Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Derivational Complexity: TRS Innermost pair #487107710
details
property
value
status
complete
benchmark
tower.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
AProVE_06
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
292.084 seconds
cpu usage
1132.58
user time
1120.49
system time
12.0923
max virtual memory
1.919508E7
max residence set size
1.480104E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), ?)
output
WORST_CASE(Omega(n^3), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^3, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 244 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), 250 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), 24 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^2, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 21 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^3, INF) (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 617 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 534 ms] (32) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^3, INF). The TRS R consists of the following rules: plus(0, x) -> x plus(s(x), y) -> s(plus(p(s(x)), y)) times(0, y) -> 0 times(s(x), y) -> plus(y, times(p(s(x)), y)) exp(x, 0) -> s(0) exp(x, s(y)) -> times(x, exp(x, y)) p(s(0)) -> 0 p(s(s(x))) -> s(p(s(x))) tower(x, y) -> towerIter(x, y, s(0)) towerIter(0, y, z) -> z towerIter(s(x), y, z) -> towerIter(p(s(x)), y, exp(y, z)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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(s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_times(x_1, x_2)) -> times(encArg(x_1), encArg(x_2)) encArg(cons_exp(x_1, x_2)) -> exp(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_tower(x_1, x_2)) -> tower(encArg(x_1), encArg(x_2)) encArg(cons_towerIter(x_1, x_2, x_3)) -> towerIter(encArg(x_1), encArg(x_2), encArg(x_3)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_p(x_1) -> p(encArg(x_1)) encode_times(x_1, x_2) -> times(encArg(x_1), encArg(x_2)) encode_exp(x_1, x_2) -> exp(encArg(x_1), encArg(x_2)) encode_tower(x_1, x_2) -> tower(encArg(x_1), encArg(x_2)) encode_towerIter(x_1, x_2, x_3) -> towerIter(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^3, INF). The TRS R consists of the following rules: plus(0, x) -> x plus(s(x), y) -> s(plus(p(s(x)), y)) times(0, y) -> 0
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Derivational Complexity: TRS Innermost