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Derivational Complexity: TRS Innermost pair #487108136
details
property
value
status
complete
benchmark
Ex2_Luc03b_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.629 seconds
cpu usage
1140.98
user time
1129.16
system time
11.826
max virtual memory
1.9159092E7
max residence set size
1.4928548E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 393 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), 428 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), 172 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 114 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 108 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 118 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 2184 ms] (26) BOUNDS(1, INF) ---------------------------------------- (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: active(fst(0, Z)) -> mark(nil) active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))) active(from(X)) -> mark(cons(X, from(s(X)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(len(nil)) -> mark(0) active(len(cons(X, Z))) -> mark(s(len(Z))) active(cons(X1, X2)) -> cons(active(X1), X2) active(fst(X1, X2)) -> fst(active(X1), X2) active(fst(X1, X2)) -> fst(X1, active(X2)) active(from(X)) -> from(active(X)) active(add(X1, X2)) -> add(active(X1), X2) active(add(X1, X2)) -> add(X1, active(X2)) active(len(X)) -> len(active(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) fst(mark(X1), X2) -> mark(fst(X1, X2)) fst(X1, mark(X2)) -> mark(fst(X1, X2)) from(mark(X)) -> mark(from(X)) add(mark(X1), X2) -> mark(add(X1, X2)) add(X1, mark(X2)) -> mark(add(X1, X2)) len(mark(X)) -> mark(len(X)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(nil) -> ok(nil) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)) proper(from(X)) -> from(proper(X)) proper(add(X1, X2)) -> add(proper(X1), proper(X2)) proper(len(X)) -> len(proper(X)) s(ok(X)) -> ok(s(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)) from(ok(X)) -> ok(from(X)) add(ok(X1), ok(X2)) -> ok(add(X1, X2)) len(ok(X)) -> ok(len(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(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(0) -> 0 encArg(mark(x_1)) -> mark(encArg(x_1)) encArg(nil) -> nil encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_fst(x_1, x_2)) -> fst(encArg(x_1), encArg(x_2)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encArg(cons_len(x_1)) -> len(encArg(x_1))
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