> a notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False op(x, S(0)) -> S(x) op(S(0), y) -> S(y) fold(a, xs) -> Cons(foldl(a, xs), Cons(foldr(a, xs), Nil)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: foldl(z0, Cons(S(0), z1)) -> foldl(S(z0), z1) foldl(S(0), Cons(z0, z1)) -> foldl(S(z0), z1) foldl(z0, Nil) -> z0 foldr(z0, Cons(z1, z2)) -> op(z1, foldr(z0, z2)) foldr(z0, Nil) -> z0 notEmpty(Cons(z0, z1)) -> True notEmpty(Nil) -> False op(z0, S(0)) -> S(z0) op(S(0), z0) -> S(z0) fold(z0, z1) -> Cons(foldl(z0, z1), Cons(foldr(z0, z1), Nil)) Tuples: FOLDL(z0, Cons(S(0), z1)) -> c(FOLDL(S(z0), z1)) FOLDL(S(0), Cons(z0, z1)) -> c1(FOLDL(S(z0), z1)) FOLDL(z0, Nil) -> c2 FOLDR(z0, Cons(z1, z2)) -> c3(OP(z1, foldr(z0, z2)), FOLDR(z0, z2)) FOLDR(z0, Nil) -> c4 NOTEMPTY(Cons(z0, z1)) -> c5 NOTEMPTY(Nil) -> c6 OP(z0, S(0)) -> c7 OP(S(0), z0) -> c8 FOLD(z0, z1) -> c9(FOLDL(z0, z1), FOLDR(z0, z1)) S tuples: FOLDL(z0, Cons(S(0), z1)) -> c(FOLDL(S(z0), z1)) FOLDL(S(0), Cons(z0, z1)) -> c1(FOLDL(S(z0), z1)) FOLDL(z0, Nil) -> c2 FOLDR(z0, Cons(z1, z2)) -> c3(OP(z1, foldr(z0, z2)), FOLDR(z0, z2)) FOLDR(z0, Nil) -> c4 NOTEMPTY(Cons(z0, z1)) -> c5 NOTEMPTY(Nil) -> c6 OP(z0, S(0)) -> c7 OP(S(0), z0) -> c8
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