details

property	value
status	complete
benchmark	addList.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.784 seconds
cpu usage	980.204
user time	969.041
system time	11.1631
max virtual memory	1.9053232E7
max residence set size	1.5234176E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 712 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 append(nil, x) -> cons(x, nil) append(cons(y, ys), x) -> cons(y, append(ys, x)) 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) addLists(xs, ys, zs) -> if(isEmpty(xs), isEmpty(ys), isZero(head(xs)), tail(xs), tail(ys), cons(p(head(xs)), tail(xs)), cons(inc(head(ys)), tail(ys)), zs, append(zs, head(ys))) if(true, true, b, xs, ys, xs2, ys2, zs, zs2) -> zs if(true, false, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError if(false, true, b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError if(false, false, false, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs2, ys2, zs) if(false, false, true, xs, ys, xs2, ys2, zs, zs2) -> addLists(xs, ys, zs2) addList(xs, ys) -> addLists(xs, ys, nil) 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(differentLengthError) -> differentLengthError 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_append(x_1, x_2)) -> append(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_addLists(x_1, x_2, x_3)) -> addLists(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_if(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9)) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6), encArg(x_7), encArg(x_8), encArg(x_9)) encArg(cons_addList(x_1, x_2)) -> addList(encArg(x_1), encArg(x_2)) 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_append(x_1, x_2) -> append(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_inc(x_1) -> inc(encArg(x_1)) encode_addLists(x_1, x_2, x_3) -> addLists(encArg(x_1), encArg(x_2), encArg(x_3)) encode_if(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6), encArg(x_7), encArg(x_8), encArg(x_9)) encode_differentLengthError -> differentLengthError encode_addList(x_1, x_2) -> addList(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost