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Derivational Complexity: TRS Innermost pair #487105362
details
property
value
status
complete
benchmark
#4.35.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
292.458 seconds
cpu usage
1136.46
user time
1125.04
system time
11.419
max virtual memory
1.8978128E7
max residence set size
1.5114968E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 230 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 6 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: and(true, y) -> y and(false, y) -> false eq(nil, nil) -> true eq(cons(t, l), nil) -> false eq(nil, cons(t, l)) -> false eq(cons(t, l), cons(t', l')) -> and(eq(t, t'), eq(l, l')) eq(var(l), var(l')) -> eq(l, l') eq(var(l), apply(t, s)) -> false eq(var(l), lambda(x, t)) -> false eq(apply(t, s), var(l)) -> false eq(apply(t, s), apply(t', s')) -> and(eq(t, t'), eq(s, s')) eq(apply(t, s), lambda(x, t)) -> false eq(lambda(x, t), var(l)) -> false eq(lambda(x, t), apply(t, s)) -> false eq(lambda(x, t), lambda(x', t')) -> and(eq(x, x'), eq(t, t')) if(true, var(k), var(l')) -> var(k) if(false, var(k), var(l')) -> var(l') ren(var(l), var(k), var(l')) -> if(eq(l, l'), var(k), var(l')) ren(x, y, apply(t, s)) -> apply(ren(x, y, t), ren(x, y, s)) ren(x, y, lambda(z, t)) -> lambda(var(cons(x, cons(y, cons(lambda(z, t), nil)))), ren(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t))) 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(true) -> true encArg(false) -> false encArg(nil) -> nil encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(var(x_1)) -> var(encArg(x_1)) encArg(apply(x_1, x_2)) -> apply(encArg(x_1), encArg(x_2)) encArg(lambda(x_1, x_2)) -> lambda(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ren(x_1, x_2, x_3)) -> ren(encArg(x_1), encArg(x_2), encArg(x_3)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_var(x_1) -> var(encArg(x_1)) encode_apply(x_1, x_2) -> apply(encArg(x_1), encArg(x_2)) encode_lambda(x_1, x_2) -> lambda(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ren(x_1, x_2, x_3) -> ren(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (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: and(true, y) -> y and(false, y) -> false eq(nil, nil) -> true eq(cons(t, l), nil) -> false eq(nil, cons(t, l)) -> false eq(cons(t, l), cons(t', l')) -> and(eq(t, t'), eq(l, l')) eq(var(l), var(l')) -> eq(l, l') eq(var(l), apply(t, s)) -> false
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