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Derivational Complexity: TRS Innermost pair #487105240
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
n147.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
293.361 seconds
cpu usage
1101.76
user time
1091.12
system time
10.649
max virtual memory
3.8019828E7
max residence set size
1.4775152E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 1187 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 5 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs 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) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(empty) -> empty encArg(edge(x_1, x_2, x_3)) -> edge(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) encArg(cons_or(x_1, x_2)) -> or(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_size(x_1)) -> size(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_reachable(x_1, x_2, x_3)) -> reachable(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_reach(x_1, x_2, x_3, x_4, x_5)) -> reach(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encArg(cons_if1(x_1, x_2, x_3, x_4, x_5, x_6)) -> if1(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6)) encArg(cons_if2(x_1, x_2, x_3, x_4, x_5, x_6)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6)) encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_or(x_1, x_2) -> or(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_size(x_1) -> size(encArg(x_1)) encode_empty -> empty encode_edge(x_1, x_2, x_3) -> edge(encArg(x_1), encArg(x_2), encArg(x_3)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_reachable(x_1, x_2, x_3) -> reachable(encArg(x_1), encArg(x_2), encArg(x_3)) encode_reach(x_1, x_2, x_3, x_4, x_5) -> reach(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encode_if1(x_1, x_2, x_3, x_4, x_5, x_6) -> if1(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6)) encode_if2(x_1, x_2, x_3, x_4, x_5, x_6) -> if2(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules:
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