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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307622
details
property
value
status
complete
benchmark
tree.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n006.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.812 seconds
cpu usage
1077.56
user time
1066.39
system time
11.1727
max virtual memory
3.875832E7
max residence set size
1.478888E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1077.11/291.60 WORST_CASE(Omega(n^1), ?) 1077.11/291.62 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1077.11/291.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1077.11/291.62 1077.11/291.62 1077.11/291.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1077.11/291.62 1077.11/291.62 (0) CpxTRS 1077.11/291.62 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1077.11/291.62 (2) TRS for Loop Detection 1077.11/291.62 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1077.11/291.62 (4) BEST 1077.11/291.62 (5) proven lower bound 1077.11/291.62 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1077.11/291.62 (7) BOUNDS(n^1, INF) 1077.11/291.62 (8) TRS for Loop Detection 1077.11/291.62 1077.11/291.62 1077.11/291.62 ---------------------------------------- 1077.11/291.62 1077.11/291.62 (0) 1077.11/291.62 Obligation: 1077.11/291.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1077.11/291.62 1077.11/291.62 1077.11/291.62 The TRS R consists of the following rules: 1077.11/291.62 1077.11/291.62 0(#) -> # 1077.11/291.62 +(x, #) -> x 1077.11/291.62 +(#, x) -> x 1077.11/291.62 +(0(x), 0(y)) -> 0(+(x, y)) 1077.11/291.62 +(0(x), 1(y)) -> 1(+(x, y)) 1077.11/291.62 +(1(x), 0(y)) -> 1(+(x, y)) 1077.11/291.62 +(1(x), 1(y)) -> 0(+(+(x, y), 1(#))) 1077.11/291.62 +(x, +(y, z)) -> +(+(x, y), z) 1077.11/291.62 -(x, #) -> x 1077.11/291.62 -(#, x) -> # 1077.11/291.62 -(0(x), 0(y)) -> 0(-(x, y)) 1077.11/291.62 -(0(x), 1(y)) -> 1(-(-(x, y), 1(#))) 1077.11/291.62 -(1(x), 0(y)) -> 1(-(x, y)) 1077.11/291.62 -(1(x), 1(y)) -> 0(-(x, y)) 1077.11/291.62 not(false) -> true 1077.11/291.62 not(true) -> false 1077.11/291.62 and(x, true) -> x 1077.11/291.62 and(x, false) -> false 1077.11/291.62 if(true, x, y) -> x 1077.11/291.62 if(false, x, y) -> y 1077.11/291.62 ge(0(x), 0(y)) -> ge(x, y) 1077.11/291.62 ge(0(x), 1(y)) -> not(ge(y, x)) 1077.11/291.62 ge(1(x), 0(y)) -> ge(x, y) 1077.11/291.62 ge(1(x), 1(y)) -> ge(x, y) 1077.11/291.62 ge(x, #) -> true 1077.11/291.62 ge(#, 1(x)) -> false 1077.11/291.62 ge(#, 0(x)) -> ge(#, x) 1077.11/291.62 val(l(x)) -> x 1077.11/291.62 val(n(x, y, z)) -> x 1077.11/291.62 min(l(x)) -> x 1077.11/291.62 min(n(x, y, z)) -> min(y) 1077.11/291.62 max(l(x)) -> x 1077.11/291.62 max(n(x, y, z)) -> max(z) 1077.11/291.62 bs(l(x)) -> true 1077.11/291.62 bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))) 1077.11/291.62 size(l(x)) -> 1(#) 1077.11/291.62 size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#)) 1077.11/291.62 wb(l(x)) -> true 1077.11/291.62 wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z))) 1077.11/291.62 1077.11/291.62 S is empty. 1077.11/291.62 Rewrite Strategy: FULL 1077.11/291.62 ---------------------------------------- 1077.11/291.62 1077.11/291.62 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1077.11/291.62 Transformed a relative TRS into a decreasing-loop problem. 1077.11/291.62 ---------------------------------------- 1077.11/291.62 1077.11/291.62 (2) 1077.11/291.62 Obligation: 1077.11/291.62 Analyzing the following TRS for decreasing loops: 1077.11/291.62 1077.11/291.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1077.11/291.62 1077.11/291.62 1077.11/291.62 The TRS R consists of the following rules: 1077.11/291.62 1077.11/291.62 0(#) -> # 1077.11/291.62 +(x, #) -> x 1077.11/291.62 +(#, x) -> x 1077.11/291.62 +(0(x), 0(y)) -> 0(+(x, y)) 1077.11/291.62 +(0(x), 1(y)) -> 1(+(x, y)) 1077.11/291.62 +(1(x), 0(y)) -> 1(+(x, y)) 1077.11/291.62 +(1(x), 1(y)) -> 0(+(+(x, y), 1(#))) 1077.11/291.62 +(x, +(y, z)) -> +(+(x, y), z) 1077.11/291.62 -(x, #) -> x 1077.11/291.62 -(#, x) -> # 1077.11/291.62 -(0(x), 0(y)) -> 0(-(x, y)) 1077.11/291.62 -(0(x), 1(y)) -> 1(-(-(x, y), 1(#))) 1077.11/291.62 -(1(x), 0(y)) -> 1(-(x, y)) 1077.11/291.62 -(1(x), 1(y)) -> 0(-(x, y)) 1077.11/291.62 not(false) -> true 1077.11/291.62 not(true) -> false
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