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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313682
details
property
value
status
complete
benchmark
rta1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n133.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.601 seconds
cpu usage
948.049
user time
938.651
system time
9.39742
max virtual memory
3.724572E7
max residence set size
1.4968628E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
947.60/291.49 WORST_CASE(Omega(n^1), ?) 947.60/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 947.60/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 947.60/291.50 947.60/291.50 947.60/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 947.60/291.50 947.60/291.50 (0) CpxTRS 947.60/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 947.60/291.50 (2) TRS for Loop Detection 947.60/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 947.60/291.50 (4) BEST 947.60/291.50 (5) proven lower bound 947.60/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 947.60/291.50 (7) BOUNDS(n^1, INF) 947.60/291.50 (8) TRS for Loop Detection 947.60/291.50 947.60/291.50 947.60/291.50 ---------------------------------------- 947.60/291.50 947.60/291.50 (0) 947.60/291.50 Obligation: 947.60/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 947.60/291.50 947.60/291.50 947.60/291.50 The TRS R consists of the following rules: 947.60/291.50 947.60/291.50 plus(s(s(x)), y) -> s(plus(x, s(y))) 947.60/291.50 plus(x, s(s(y))) -> s(plus(s(x), y)) 947.60/291.50 plus(s(0), y) -> s(y) 947.60/291.50 plus(0, y) -> y 947.60/291.50 ack(0, y) -> s(y) 947.60/291.50 ack(s(x), 0) -> ack(x, s(0)) 947.60/291.50 ack(s(x), s(y)) -> ack(x, plus(y, ack(s(x), y))) 947.60/291.50 947.60/291.50 S is empty. 947.60/291.50 Rewrite Strategy: INNERMOST 947.60/291.50 ---------------------------------------- 947.60/291.50 947.60/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 947.60/291.50 Transformed a relative TRS into a decreasing-loop problem. 947.60/291.50 ---------------------------------------- 947.60/291.50 947.60/291.50 (2) 947.60/291.50 Obligation: 947.60/291.50 Analyzing the following TRS for decreasing loops: 947.60/291.50 947.60/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 947.60/291.50 947.60/291.50 947.60/291.50 The TRS R consists of the following rules: 947.60/291.50 947.60/291.50 plus(s(s(x)), y) -> s(plus(x, s(y))) 947.60/291.50 plus(x, s(s(y))) -> s(plus(s(x), y)) 947.60/291.50 plus(s(0), y) -> s(y) 947.60/291.50 plus(0, y) -> y 947.60/291.50 ack(0, y) -> s(y) 947.60/291.50 ack(s(x), 0) -> ack(x, s(0)) 947.60/291.50 ack(s(x), s(y)) -> ack(x, plus(y, ack(s(x), y))) 947.60/291.50 947.60/291.50 S is empty. 947.60/291.50 Rewrite Strategy: INNERMOST 947.60/291.50 ---------------------------------------- 947.60/291.50 947.60/291.50 (3) DecreasingLoopProof (LOWER BOUND(ID)) 947.60/291.50 The following loop(s) give(s) rise to the lower bound Omega(n^1): 947.60/291.50 947.60/291.50 The rewrite sequence 947.60/291.50 947.60/291.50 plus(x, s(s(y))) ->^+ s(plus(s(x), y)) 947.60/291.50 947.60/291.50 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 947.60/291.50 947.60/291.50 The pumping substitution is [y / s(s(y))]. 947.60/291.50 947.60/291.50 The result substitution is [x / s(x)]. 947.60/291.50 947.60/291.50 947.60/291.50 947.60/291.50 947.60/291.50 ---------------------------------------- 947.60/291.50 947.60/291.50 (4) 947.60/291.50 Complex Obligation (BEST) 947.60/291.50 947.60/291.50 ---------------------------------------- 947.60/291.50 947.60/291.50 (5) 947.60/291.50 Obligation: 947.60/291.50 Proved the lower bound n^1 for the following obligation: 947.60/291.50 947.60/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 947.60/291.50 947.60/291.50 947.60/291.50 The TRS R consists of the following rules: 947.60/291.50 947.60/291.50 plus(s(s(x)), y) -> s(plus(x, s(y))) 947.60/291.50 plus(x, s(s(y))) -> s(plus(s(x), y)) 947.60/291.50 plus(s(0), y) -> s(y) 947.60/291.50 plus(0, y) -> y
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