Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Derivational Complexity: TRS Innermost pair #487108930
details
property
value
status
complete
benchmark
PEANO_complete_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
295.271 seconds
cpu usage
1160.31
user time
1149.05
system time
11.2542
max virtual memory
1.9177648E7
max residence set size
1.4836724E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 824 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 13 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 513 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), 267 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 264 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 181 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 132 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 142 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 101 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 84 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 162 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 213 ms] (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 212 ms] (36) typed CpxTrs (37) RewriteLemmaProof [LOWER BOUND(ID), 214 ms] (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 107 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 157 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 221 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 173 ms] (46) typed CpxTrs (47) RewriteLemmaProof [LOWER BOUND(ID), 154 ms] (48) typed CpxTrs (49) RewriteLemmaProof [LOWER BOUND(ID), 109 ms] (50) typed CpxTrs (51) RewriteLemmaProof [LOWER BOUND(ID), 165 ms] (52) typed CpxTrs (53) RewriteLemmaProof [LOWER BOUND(ID), 249 ms] (54) 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(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2)) active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)) active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2)) active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2)) active(U15(tt, V2)) -> mark(U16(isNat(V2))) active(U16(tt)) -> mark(tt) active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1)) active(U22(tt, V1)) -> mark(U23(isNat(V1))) active(U23(tt)) -> mark(tt) active(U31(tt, V2)) -> mark(U32(isNatKind(V2))) active(U32(tt)) -> mark(tt) active(U41(tt)) -> mark(tt) active(U51(tt, N)) -> mark(U52(isNatKind(N), N)) active(U52(tt, N)) -> mark(N) active(U61(tt, M, N)) -> mark(U62(isNatKind(M), M, N)) active(U62(tt, M, N)) -> mark(U63(isNat(N), M, N)) active(U63(tt, M, N)) -> mark(U64(isNatKind(N), M, N)) active(U64(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) active(isNatKind(0)) -> mark(tt) active(isNatKind(plus(V1, V2))) -> mark(U31(isNatKind(V1), V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N, 0)) -> mark(U51(isNat(N), N)) active(plus(N, s(M))) -> mark(U61(isNat(M), M, N)) active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Derivational Complexity: TRS Innermost