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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307779
details
property
value
status
complete
benchmark
thiemann09.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n067.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.89 seconds
cpu usage
1133.1
user time
1119.45
system time
13.6503
max virtual memory
5.7098776E7
max residence set size
1.518096E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1115.71/291.53 WORST_CASE(Omega(n^1), ?) 1132.74/295.82 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1132.74/295.82 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1132.74/295.82 1132.74/295.82 1132.74/295.82 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1132.74/295.82 1132.74/295.82 (0) CpxTRS 1132.74/295.82 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1132.74/295.82 (2) TRS for Loop Detection 1132.74/295.82 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1132.74/295.82 (4) BEST 1132.74/295.82 (5) proven lower bound 1132.74/295.82 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1132.74/295.82 (7) BOUNDS(n^1, INF) 1132.74/295.82 (8) TRS for Loop Detection 1132.74/295.82 1132.74/295.82 1132.74/295.82 ---------------------------------------- 1132.74/295.82 1132.74/295.82 (0) 1132.74/295.82 Obligation: 1132.74/295.82 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1132.74/295.82 1132.74/295.82 1132.74/295.82 The TRS R consists of the following rules: 1132.74/295.82 1132.74/295.82 minus(minus(x, y), z) -> minus(x, plus(y, z)) 1132.74/295.82 minus(0, y) -> 0 1132.74/295.82 minus(x, 0) -> x 1132.74/295.82 minus(s(x), s(y)) -> minus(x, y) 1132.74/295.82 plus(0, y) -> y 1132.74/295.82 plus(s(x), y) -> plus(x, s(y)) 1132.74/295.82 plus(s(x), y) -> s(plus(y, x)) 1132.74/295.82 zero(s(x)) -> false 1132.74/295.82 zero(0) -> true 1132.74/295.82 p(s(x)) -> x 1132.74/295.82 p(0) -> 0 1132.74/295.82 div(x, y) -> quot(x, y, 0) 1132.74/295.82 quot(s(x), s(y), z) -> quot(minus(p(ack(0, x)), y), s(y), s(z)) 1132.74/295.82 quot(0, s(y), z) -> z 1132.74/295.82 ack(0, x) -> s(x) 1132.74/295.82 ack(0, x) -> plus(x, s(0)) 1132.74/295.82 ack(s(x), 0) -> ack(x, s(0)) 1132.74/295.82 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 1132.74/295.82 1132.74/295.82 S is empty. 1132.74/295.82 Rewrite Strategy: FULL 1132.74/295.82 ---------------------------------------- 1132.74/295.82 1132.74/295.82 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1132.74/295.82 Transformed a relative TRS into a decreasing-loop problem. 1132.74/295.82 ---------------------------------------- 1132.74/295.82 1132.74/295.82 (2) 1132.74/295.82 Obligation: 1132.74/295.82 Analyzing the following TRS for decreasing loops: 1132.74/295.82 1132.74/295.82 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1132.74/295.82 1132.74/295.82 1132.74/295.82 The TRS R consists of the following rules: 1132.74/295.82 1132.74/295.82 minus(minus(x, y), z) -> minus(x, plus(y, z)) 1132.74/295.82 minus(0, y) -> 0 1132.74/295.82 minus(x, 0) -> x 1132.74/295.82 minus(s(x), s(y)) -> minus(x, y) 1132.74/295.82 plus(0, y) -> y 1132.74/295.82 plus(s(x), y) -> plus(x, s(y)) 1132.74/295.82 plus(s(x), y) -> s(plus(y, x)) 1132.74/295.82 zero(s(x)) -> false 1132.74/295.82 zero(0) -> true 1132.74/295.82 p(s(x)) -> x 1132.74/295.82 p(0) -> 0 1132.74/295.82 div(x, y) -> quot(x, y, 0) 1132.74/295.82 quot(s(x), s(y), z) -> quot(minus(p(ack(0, x)), y), s(y), s(z)) 1132.74/295.82 quot(0, s(y), z) -> z 1132.74/295.82 ack(0, x) -> s(x) 1132.74/295.82 ack(0, x) -> plus(x, s(0)) 1132.74/295.82 ack(s(x), 0) -> ack(x, s(0)) 1132.74/295.82 ack(s(x), s(y)) -> ack(x, ack(s(x), y)) 1132.74/295.82 1132.74/295.82 S is empty. 1132.74/295.82 Rewrite Strategy: FULL 1132.74/295.82 ---------------------------------------- 1132.74/295.82 1132.74/295.82 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1132.74/295.82 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1132.74/295.82 1132.74/295.82 The rewrite sequence 1132.74/295.82 1132.74/295.82 plus(s(x), y) ->^+ plus(x, s(y)) 1132.74/295.82 1132.74/295.82 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1132.74/295.82 1132.74/295.82 The pumping substitution is [x / s(x)]. 1132.74/295.82 1132.74/295.82 The result substitution is [y / s(y)]. 1132.74/295.82 1132.74/295.82
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