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Runti Compl Inner Rewri 22807 pair #381904793
details
property
value
status
complete
benchmark
thiemann04.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)
292.354243994 seconds
cpu usage
1138.29680998
max memory
1.5576240128E10
stage attributes
key
value
output-size
6598
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (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 union(empty, h) -> h union(edge(x, y, i), h) -> edge(x, y, union(i, h)) isEmpty(empty) -> true isEmpty(edge(x, y, i)) -> false from(edge(x, y, i)) -> x to(edge(x, y, i)) -> y rest(edge(x, y, i)) -> i rest(empty) -> empty reach(x, y, i, h) -> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) if1(true, b1, b2, b3, x, y, i, h) -> true if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h) if2(true, b2, b3, x, y, i, h) -> false if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) if3(false, b3, x, y, i, h) -> reach(x, y, rest(i), edge(from(i), to(i), h)) if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h) if4(true, x, y, i, h) -> true if4(false, x, y, i, h) -> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), empty)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: 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 union(empty, h) -> h union(edge(x, y, i), h) -> edge(x, y, union(i, h)) isEmpty(empty) -> true isEmpty(edge(x, y, i)) -> false from(edge(x, y, i)) -> x to(edge(x, y, i)) -> y rest(edge(x, y, i)) -> i rest(empty) -> empty reach(x, y, i, h) -> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) if1(true, b1, b2, b3, x, y, i, h) -> true if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h) if2(true, b2, b3, x, y, i, h) -> false if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) if3(false, b3, x, y, i, h) -> reach(x, y, rest(i), edge(from(i), to(i), h)) if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h) if4(true, x, y, i, h) -> true if4(false, x, y, i, h) -> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), empty)) S is empty. Rewrite Strategy: INNERMOST
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