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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307634
details
property
value
status
complete
benchmark
filliatre3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n117.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.631 seconds
cpu usage
1120.54
user time
1106.77
system time
13.7775
max virtual memory
3.724416E7
max residence set size
1.4875124E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1120.17/291.51 WORST_CASE(Omega(n^1), ?) 1120.38/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1120.38/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1120.38/291.55 1120.38/291.55 1120.38/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1120.38/291.55 1120.38/291.55 (0) CpxTRS 1120.38/291.55 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1120.38/291.55 (2) TRS for Loop Detection 1120.38/291.55 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1120.38/291.55 (4) BEST 1120.38/291.55 (5) proven lower bound 1120.38/291.55 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1120.38/291.55 (7) BOUNDS(n^1, INF) 1120.38/291.55 (8) TRS for Loop Detection 1120.38/291.55 1120.38/291.55 1120.38/291.55 ---------------------------------------- 1120.38/291.55 1120.38/291.55 (0) 1120.38/291.55 Obligation: 1120.38/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1120.38/291.55 1120.38/291.55 1120.38/291.55 The TRS R consists of the following rules: 1120.38/291.55 1120.38/291.55 g(A) -> A 1120.38/291.55 g(B) -> A 1120.38/291.55 g(B) -> B 1120.38/291.55 g(C) -> A 1120.38/291.55 g(C) -> B 1120.38/291.55 g(C) -> C 1120.38/291.55 foldB(t, 0) -> t 1120.38/291.55 foldB(t, s(n)) -> f(foldB(t, n), B) 1120.38/291.55 foldC(t, 0) -> t 1120.38/291.55 foldC(t, s(n)) -> f(foldC(t, n), C) 1120.38/291.55 f(t, x) -> f'(t, g(x)) 1120.38/291.55 f'(triple(a, b, c), C) -> triple(a, b, s(c)) 1120.38/291.55 f'(triple(a, b, c), B) -> f(triple(a, b, c), A) 1120.38/291.55 f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b)) 1120.38/291.55 f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c) 1120.38/291.55 fold(t, x, 0) -> t 1120.38/291.55 fold(t, x, s(n)) -> f(fold(t, x, n), x) 1120.38/291.55 1120.38/291.55 S is empty. 1120.38/291.55 Rewrite Strategy: FULL 1120.38/291.55 ---------------------------------------- 1120.38/291.55 1120.38/291.55 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1120.38/291.55 Transformed a relative TRS into a decreasing-loop problem. 1120.38/291.55 ---------------------------------------- 1120.38/291.55 1120.38/291.55 (2) 1120.38/291.55 Obligation: 1120.38/291.55 Analyzing the following TRS for decreasing loops: 1120.38/291.55 1120.38/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1120.38/291.55 1120.38/291.55 1120.38/291.55 The TRS R consists of the following rules: 1120.38/291.55 1120.38/291.55 g(A) -> A 1120.38/291.55 g(B) -> A 1120.38/291.55 g(B) -> B 1120.38/291.55 g(C) -> A 1120.38/291.55 g(C) -> B 1120.38/291.55 g(C) -> C 1120.38/291.55 foldB(t, 0) -> t 1120.38/291.55 foldB(t, s(n)) -> f(foldB(t, n), B) 1120.38/291.55 foldC(t, 0) -> t 1120.38/291.55 foldC(t, s(n)) -> f(foldC(t, n), C) 1120.38/291.55 f(t, x) -> f'(t, g(x)) 1120.38/291.55 f'(triple(a, b, c), C) -> triple(a, b, s(c)) 1120.38/291.55 f'(triple(a, b, c), B) -> f(triple(a, b, c), A) 1120.38/291.55 f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b)) 1120.38/291.55 f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c) 1120.38/291.55 fold(t, x, 0) -> t 1120.38/291.55 fold(t, x, s(n)) -> f(fold(t, x, n), x) 1120.38/291.55 1120.38/291.55 S is empty. 1120.38/291.55 Rewrite Strategy: FULL 1120.38/291.55 ---------------------------------------- 1120.38/291.55 1120.38/291.55 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1120.38/291.55 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1120.38/291.55 1120.38/291.55 The rewrite sequence 1120.38/291.55 1120.38/291.55 foldC(t, s(n)) ->^+ f(foldC(t, n), C) 1120.38/291.55 1120.38/291.55 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1120.38/291.55 1120.38/291.55 The pumping substitution is [n / s(n)]. 1120.38/291.55 1120.38/291.55 The result substitution is [ ]. 1120.38/291.55 1120.38/291.55 1120.38/291.55 1120.38/291.55
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