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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307633
details
property
value
status
complete
benchmark
ternary.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n104.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.608 seconds
cpu usage
1108.01
user time
1097.0
system time
11.0174
max virtual memory
3.7840968E7
max residence set size
1.5043312E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1107.66/291.53 WORST_CASE(Omega(n^1), ?) 1107.66/291.54 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1107.66/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1107.66/291.54 1107.66/291.54 1107.66/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1107.66/291.54 1107.66/291.54 (0) CpxTRS 1107.66/291.54 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1107.66/291.54 (2) TRS for Loop Detection 1107.66/291.54 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1107.66/291.54 (4) BEST 1107.66/291.54 (5) proven lower bound 1107.66/291.54 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1107.66/291.54 (7) BOUNDS(n^1, INF) 1107.66/291.54 (8) TRS for Loop Detection 1107.66/291.54 1107.66/291.54 1107.66/291.54 ---------------------------------------- 1107.66/291.54 1107.66/291.54 (0) 1107.66/291.54 Obligation: 1107.66/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1107.66/291.54 1107.66/291.54 1107.66/291.54 The TRS R consists of the following rules: 1107.66/291.54 1107.66/291.54 0(#) -> # 1107.66/291.54 +(#, x) -> x 1107.66/291.54 +(x, #) -> x 1107.66/291.54 +(0(x), 0(y)) -> 0(+(x, y)) 1107.66/291.54 +(0(x), 1(y)) -> 1(+(x, y)) 1107.66/291.54 +(1(x), 0(y)) -> 1(+(x, y)) 1107.66/291.54 +(0(x), j(y)) -> j(+(x, y)) 1107.66/291.54 +(j(x), 0(y)) -> j(+(x, y)) 1107.66/291.54 +(1(x), 1(y)) -> j(+(+(x, y), 1(#))) 1107.66/291.54 +(j(x), j(y)) -> 1(+(+(x, y), j(#))) 1107.66/291.54 +(1(x), j(y)) -> 0(+(x, y)) 1107.66/291.54 +(j(x), 1(y)) -> 0(+(x, y)) 1107.66/291.54 +(+(x, y), z) -> +(x, +(y, z)) 1107.66/291.54 opp(#) -> # 1107.66/291.54 opp(0(x)) -> 0(opp(x)) 1107.66/291.54 opp(1(x)) -> j(opp(x)) 1107.66/291.54 opp(j(x)) -> 1(opp(x)) 1107.66/291.54 -(x, y) -> +(x, opp(y)) 1107.66/291.54 *(#, x) -> # 1107.66/291.54 *(0(x), y) -> 0(*(x, y)) 1107.66/291.54 *(1(x), y) -> +(0(*(x, y)), y) 1107.66/291.54 *(j(x), y) -> -(0(*(x, y)), y) 1107.66/291.54 *(*(x, y), z) -> *(x, *(y, z)) 1107.66/291.54 1107.66/291.54 S is empty. 1107.66/291.54 Rewrite Strategy: FULL 1107.66/291.54 ---------------------------------------- 1107.66/291.54 1107.66/291.54 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1107.66/291.54 Transformed a relative TRS into a decreasing-loop problem. 1107.66/291.54 ---------------------------------------- 1107.66/291.54 1107.66/291.54 (2) 1107.66/291.54 Obligation: 1107.66/291.54 Analyzing the following TRS for decreasing loops: 1107.66/291.54 1107.66/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1107.66/291.54 1107.66/291.54 1107.66/291.54 The TRS R consists of the following rules: 1107.66/291.54 1107.66/291.54 0(#) -> # 1107.66/291.54 +(#, x) -> x 1107.66/291.54 +(x, #) -> x 1107.66/291.54 +(0(x), 0(y)) -> 0(+(x, y)) 1107.66/291.54 +(0(x), 1(y)) -> 1(+(x, y)) 1107.66/291.54 +(1(x), 0(y)) -> 1(+(x, y)) 1107.66/291.54 +(0(x), j(y)) -> j(+(x, y)) 1107.66/291.54 +(j(x), 0(y)) -> j(+(x, y)) 1107.66/291.54 +(1(x), 1(y)) -> j(+(+(x, y), 1(#))) 1107.66/291.54 +(j(x), j(y)) -> 1(+(+(x, y), j(#))) 1107.66/291.54 +(1(x), j(y)) -> 0(+(x, y)) 1107.66/291.54 +(j(x), 1(y)) -> 0(+(x, y)) 1107.66/291.54 +(+(x, y), z) -> +(x, +(y, z)) 1107.66/291.54 opp(#) -> # 1107.66/291.54 opp(0(x)) -> 0(opp(x)) 1107.66/291.54 opp(1(x)) -> j(opp(x)) 1107.66/291.54 opp(j(x)) -> 1(opp(x)) 1107.66/291.54 -(x, y) -> +(x, opp(y)) 1107.66/291.54 *(#, x) -> # 1107.66/291.54 *(0(x), y) -> 0(*(x, y)) 1107.66/291.54 *(1(x), y) -> +(0(*(x, y)), y) 1107.66/291.54 *(j(x), y) -> -(0(*(x, y)), y) 1107.66/291.54 *(*(x, y), z) -> *(x, *(y, z)) 1107.66/291.54 1107.66/291.54 S is empty. 1107.66/291.54 Rewrite Strategy: FULL 1107.66/291.54 ---------------------------------------- 1107.66/291.54 1107.66/291.54 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1107.66/291.54 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1107.66/291.54 1107.66/291.54 The rewrite sequence
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