details

property	value
status	complete
benchmark	AC18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.44439315796 seconds
cpu usage	11.676195825
max memory	6.37841408E8

stage attributes

key	value
output-size	17841
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 144 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 36 ms] (4) ETRS (5) RRRPoloETRSProof [EQUIVALENT, 30 ms] (6) ETRS (7) RRRPoloETRSProof [EQUIVALENT, 1126 ms] (8) ETRS (9) EquationalDependencyPairsProof [EQUIVALENT, 141 ms] (10) EDP (11) EUsableRulesReductionPairsProof [EQUIVALENT, 57 ms] (12) EDP (13) ERuleRemovalProof [EQUIVALENT, 0 ms] (14) EDP (15) EDPPoloProof [EQUIVALENT, 19 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: 0(S) -> S plus(S, x) -> x plus(0(x), 0(y)) -> 0(plus(x, y)) plus(0(x), 1(y)) -> 1(plus(x, y)) plus(0(x), j(y)) -> j(plus(x, y)) plus(1(x), 1(y)) -> j(plus(1(S), plus(x, y))) plus(j(x), j(y)) -> 1(plus(j(S), plus(x, y))) plus(1(x), j(y)) -> 0(plus(x, y)) opp(S) -> S opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) minus(x, y) -> plus(opp(y), x) times(S, x) -> S times(0(x), y) -> 0(times(x, y)) times(1(x), y) -> plus(0(times(x, y)), y) times(j(x), y) -> minus(0(times(x, y)), y) The set E consists of the following equations: plus(x, y) == plus(y, x) times(x, y) == times(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) times(times(x, y), z) == times(x, times(y, z)) ---------------------------------------- (1) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: 0(S) -> S plus(S, x) -> x plus(0(x), 0(y)) -> 0(plus(x, y)) plus(0(x), 1(y)) -> 1(plus(x, y)) plus(0(x), j(y)) -> j(plus(x, y)) plus(1(x), 1(y)) -> j(plus(1(S), plus(x, y))) plus(j(x), j(y)) -> 1(plus(j(S), plus(x, y))) plus(1(x), j(y)) -> 0(plus(x, y)) opp(S) -> S opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) minus(x, y) -> plus(opp(y), x) times(S, x) -> S times(0(x), y) -> 0(times(x, y)) times(1(x), y) -> plus(0(times(x, y)), y) times(j(x), y) -> minus(0(times(x, y)), y) The set E consists of the following equations: plus(x, y) == plus(y, x) times(x, y) == times(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) times(times(x, y), z) == times(x, times(y, z)) The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: popout

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

job log

popout

actions

all output return to TRS Equational