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TRS Standard pair #516966550
details
property
value
status
complete
benchmark
4.02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n031.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.20811414719 seconds
cpu usage
5.757214319
max memory
4.76532736E8
stage attributes
key
value
output-size
2066
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 113 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: *(x, 1) -> x *(1, y) -> y *(i(x), x) -> 1 *(x, i(x)) -> 1 *(x, *(y, z)) -> *(*(x, y), z) i(1) -> 1 *(*(x, y), i(y)) -> x *(*(x, i(y)), y) -> x i(i(x)) -> x i(*(x, y)) -> *(i(y), i(x)) k(x, 1) -> 1 k(x, x) -> 1 *(k(x, y), k(y, x)) -> 1 *(*(i(x), k(y, z)), x) -> k(*(*(i(x), y), x), *(*(i(x), z), x)) k(*(x, i(y)), *(y, i(x))) -> 1 Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: i_1 > *_2 > [1, k_2] Status: *_2: [2,1] 1: multiset status i_1: [1] k_2: [1,2] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: *(x, 1) -> x *(1, y) -> y *(i(x), x) -> 1 *(x, i(x)) -> 1 *(x, *(y, z)) -> *(*(x, y), z) i(1) -> 1 *(*(x, y), i(y)) -> x *(*(x, i(y)), y) -> x i(i(x)) -> x i(*(x, y)) -> *(i(y), i(x)) k(x, 1) -> 1 k(x, x) -> 1 *(k(x, y), k(y, x)) -> 1 *(*(i(x), k(y, z)), x) -> k(*(*(i(x), y), x), *(*(i(x), z), x)) k(*(x, i(y)), *(y, i(x))) -> 1 ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
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