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Derivational Complexity: TRS Innermost pair #487109064
details
property
value
status
complete
benchmark
Ex1_2_AEL03_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)
293.94 seconds
cpu usage
1146.04
user time
1132.25
system time
13.7909
max virtual memory
3.7780348E7
max residence set size
1.4773148E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 638 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), 422 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), 146 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 102 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 162 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 116 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 160 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 123 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 163 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 154 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 163 ms] (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 132 ms] (36) typed CpxTrs (37) RewriteLemmaProof [LOWER BOUND(ID), 124 ms] (38) 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(from(X)) -> mark(cons(X, from(s(X)))) active(2ndspos(0, Z)) -> mark(rnil) active(2ndspos(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(posrecip(Y), 2ndsneg(N, Z))) active(2ndsneg(0, Z)) -> mark(rnil) active(2ndsneg(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(negrecip(Y), 2ndspos(N, Z))) active(pi(X)) -> mark(2ndspos(X, from(0))) active(plus(0, Y)) -> mark(Y) active(plus(s(X), Y)) -> mark(s(plus(X, Y))) active(times(0, Y)) -> mark(0) active(times(s(X), Y)) -> mark(plus(Y, times(X, Y))) active(square(X)) -> mark(times(X, X)) active(s(X)) -> s(active(X)) active(posrecip(X)) -> posrecip(active(X)) active(negrecip(X)) -> negrecip(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(rcons(X1, X2)) -> rcons(active(X1), X2) active(rcons(X1, X2)) -> rcons(X1, active(X2)) active(from(X)) -> from(active(X)) active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2) active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2)) active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2) active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2)) active(pi(X)) -> pi(active(X)) active(plus(X1, X2)) -> plus(active(X1), X2) active(plus(X1, X2)) -> plus(X1, active(X2)) active(times(X1, X2)) -> times(active(X1), X2) active(times(X1, X2)) -> times(X1, active(X2)) active(square(X)) -> square(active(X)) s(mark(X)) -> mark(s(X)) posrecip(mark(X)) -> mark(posrecip(X)) negrecip(mark(X)) -> mark(negrecip(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) rcons(mark(X1), X2) -> mark(rcons(X1, X2)) rcons(X1, mark(X2)) -> mark(rcons(X1, X2)) from(mark(X)) -> mark(from(X)) 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2)) 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2)) 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2)) 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2)) pi(mark(X)) -> mark(pi(X)) plus(mark(X1), X2) -> mark(plus(X1, X2)) plus(X1, mark(X2)) -> mark(plus(X1, X2)) times(mark(X1), X2) -> mark(times(X1, X2))
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