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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307626
details
property
value
status
complete
benchmark
ternary-hard.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.393 seconds
cpu usage
1132.71
user time
1121.32
system time
11.3931
max virtual memory
1.8938276E7
max residence set size
1.5070508E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1132.03/295.20 WORST_CASE(Omega(n^1), ?) 1132.38/295.32 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1132.38/295.32 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1132.38/295.32 1132.38/295.32 1132.38/295.32 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1132.38/295.32 1132.38/295.32 (0) CpxTRS 1132.38/295.32 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1132.38/295.32 (2) TRS for Loop Detection 1132.38/295.32 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1132.38/295.32 (4) BEST 1132.38/295.32 (5) proven lower bound 1132.38/295.32 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1132.38/295.32 (7) BOUNDS(n^1, INF) 1132.38/295.32 (8) TRS for Loop Detection 1132.38/295.32 1132.38/295.32 1132.38/295.32 ---------------------------------------- 1132.38/295.32 1132.38/295.32 (0) 1132.38/295.32 Obligation: 1132.38/295.32 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1132.38/295.32 1132.38/295.32 1132.38/295.32 The TRS R consists of the following rules: 1132.38/295.32 1132.38/295.32 0(#) -> # 1132.38/295.32 +(#, x) -> x 1132.38/295.32 +(x, #) -> x 1132.38/295.32 +(0(x), 0(y)) -> 0(+(x, y)) 1132.38/295.32 +(0(x), 1(y)) -> 1(+(x, y)) 1132.38/295.32 +(1(x), 0(y)) -> 1(+(x, y)) 1132.38/295.32 +(0(x), j(y)) -> j(+(x, y)) 1132.38/295.32 +(j(x), 0(y)) -> j(+(x, y)) 1132.38/295.32 +(1(x), 1(y)) -> j(+(+(x, y), 1(#))) 1132.38/295.32 +(j(x), j(y)) -> 1(+(+(x, y), j(#))) 1132.38/295.32 +(1(x), j(y)) -> 0(+(x, y)) 1132.38/295.32 +(j(x), 1(y)) -> 0(+(x, y)) 1132.38/295.32 +(+(x, y), z) -> +(x, +(y, z)) 1132.38/295.32 opp(#) -> # 1132.38/295.32 opp(0(x)) -> 0(opp(x)) 1132.38/295.32 opp(1(x)) -> j(opp(x)) 1132.38/295.32 opp(j(x)) -> 1(opp(x)) 1132.38/295.32 -(x, y) -> +(x, opp(y)) 1132.38/295.32 *(#, x) -> # 1132.38/295.32 *(0(x), y) -> 0(*(x, y)) 1132.38/295.32 *(1(x), y) -> +(0(*(x, y)), y) 1132.38/295.32 *(j(x), y) -> -(0(*(x, y)), y) 1132.38/295.32 *(*(x, y), z) -> *(x, *(y, z)) 1132.38/295.32 *(+(x, y), z) -> +(*(x, z), *(y, z)) 1132.38/295.32 *(x, +(y, z)) -> +(*(x, y), *(x, z)) 1132.38/295.32 1132.38/295.32 S is empty. 1132.38/295.32 Rewrite Strategy: FULL 1132.38/295.32 ---------------------------------------- 1132.38/295.32 1132.38/295.32 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1132.38/295.32 Transformed a relative TRS into a decreasing-loop problem. 1132.38/295.32 ---------------------------------------- 1132.38/295.32 1132.38/295.32 (2) 1132.38/295.32 Obligation: 1132.38/295.32 Analyzing the following TRS for decreasing loops: 1132.38/295.32 1132.38/295.32 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1132.38/295.32 1132.38/295.32 1132.38/295.32 The TRS R consists of the following rules: 1132.38/295.32 1132.38/295.32 0(#) -> # 1132.38/295.32 +(#, x) -> x 1132.38/295.32 +(x, #) -> x 1132.38/295.32 +(0(x), 0(y)) -> 0(+(x, y)) 1132.38/295.32 +(0(x), 1(y)) -> 1(+(x, y)) 1132.38/295.32 +(1(x), 0(y)) -> 1(+(x, y)) 1132.38/295.32 +(0(x), j(y)) -> j(+(x, y)) 1132.38/295.32 +(j(x), 0(y)) -> j(+(x, y)) 1132.38/295.32 +(1(x), 1(y)) -> j(+(+(x, y), 1(#))) 1132.38/295.32 +(j(x), j(y)) -> 1(+(+(x, y), j(#))) 1132.38/295.32 +(1(x), j(y)) -> 0(+(x, y)) 1132.38/295.32 +(j(x), 1(y)) -> 0(+(x, y)) 1132.38/295.32 +(+(x, y), z) -> +(x, +(y, z)) 1132.38/295.32 opp(#) -> # 1132.38/295.32 opp(0(x)) -> 0(opp(x)) 1132.38/295.32 opp(1(x)) -> j(opp(x)) 1132.38/295.32 opp(j(x)) -> 1(opp(x)) 1132.38/295.32 -(x, y) -> +(x, opp(y)) 1132.38/295.32 *(#, x) -> # 1132.38/295.32 *(0(x), y) -> 0(*(x, y)) 1132.38/295.32 *(1(x), y) -> +(0(*(x, y)), y) 1132.38/295.32 *(j(x), y) -> -(0(*(x, y)), y) 1132.38/295.32 *(*(x, y), z) -> *(x, *(y, z)) 1132.38/295.32 *(+(x, y), z) -> +(*(x, z), *(y, z)) 1132.38/295.32 *(x, +(y, z)) -> +(*(x, y), *(x, z)) 1132.38/295.32 1132.38/295.32 S is empty. 1132.38/295.32 Rewrite Strategy: FULL 1132.38/295.32 ---------------------------------------- 1132.38/295.32
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