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	n078.star.cs.uiowa.edu
space	Kaliszyk_19

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.75507903099 seconds
cpu usage	7.47142934
max memory	5.39078656E8

stage attributes

key	value
output-size	9835
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 518 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES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) popout

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

job log

popout

actions

all output return to TRS Standard