details

property	value
status	complete
benchmark	bag-sum-prod-distr.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n183.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.40277481079 seconds
cpu usage	6.261894257
max memory	4.73063424E8

stage attributes

key	value
output-size	7935
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 221 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 0 ms] (4) ETRS (5) RRRPoloETRSProof [EQUIVALENT, 20 ms] (6) ETRS (7) RRRPoloETRSProof [EQUIVALENT, 0 ms] (8) ETRS (9) RisEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: 0(#) -> # +(#, x) -> x +(0(x), 0(y)) -> 0(+(x, y)) +(0(x), 1(y)) -> 1(+(x, y)) +(1(x), 1(y)) -> 0(+(1(#), +(x, y))) *(#, x) -> # *(0(x), y) -> 0(*(x, y)) *(1(x), y) -> +(0(*(x, y)), y) *(+(y, z), x) -> +(*(x, y), *(x, z)) U(empty, b) -> b sum(empty) -> 0(#) sum(singl(x)) -> x sum(U(x, y)) -> +(sum(x), sum(y)) prod(empty) -> 1(#) prod(singl(x)) -> x prod(U(x, y)) -> *(prod(x), prod(y)) The set E consists of the following equations: *(x, y) == *(y, x) +(x, y) == +(y, x) U(x, y) == U(y, x) *(*(x, y), z) == *(x, *(y, z)) +(+(x, y), z) == +(x, +(y, z)) U(U(x, y), z) == U(x, U(y, z)) ---------------------------------------- (1) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: 0(#) -> # +(#, x) -> x +(0(x), 0(y)) -> 0(+(x, y)) +(0(x), 1(y)) -> 1(+(x, y)) +(1(x), 1(y)) -> 0(+(1(#), +(x, y))) *(#, x) -> # *(0(x), y) -> 0(*(x, y)) *(1(x), y) -> +(0(*(x, y)), y) *(+(y, z), x) -> +(*(x, y), *(x, z)) U(empty, b) -> b sum(empty) -> 0(#) sum(singl(x)) -> x sum(U(x, y)) -> +(sum(x), sum(y)) prod(empty) -> 1(#) prod(singl(x)) -> x prod(U(x, y)) -> *(prod(x), prod(y)) The set E consists of the following equations: *(x, y) == *(y, x) +(x, y) == +(y, x) U(x, y) == U(y, x) *(*(x, y), z) == *(x, *(y, z)) +(+(x, y), z) == +(x, +(y, z)) U(U(x, y), z) == U(x, U(y, z)) The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: +(#, x) -> x *(#, x) -> # *(1(x), y) -> +(0(*(x, y)), y) U(empty, b) -> b sum(empty) -> 0(#) sum(singl(x)) -> x popout

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

job log

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actions

all output return to TRS Equational