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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307639
details
property
value
status
complete
benchmark
log2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n110.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.578 seconds
cpu usage
1122.02
user time
1111.59
system time
10.4314
max virtual memory
5.6115724E7
max residence set size
1.484328E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1121.71/291.50 WORST_CASE(Omega(n^1), ?) 1121.71/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1121.71/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1121.71/291.51 1121.71/291.51 1121.71/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1121.71/291.51 1121.71/291.51 (0) CpxTRS 1121.71/291.51 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1121.71/291.51 (2) TRS for Loop Detection 1121.71/291.51 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1121.71/291.51 (4) BEST 1121.71/291.51 (5) proven lower bound 1121.71/291.51 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1121.71/291.51 (7) BOUNDS(n^1, INF) 1121.71/291.51 (8) TRS for Loop Detection 1121.71/291.51 1121.71/291.51 1121.71/291.51 ---------------------------------------- 1121.71/291.51 1121.71/291.51 (0) 1121.71/291.51 Obligation: 1121.71/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1121.71/291.51 1121.71/291.51 1121.71/291.51 The TRS R consists of the following rules: 1121.71/291.51 1121.71/291.51 0(#) -> # 1121.71/291.51 +(#, x) -> x 1121.71/291.51 +(x, #) -> x 1121.71/291.51 +(0(x), 0(y)) -> 0(+(x, y)) 1121.71/291.51 +(0(x), 1(y)) -> 1(+(x, y)) 1121.71/291.51 +(1(x), 0(y)) -> 1(+(x, y)) 1121.71/291.51 +(1(x), 1(y)) -> 0(+(+(x, y), 1(#))) 1121.71/291.51 +(+(x, y), z) -> +(x, +(y, z)) 1121.71/291.51 -(#, x) -> # 1121.71/291.51 -(x, #) -> x 1121.71/291.51 -(0(x), 0(y)) -> 0(-(x, y)) 1121.71/291.51 -(0(x), 1(y)) -> 1(-(-(x, y), 1(#))) 1121.71/291.51 -(1(x), 0(y)) -> 1(-(x, y)) 1121.71/291.51 -(1(x), 1(y)) -> 0(-(x, y)) 1121.71/291.51 not(true) -> false 1121.71/291.51 not(false) -> true 1121.71/291.51 if(true, x, y) -> x 1121.71/291.51 if(false, x, y) -> y 1121.71/291.51 ge(0(x), 0(y)) -> ge(x, y) 1121.71/291.51 ge(0(x), 1(y)) -> not(ge(y, x)) 1121.71/291.51 ge(1(x), 0(y)) -> ge(x, y) 1121.71/291.51 ge(1(x), 1(y)) -> ge(x, y) 1121.71/291.51 ge(x, #) -> true 1121.71/291.51 ge(#, 0(x)) -> ge(#, x) 1121.71/291.51 ge(#, 1(x)) -> false 1121.71/291.51 log(x) -> -(log'(x), 1(#)) 1121.71/291.51 log'(#) -> # 1121.71/291.51 log'(1(x)) -> +(log'(x), 1(#)) 1121.71/291.51 log'(0(x)) -> if(ge(x, 1(#)), +(log'(x), 1(#)), #) 1121.71/291.51 1121.71/291.51 S is empty. 1121.71/291.51 Rewrite Strategy: FULL 1121.71/291.51 ---------------------------------------- 1121.71/291.51 1121.71/291.51 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1121.71/291.51 Transformed a relative TRS into a decreasing-loop problem. 1121.71/291.51 ---------------------------------------- 1121.71/291.51 1121.71/291.51 (2) 1121.71/291.51 Obligation: 1121.71/291.51 Analyzing the following TRS for decreasing loops: 1121.71/291.51 1121.71/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1121.71/291.51 1121.71/291.51 1121.71/291.51 The TRS R consists of the following rules: 1121.71/291.51 1121.71/291.51 0(#) -> # 1121.71/291.51 +(#, x) -> x 1121.71/291.51 +(x, #) -> x 1121.71/291.51 +(0(x), 0(y)) -> 0(+(x, y)) 1121.71/291.51 +(0(x), 1(y)) -> 1(+(x, y)) 1121.71/291.51 +(1(x), 0(y)) -> 1(+(x, y)) 1121.71/291.51 +(1(x), 1(y)) -> 0(+(+(x, y), 1(#))) 1121.71/291.51 +(+(x, y), z) -> +(x, +(y, z)) 1121.71/291.51 -(#, x) -> # 1121.71/291.51 -(x, #) -> x 1121.71/291.51 -(0(x), 0(y)) -> 0(-(x, y)) 1121.71/291.51 -(0(x), 1(y)) -> 1(-(-(x, y), 1(#))) 1121.71/291.51 -(1(x), 0(y)) -> 1(-(x, y)) 1121.71/291.51 -(1(x), 1(y)) -> 0(-(x, y)) 1121.71/291.51 not(true) -> false 1121.71/291.51 not(false) -> true 1121.71/291.51 if(true, x, y) -> x 1121.71/291.51 if(false, x, y) -> y 1121.71/291.51 ge(0(x), 0(y)) -> ge(x, y) 1121.71/291.51 ge(0(x), 1(y)) -> not(ge(y, x)) 1121.71/291.51 ge(1(x), 0(y)) -> ge(x, y) 1121.71/291.51 ge(1(x), 1(y)) -> ge(x, y) 1121.71/291.51 ge(x, #) -> true 1121.71/291.51 ge(#, 0(x)) -> ge(#, x) 1121.71/291.51 ge(#, 1(x)) -> false 1121.71/291.51 log(x) -> -(log'(x), 1(#))
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