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Derivational Complexity: TRS Innermost pair #487108584
details
property
value
status
complete
benchmark
OvConsOS_complete_C.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
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
295.519 seconds
cpu usage
1162.22
user time
1152.4
system time
9.82561
max virtual memory
1.9842344E7
max residence set size
1.4328528E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 1207 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), 5 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 511 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), 164 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 155 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 155 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 197 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 103 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 225 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 131 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 137 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 80 ms] (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 111 ms] (36) typed CpxTrs (37) RewriteLemmaProof [LOWER BOUND(ID), 128 ms] (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 169 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 189 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 186 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 167 ms] (46) typed CpxTrs (47) RewriteLemmaProof [LOWER BOUND(ID), 262 ms] (48) typed CpxTrs (49) RewriteLemmaProof [LOWER BOUND(ID), 205 ms] (50) typed CpxTrs (51) RewriteLemmaProof [LOWER BOUND(ID), 250 ms] (52) typed CpxTrs (53) RewriteLemmaProof [LOWER BOUND(ID), 283 ms] (54) typed CpxTrs (55) RewriteLemmaProof [LOWER BOUND(ID), 212 ms] (56) typed CpxTrs (57) RewriteLemmaProof [LOWER BOUND(ID), 114 ms] (58) typed CpxTrs (59) RewriteLemmaProof [LOWER BOUND(ID), 376 ms] (60) typed CpxTrs ---------------------------------------- (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(zeros) -> mark(cons(0, zeros)) active(U11(tt, V1)) -> mark(U12(isNatList(V1))) active(U12(tt)) -> mark(tt) active(U21(tt, V1)) -> mark(U22(isNat(V1))) active(U22(tt)) -> mark(tt) active(U31(tt, V)) -> mark(U32(isNatList(V))) active(U32(tt)) -> mark(tt) active(U41(tt, V1, V2)) -> mark(U42(isNat(V1), V2)) active(U42(tt, V2)) -> mark(U43(isNatIList(V2))) active(U43(tt)) -> mark(tt) active(U51(tt, V1, V2)) -> mark(U52(isNat(V1), V2)) active(U52(tt, V2)) -> mark(U53(isNatList(V2))) active(U53(tt)) -> mark(tt) active(U61(tt, V1, V2)) -> mark(U62(isNat(V1), V2)) active(U62(tt, V2)) -> mark(U63(isNatIList(V2))) active(U63(tt)) -> mark(tt) active(U71(tt, L)) -> mark(s(length(L))) active(U81(tt)) -> mark(nil) active(U91(tt, IL, M, N)) -> mark(cons(N, take(M, IL))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt)
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