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Derivational Complexity: TRS Innermost pair #487108644
details
property
value
status
complete
benchmark
PALINDROME_complete_C.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
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
296.83 seconds
cpu usage
1159.75
user time
1149.72
system time
10.0271
max virtual memory
1.9504136E7
max residence set size
1.496774E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 2861 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 7 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 11 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 490 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), 219 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 99 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 55 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 198 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 115 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 201 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 82 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 105 ms] (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 123 ms] (36) typed CpxTrs (37) RewriteLemmaProof [LOWER BOUND(ID), 191 ms] (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 267 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 193 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 172 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 253 ms] (46) typed CpxTrs (47) RewriteLemmaProof [LOWER BOUND(ID), 244 ms] (48) typed CpxTrs (49) RewriteLemmaProof [LOWER BOUND(ID), 165 ms] (50) typed CpxTrs (51) RewriteLemmaProof [LOWER BOUND(ID), 176 ms] (52) 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(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) active(__(X, nil)) -> mark(X) active(__(nil, X)) -> mark(X) active(U11(tt, V)) -> mark(U12(isNeList(V))) active(U12(tt)) -> mark(tt) active(U21(tt, V1, V2)) -> mark(U22(isList(V1), V2)) active(U22(tt, V2)) -> mark(U23(isList(V2))) active(U23(tt)) -> mark(tt) active(U31(tt, V)) -> mark(U32(isQid(V))) active(U32(tt)) -> mark(tt) active(U41(tt, V1, V2)) -> mark(U42(isList(V1), V2)) active(U42(tt, V2)) -> mark(U43(isNeList(V2))) active(U43(tt)) -> mark(tt) active(U51(tt, V1, V2)) -> mark(U52(isNeList(V1), V2)) active(U52(tt, V2)) -> mark(U53(isList(V2))) active(U53(tt)) -> mark(tt) active(U61(tt, V)) -> mark(U62(isQid(V))) active(U62(tt)) -> mark(tt) active(U71(tt, V)) -> mark(U72(isNePal(V))) active(U72(tt)) -> mark(tt) active(and(tt, X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V), V)) active(isList(nil)) -> mark(tt) active(isList(__(V1, V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) active(isNeList(__(V1, V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) active(isNeList(__(V1, V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) active(isNePal(__(I, __(P, I)))) -> mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))))
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