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Derivational Complexity: TRS Innermost pair #487109102
details
property
value
status
complete
benchmark
Ex49_GM04_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
292.831 seconds
cpu usage
1144.23
user time
1133.56
system time
10.6731
max virtual memory
3.8601636E7
max residence set size
1.5085628E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
WORST_CASE(Omega(n^2), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^2, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 291 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 259 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 107 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^2, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 175 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 74 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 122 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 1955 ms] (30) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: minus(n__0, Y) -> 0 minus(n__s(X), n__s(Y)) -> minus(activate(X), activate(Y)) geq(X, n__0) -> true geq(n__0, n__s(Y)) -> false geq(n__s(X), n__s(Y)) -> geq(activate(X), activate(Y)) div(0, n__s(Y)) -> 0 div(s(X), n__s(Y)) -> if(geq(X, activate(Y)), n__s(n__div(n__minus(X, activate(Y)), n__s(activate(Y)))), n__0) if(true, X, Y) -> activate(X) if(false, X, Y) -> activate(Y) 0 -> n__0 s(X) -> n__s(X) div(X1, X2) -> n__div(X1, X2) minus(X1, X2) -> n__minus(X1, X2) activate(n__0) -> 0 activate(n__s(X)) -> s(activate(X)) activate(n__div(X1, X2)) -> div(activate(X1), X2) activate(n__minus(X1, X2)) -> minus(X1, X2) activate(X) -> X 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(n__0) -> n__0 encArg(n__s(x_1)) -> n__s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(n__div(x_1, x_2)) -> n__div(encArg(x_1), encArg(x_2)) encArg(n__minus(x_1, x_2)) -> n__minus(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_geq(x_1, x_2)) -> geq(encArg(x_1), encArg(x_2)) encArg(cons_div(x_1, x_2)) -> div(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_0) -> 0 encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_n__0 -> n__0 encode_0 -> 0 encode_n__s(x_1) -> n__s(encArg(x_1)) encode_activate(x_1) -> activate(encArg(x_1)) encode_geq(x_1, x_2) -> geq(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_div(x_1, x_2) -> div(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_n__div(x_1, x_2) -> n__div(encArg(x_1), encArg(x_2))
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