Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Derivational Complexity: TRS pair #487103892
details
property
value
status
complete
benchmark
ExProp7_Luc06_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
292.184 seconds
cpu usage
1122.21
user time
1107.82
system time
14.3902
max virtual memory
3.751866E7
max residence set size
1.5041428E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 168 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), 423 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), 91 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 68 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 57 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 312 ms] (24) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: active(f(0)) -> mark(cons(0, f(s(0)))) active(f(s(0))) -> mark(f(p(s(0)))) active(p(s(X))) -> mark(X) active(f(X)) -> f(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(s(X)) -> s(active(X)) active(p(X)) -> p(active(X)) f(mark(X)) -> mark(f(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) s(mark(X)) -> mark(s(X)) p(mark(X)) -> mark(p(X)) proper(f(X)) -> f(proper(X)) proper(0) -> ok(0) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(p(X)) -> p(proper(X)) f(ok(X)) -> ok(f(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) s(ok(X)) -> ok(s(X)) p(ok(X)) -> ok(p(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (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(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_f(x_1)) -> f(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_f(x_1) -> f(encArg(x_1)) encode_0 -> 0 encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_p(x_1) -> p(encArg(x_1)) encode_proper(x_1) -> proper(encArg(x_1)) encode_ok(x_1) -> ok(encArg(x_1)) encode_top(x_1) -> top(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Derivational Complexity: TRS