details

property	value
status	complete
benchmark	2.30.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n088.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.18416404724 seconds
cpu usage	5.568452867
max memory	4.75959296E8

stage attributes

key	value
output-size	2573
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 79 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: not(x) -> xor(x, true) implies(x, y) -> xor(and(x, y), xor(x, true)) or(x, y) -> xor(and(x, y), xor(x, y)) =(x, y) -> xor(x, xor(y, true)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(=(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 POL(and(x_1, x_2)) = 1 + x_1 + x_2 POL(implies(x_1, x_2)) = 2 + 2*x_1 + x_2 POL(not(x_1)) = 1 + x_1 POL(or(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 POL(true) = 1 POL(xor(x_1, x_2)) = x_1 + x_2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: =(x, y) -> xor(x, xor(y, true)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: not(x) -> xor(x, true) implies(x, y) -> xor(and(x, y), xor(x, true)) or(x, y) -> xor(and(x, y), xor(x, y)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: not_1 > xor_2 not_1 > true implies_2 > xor_2 implies_2 > true implies_2 > and_2 or_2 > xor_2 or_2 > and_2 Status: not_1: [1] xor_2: multiset status true: multiset status implies_2: multiset status and_2: [1,2] or_2: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: not(x) -> xor(x, true) implies(x, y) -> xor(and(x, y), xor(x, true)) or(x, y) -> xor(and(x, y), xor(x, y)) popout

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all output return to TRS Standard