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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308086
details
property
value
status
complete
benchmark
ExIntrod_GM04_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n166.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.78586 seconds
cpu usage
11.5127
user time
10.8803
system time
0.632388
max virtual memory
1.8515008E7
max residence set size
1816696.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
11.12/3.73 WORST_CASE(NON_POLY, ?) 11.12/3.74 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.12/3.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.12/3.74 11.12/3.74 11.12/3.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 11.12/3.74 11.12/3.74 (0) CpxTRS 11.12/3.74 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 11.12/3.74 (2) TRS for Loop Detection 11.12/3.74 (3) DecreasingLoopProof [LOWER BOUND(ID), 43 ms] 11.12/3.74 (4) BEST 11.12/3.74 (5) proven lower bound 11.12/3.74 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 11.12/3.74 (7) BOUNDS(n^1, INF) 11.12/3.74 (8) TRS for Loop Detection 11.12/3.74 (9) InfiniteLowerBoundProof [FINISHED, 1361 ms] 11.12/3.74 (10) BOUNDS(INF, INF) 11.12/3.74 11.12/3.74 11.12/3.74 ---------------------------------------- 11.12/3.74 11.12/3.74 (0) 11.12/3.74 Obligation: 11.12/3.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 11.12/3.74 11.12/3.74 11.12/3.74 The TRS R consists of the following rules: 11.12/3.74 11.12/3.74 nats -> adx(zeros) 11.12/3.74 zeros -> cons(n__0, n__zeros) 11.12/3.74 incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) 11.12/3.74 adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) 11.12/3.74 hd(cons(X, Y)) -> activate(X) 11.12/3.74 tl(cons(X, Y)) -> activate(Y) 11.12/3.74 0 -> n__0 11.12/3.74 zeros -> n__zeros 11.12/3.74 s(X) -> n__s(X) 11.12/3.74 incr(X) -> n__incr(X) 11.12/3.74 adx(X) -> n__adx(X) 11.12/3.74 activate(n__0) -> 0 11.12/3.74 activate(n__zeros) -> zeros 11.12/3.74 activate(n__s(X)) -> s(X) 11.12/3.74 activate(n__incr(X)) -> incr(X) 11.12/3.74 activate(n__adx(X)) -> adx(X) 11.12/3.74 activate(X) -> X 11.12/3.74 11.12/3.74 S is empty. 11.12/3.74 Rewrite Strategy: FULL 11.12/3.74 ---------------------------------------- 11.12/3.74 11.12/3.74 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 11.12/3.74 Transformed a relative TRS into a decreasing-loop problem. 11.12/3.74 ---------------------------------------- 11.12/3.74 11.12/3.74 (2) 11.12/3.74 Obligation: 11.12/3.74 Analyzing the following TRS for decreasing loops: 11.12/3.74 11.12/3.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 11.12/3.74 11.12/3.74 11.12/3.74 The TRS R consists of the following rules: 11.12/3.74 11.12/3.74 nats -> adx(zeros) 11.12/3.74 zeros -> cons(n__0, n__zeros) 11.12/3.74 incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) 11.12/3.74 adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) 11.12/3.74 hd(cons(X, Y)) -> activate(X) 11.12/3.74 tl(cons(X, Y)) -> activate(Y) 11.12/3.74 0 -> n__0 11.12/3.74 zeros -> n__zeros 11.12/3.74 s(X) -> n__s(X) 11.12/3.74 incr(X) -> n__incr(X) 11.12/3.74 adx(X) -> n__adx(X) 11.12/3.74 activate(n__0) -> 0 11.12/3.74 activate(n__zeros) -> zeros 11.12/3.74 activate(n__s(X)) -> s(X) 11.12/3.74 activate(n__incr(X)) -> incr(X) 11.12/3.74 activate(n__adx(X)) -> adx(X) 11.12/3.74 activate(X) -> X 11.12/3.74 11.12/3.74 S is empty. 11.12/3.74 Rewrite Strategy: FULL 11.12/3.74 ---------------------------------------- 11.12/3.74 11.12/3.74 (3) DecreasingLoopProof (LOWER BOUND(ID)) 11.12/3.74 The following loop(s) give(s) rise to the lower bound Omega(n^1): 11.12/3.74 11.12/3.74 The rewrite sequence 11.12/3.74 11.12/3.74 activate(n__incr(cons(X1_0, Y2_0))) ->^+ cons(n__s(activate(X1_0)), n__incr(activate(Y2_0))) 11.12/3.74 11.12/3.74 gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0]. 11.12/3.74 11.12/3.74 The pumping substitution is [X1_0 / n__incr(cons(X1_0, Y2_0))]. 11.12/3.74 11.12/3.74 The result substitution is [ ]. 11.12/3.74 11.12/3.74
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