Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Derivational Complexity: TRS Innermost pair #487108058
details
property
value
status
complete
benchmark
sumList.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.557 seconds
cpu usage
1129.41
user time
1119.19
system time
10.2256
max virtual memory
1.942288E7
max residence set size
1.5014928E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 402 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (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: isEmpty(cons(x, xs)) -> false isEmpty(nil) -> true isZero(0) -> true isZero(s(x)) -> false head(cons(x, xs)) -> x tail(cons(x, xs)) -> xs tail(nil) -> nil p(s(s(x))) -> s(p(s(x))) p(s(0)) -> 0 p(0) -> 0 inc(s(x)) -> s(inc(x)) inc(0) -> s(0) sumList(xs, y) -> if(isEmpty(xs), isZero(head(xs)), y, tail(xs), cons(p(head(xs)), tail(xs)), inc(y)) if(true, b, y, xs, ys, x) -> y if(false, true, y, xs, ys, x) -> sumList(xs, y) if(false, false, y, xs, ys, x) -> sumList(ys, x) sum(xs) -> sumList(xs, 0) 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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(false) -> false encArg(nil) -> nil encArg(true) -> true encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_isEmpty(x_1)) -> isEmpty(encArg(x_1)) encArg(cons_isZero(x_1)) -> isZero(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_sumList(x_1, x_2)) -> sumList(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3, x_4, x_5, x_6)) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6)) encArg(cons_sum(x_1)) -> sum(encArg(x_1)) encode_isEmpty(x_1) -> isEmpty(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_false -> false encode_nil -> nil encode_true -> true encode_isZero(x_1) -> isZero(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_p(x_1) -> p(encArg(x_1)) encode_inc(x_1) -> inc(encArg(x_1)) encode_sumList(x_1, x_2) -> sumList(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3, x_4, x_5, x_6) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6)) encode_sum(x_1) -> sum(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: isEmpty(cons(x, xs)) -> false isEmpty(nil) -> true isZero(0) -> true
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Derivational Complexity: TRS Innermost