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Runti Compl Inner Rewri 22807 pair #381904777
details
property
value
status
complete
benchmark
thiemann37.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.766068935 seconds
cpu usage
1146.93844758
max memory
1.539618816E10
stage attributes
key
value
output-size
20371
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 297 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 72 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 60 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 1303 ms] (18) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) or(true, y) -> true or(false, y) -> y and(true, y) -> y and(false, y) -> false size(empty) -> 0 size(edge(x, y, i)) -> s(size(i)) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) reachable(x, y, i) -> reach(x, y, 0, i, i) reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j) if1(true, x, y, c, i, j) -> true if1(false, x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j) if2(false, x, y, c, i, j) -> false if2(true, x, y, c, empty, j) -> false if2(true, x, y, c, edge(u, v, i), j) -> or(if2(true, x, y, c, i, j), and(eq(x, u), reach(v, y, s(c), j, j))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: eq(0', 0') -> true eq(0', s(x)) -> false eq(s(x), 0') -> false eq(s(x), s(y)) -> eq(x, y) or(true, y) -> true or(false, y) -> y and(true, y) -> y and(false, y) -> false size(empty) -> 0' size(edge(x, y, i)) -> s(size(i)) le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) reachable(x, y, i) -> reach(x, y, 0', i, i) reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j) if1(true, x, y, c, i, j) -> true if1(false, x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j) if2(false, x, y, c, i, j) -> false if2(true, x, y, c, empty, j) -> false if2(true, x, y, c, edge(u, v, i), j) -> or(if2(true, x, y, c, i, j), and(eq(x, u), reach(v, y, s(c), j, j)))
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