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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313930
details
property
value
status
complete
benchmark
ack_prolog.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n154.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.677 seconds
cpu usage
1054.42
user time
1043.6
system time
10.8279
max virtual memory
3.8111996E7
max residence set size
1.4910656E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1054.18/291.60 WORST_CASE(Omega(n^1), ?) 1054.18/291.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1054.18/291.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1054.18/291.61 1054.18/291.61 1054.18/291.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1054.18/291.61 1054.18/291.61 (0) CpxTRS 1054.18/291.61 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1054.18/291.61 (2) TRS for Loop Detection 1054.18/291.61 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1054.18/291.61 (4) BEST 1054.18/291.61 (5) proven lower bound 1054.18/291.61 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1054.18/291.61 (7) BOUNDS(n^1, INF) 1054.18/291.61 (8) TRS for Loop Detection 1054.18/291.61 1054.18/291.61 1054.18/291.61 ---------------------------------------- 1054.18/291.61 1054.18/291.61 (0) 1054.18/291.61 Obligation: 1054.18/291.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1054.18/291.61 1054.18/291.61 1054.18/291.61 The TRS R consists of the following rules: 1054.18/291.61 1054.18/291.61 ack_in(0, n) -> ack_out(s(n)) 1054.18/291.61 ack_in(s(m), 0) -> u11(ack_in(m, s(0))) 1054.18/291.61 u11(ack_out(n)) -> ack_out(n) 1054.18/291.61 ack_in(s(m), s(n)) -> u21(ack_in(s(m), n), m) 1054.18/291.61 u21(ack_out(n), m) -> u22(ack_in(m, n)) 1054.18/291.61 u22(ack_out(n)) -> ack_out(n) 1054.18/291.61 1054.18/291.61 S is empty. 1054.18/291.61 Rewrite Strategy: INNERMOST 1054.18/291.61 ---------------------------------------- 1054.18/291.61 1054.18/291.61 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1054.18/291.61 Transformed a relative TRS into a decreasing-loop problem. 1054.18/291.61 ---------------------------------------- 1054.18/291.61 1054.18/291.61 (2) 1054.18/291.61 Obligation: 1054.18/291.61 Analyzing the following TRS for decreasing loops: 1054.18/291.61 1054.18/291.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1054.18/291.61 1054.18/291.61 1054.18/291.61 The TRS R consists of the following rules: 1054.18/291.61 1054.18/291.61 ack_in(0, n) -> ack_out(s(n)) 1054.18/291.61 ack_in(s(m), 0) -> u11(ack_in(m, s(0))) 1054.18/291.61 u11(ack_out(n)) -> ack_out(n) 1054.18/291.61 ack_in(s(m), s(n)) -> u21(ack_in(s(m), n), m) 1054.18/291.61 u21(ack_out(n), m) -> u22(ack_in(m, n)) 1054.18/291.61 u22(ack_out(n)) -> ack_out(n) 1054.18/291.61 1054.18/291.61 S is empty. 1054.18/291.61 Rewrite Strategy: INNERMOST 1054.18/291.61 ---------------------------------------- 1054.18/291.61 1054.18/291.61 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1054.18/291.61 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1054.18/291.61 1054.18/291.61 The rewrite sequence 1054.18/291.61 1054.18/291.61 ack_in(s(m), s(n)) ->^+ u21(ack_in(s(m), n), m) 1054.18/291.61 1054.18/291.61 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1054.18/291.61 1054.18/291.61 The pumping substitution is [n / s(n)]. 1054.18/291.61 1054.18/291.61 The result substitution is [ ]. 1054.18/291.61 1054.18/291.61 1054.18/291.61 1054.18/291.61 1054.18/291.61 ---------------------------------------- 1054.18/291.61 1054.18/291.61 (4) 1054.18/291.61 Complex Obligation (BEST) 1054.18/291.61 1054.18/291.61 ---------------------------------------- 1054.18/291.61 1054.18/291.61 (5) 1054.18/291.61 Obligation: 1054.18/291.61 Proved the lower bound n^1 for the following obligation: 1054.18/291.61 1054.18/291.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1054.18/291.61 1054.18/291.61 1054.18/291.61 The TRS R consists of the following rules: 1054.18/291.61 1054.18/291.61 ack_in(0, n) -> ack_out(s(n)) 1054.18/291.61 ack_in(s(m), 0) -> u11(ack_in(m, s(0))) 1054.18/291.61 u11(ack_out(n)) -> ack_out(n) 1054.18/291.61 ack_in(s(m), s(n)) -> u21(ack_in(s(m), n), m) 1054.18/291.61 u21(ack_out(n), m) -> u22(ack_in(m, n)) 1054.18/291.61 u22(ack_out(n)) -> ack_out(n)
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