details

property	value
status	complete
benchmark	arith.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	Kaliszyk_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.44037 seconds
cpu usage	5.76683
user time	5.53568
system time	0.231145
max virtual memory	1.8434048E7
max residence set size	324280.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 482 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: NUMERAL(0) -> 0 BIT0(0) -> 0 SUC(NUMERAL(n)) -> NUMERAL(SUC(n)) SUC(0) -> BIT1(0) SUC(BIT0(n)) -> BIT1(n) SUC(BIT1(n)) -> BIT0(SUC(n)) PRE(NUMERAL(n)) -> NUMERAL(PRE(n)) PRE(0) -> 0 PRE(BIT0(n)) -> if(eq(n, 0), 0, BIT1(PRE(n))) PRE(BIT1(n)) -> BIT0(n) plus(NUMERAL(m), NUMERAL(n)) -> NUMERAL(plus(m, n)) plus(0, 0) -> 0 plus(0, BIT0(n)) -> BIT0(n) plus(0, BIT1(n)) -> BIT1(n) plus(BIT0(n), 0) -> BIT0(n) plus(BIT1(n), 0) -> BIT1(n) plus(BIT0(m), BIT0(n)) -> BIT0(plus(m, n)) plus(BIT0(m), BIT1(n)) -> BIT1(plus(m, n)) plus(BIT1(m), BIT0(n)) -> BIT1(plus(m, n)) plus(BIT1(m), BIT1(n)) -> BIT0(SUC(plus(m, n))) mult(NUMERAL(m), NUMERAL(n)) -> NUMERAL(mult(m, n)) mult(0, 0) -> 0 mult(0, BIT0(n)) -> 0 mult(0, BIT1(n)) -> 0 mult(BIT0(n), 0) -> 0 mult(BIT1(n), 0) -> 0 mult(BIT0(m), BIT0(n)) -> BIT0(BIT0(mult(m, n))) mult(BIT0(m), BIT1(n)) -> plus(BIT0(m), BIT0(BIT0(mult(m, n)))) mult(BIT1(m), BIT0(n)) -> plus(BIT0(n), BIT0(BIT0(mult(m, n)))) mult(BIT1(m), BIT1(n)) -> plus(plus(BIT1(m), BIT0(n)), BIT0(BIT0(mult(m, n)))) exp(NUMERAL(m), NUMERAL(n)) -> NUMERAL(exp(m, n)) exp(0, 0) -> BIT1(0) exp(BIT0(m), 0) -> BIT1(0) exp(BIT1(m), 0) -> BIT1(0) exp(0, BIT0(n)) -> mult(exp(0, n), exp(0, n)) exp(BIT0(m), BIT0(n)) -> mult(exp(BIT0(m), n), exp(BIT0(m), n)) exp(BIT1(m), BIT0(n)) -> mult(exp(BIT1(m), n), exp(BIT1(m), n)) exp(0, BIT1(n)) -> 0 exp(BIT0(m), BIT1(n)) -> mult(mult(BIT0(m), exp(BIT0(m), n)), exp(BIT0(m), n)) exp(BIT1(m), BIT1(n)) -> mult(mult(BIT1(m), exp(BIT1(m), n)), exp(BIT1(m), n)) EVEN(NUMERAL(n)) -> EVEN(n) EVEN(0) -> T EVEN(BIT0(n)) -> T EVEN(BIT1(n)) -> F ODD(NUMERAL(n)) -> ODD(n) ODD(0) -> F ODD(BIT0(n)) -> F ODD(BIT1(n)) -> T eq(NUMERAL(m), NUMERAL(n)) -> eq(m, n) eq(0, 0) -> T eq(BIT0(n), 0) -> eq(n, 0) eq(BIT1(n), 0) -> F eq(0, BIT0(n)) -> eq(0, n) eq(0, BIT1(n)) -> F eq(BIT0(m), BIT0(n)) -> eq(m, n) eq(BIT0(m), BIT1(n)) -> F eq(BIT1(m), BIT0(n)) -> F eq(BIT1(m), BIT1(n)) -> eq(m, n) le(NUMERAL(m), NUMERAL(n)) -> le(m, n) le(0, 0) -> T le(BIT0(n), 0) -> le(n, 0) le(BIT1(n), 0) -> F le(0, BIT0(n)) -> T le(0, BIT1(n)) -> T le(BIT0(m), BIT0(n)) -> le(m, n) le(BIT0(m), BIT1(n)) -> le(m, n) le(BIT1(m), BIT0(n)) -> lt(m, n) le(BIT1(m), BIT1(n)) -> le(m, n) lt(NUMERAL(m), NUMERAL(n)) -> lt(m, n) lt(0, 0) -> F lt(BIT0(n), 0) -> F lt(BIT1(n), 0) -> F lt(0, BIT0(n)) -> lt(0, n) lt(0, BIT1(n)) -> T lt(BIT0(m), BIT0(n)) -> lt(m, n) lt(BIT0(m), BIT1(n)) -> le(m, n) lt(BIT1(m), BIT0(n)) -> lt(m, n) lt(BIT1(m), BIT1(n)) -> lt(m, n) ge(NUMERAL(n), NUMERAL(m)) -> ge(n, m) popout

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

job log

popout

actions

all output return to TRS Standard