Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Derivational Complexity: TRS Innermost pair #487106006
details
property
value
status
complete
benchmark
ex4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
AProVE_10
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.676 seconds
cpu usage
1107.77
user time
1094.71
system time
13.0604
max virtual memory
3.8239236E7
max residence set size
1.48181E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 281 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: add(true, x, xs) -> add(and(isNat(x), isList(xs)), x, Cons(x, xs)) isList(Cons(x, xs)) -> isList(xs) isList(nil) -> true isNat(s(x)) -> isNat(x) isNat(0) -> true if(true, x, y) -> x if(false, x, y) -> y and(true, true) -> true and(false, x) -> false and(x, false) -> false 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(true) -> true encArg(Cons(x_1, x_2)) -> Cons(encArg(x_1), encArg(x_2)) encArg(nil) -> nil encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(false) -> false encArg(cons_add(x_1, x_2, x_3)) -> add(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_isList(x_1)) -> isList(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2, x_3) -> add(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_isList(x_1) -> isList(encArg(x_1)) encode_Cons(x_1, x_2) -> Cons(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_false -> false ---------------------------------------- (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: add(true, x, xs) -> add(and(isNat(x), isList(xs)), x, Cons(x, xs)) isList(Cons(x, xs)) -> isList(xs) isList(nil) -> true isNat(s(x)) -> isNat(x) isNat(0) -> true if(true, x, y) -> x if(false, x, y) -> y and(true, true) -> true and(false, x) -> false and(x, false) -> false The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(Cons(x_1, x_2)) -> Cons(encArg(x_1), encArg(x_2)) encArg(nil) -> nil encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Derivational Complexity: TRS Innermost