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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308451
details
property
value
status
complete
benchmark
2.61.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n114.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.586 seconds
cpu usage
329.325
user time
325.801
system time
3.52358
max virtual memory
3.7634192E7
max residence set size
5975824.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
329.21/291.53 WORST_CASE(?, O(n^2)) 329.21/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 329.21/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 329.21/291.55 329.21/291.55 329.21/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 329.21/291.55 329.21/291.55 (0) CpxTRS 329.21/291.55 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 329.21/291.55 (2) CpxTRS 329.21/291.55 (3) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] 329.21/291.55 (4) CpxRelTRS 329.21/291.55 (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 329.21/291.55 (6) CpxRelTRS 329.21/291.55 (7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 329.21/291.55 (8) CpxWeightedTrs 329.21/291.55 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 329.21/291.55 (10) CpxTypedWeightedTrs 329.21/291.55 (11) CompletionProof [UPPER BOUND(ID), 0 ms] 329.21/291.55 (12) CpxTypedWeightedCompleteTrs 329.21/291.55 (13) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 329.21/291.55 (14) CpxTypedWeightedCompleteTrs 329.21/291.55 (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 5 ms] 329.21/291.55 (16) CpxRNTS 329.21/291.55 (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 329.21/291.55 (18) CpxRNTS 329.21/291.55 (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 329.21/291.55 (20) CpxRNTS 329.21/291.55 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 329.21/291.55 (22) CpxRNTS 329.21/291.55 (23) IntTrsBoundProof [UPPER BOUND(ID), 589 ms] 329.21/291.55 (24) CpxRNTS 329.21/291.55 (25) IntTrsBoundProof [UPPER BOUND(ID), 141 ms] 329.21/291.55 (26) CpxRNTS 329.21/291.55 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 329.21/291.55 (28) CpxRNTS 329.21/291.55 (29) IntTrsBoundProof [UPPER BOUND(ID), 233 ms] 329.21/291.55 (30) CpxRNTS 329.21/291.55 (31) IntTrsBoundProof [UPPER BOUND(ID), 26 ms] 329.21/291.55 (32) CpxRNTS 329.21/291.55 (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 329.21/291.55 (34) CpxRNTS 329.21/291.55 (35) IntTrsBoundProof [UPPER BOUND(ID), 130 ms] 329.21/291.55 (36) CpxRNTS 329.21/291.55 (37) IntTrsBoundProof [UPPER BOUND(ID), 15 ms] 329.21/291.55 (38) CpxRNTS 329.21/291.55 (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 329.21/291.55 (40) CpxRNTS 329.21/291.55 (41) IntTrsBoundProof [UPPER BOUND(ID), 820 ms] 329.21/291.55 (42) CpxRNTS 329.21/291.55 (43) IntTrsBoundProof [UPPER BOUND(ID), 511 ms] 329.21/291.55 (44) CpxRNTS 329.21/291.55 (45) FinalProof [FINISHED, 0 ms] 329.21/291.55 (46) BOUNDS(1, n^2) 329.21/291.55 329.21/291.55 329.21/291.55 ---------------------------------------- 329.21/291.55 329.21/291.55 (0) 329.21/291.55 Obligation: 329.21/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 329.21/291.55 329.21/291.55 329.21/291.55 The TRS R consists of the following rules: 329.21/291.55 329.21/291.55 f(j(x, y), y) -> g(f(x, k(y))) 329.21/291.55 f(x, h1(y, z)) -> h2(0, x, h1(y, z)) 329.21/291.55 g(h2(x, y, h1(z, u))) -> h2(s(x), y, h1(z, u)) 329.21/291.55 h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s(x), y, h1(s(z), u)) 329.21/291.55 i(f(x, h(y))) -> y 329.21/291.55 i(h2(s(x), y, h1(x, z))) -> z 329.21/291.55 k(h(x)) -> h1(0, x) 329.21/291.55 k(h1(x, y)) -> h1(s(x), y) 329.21/291.55 329.21/291.55 S is empty. 329.21/291.55 Rewrite Strategy: FULL 329.21/291.55 ---------------------------------------- 329.21/291.55 329.21/291.55 (1) DependencyGraphProof (UPPER BOUND(ID)) 329.21/291.55 The following rules are not reachable from basic terms in the dependency graph and can be removed: 329.21/291.55 329.21/291.55 i(f(x, h(y))) -> y 329.21/291.55 i(h2(s(x), y, h1(x, z))) -> z 329.21/291.55 329.21/291.55 ---------------------------------------- 329.21/291.55 329.21/291.55 (2) 329.21/291.55 Obligation: 329.21/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 329.21/291.55 329.21/291.55 329.21/291.55 The TRS R consists of the following rules: 329.21/291.55 329.21/291.55 f(j(x, y), y) -> g(f(x, k(y))) 329.21/291.55 f(x, h1(y, z)) -> h2(0, x, h1(y, z)) 329.21/291.55 g(h2(x, y, h1(z, u))) -> h2(s(x), y, h1(z, u)) 329.21/291.55 h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s(x), y, h1(s(z), u)) 329.21/291.55 k(h(x)) -> h1(0, x) 329.21/291.55 k(h1(x, y)) -> h1(s(x), y) 329.21/291.55
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