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TRS Equat 89423 pair #381732767
details
property
value
status
complete
benchmark
bag-sum-prod.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n010.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.51479697227 seconds
cpu usage
3.064871711
max memory
2.08154624E8
stage attributes
key
value
output-size
1499
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EDirectTerminationProof [EQUIVALENT, 0 ms] (2) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: +(0, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) *(0, x) -> 0 *(s(x), s(y)) -> s(+(+(x, y), *(x, y))) U(empty, b) -> b sum(empty) -> 0 sum(singl(x)) -> x sum(U(x, y)) -> +(sum(x), sum(y)) prod(empty) -> s(0) 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) EDirectTerminationProof (EQUIVALENT) We use [DA_FALKE] with the following order to prove termination. Precedence: U_2 > +_2 > s_1 U_2 > sum_1 empty > 0 prod_1 > *_2 > +_2 > s_1 Status: *_2: flat status +_2: flat status U_2: flat status ---------------------------------------- (2) YES
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