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TRS Equational pair #516978137
details
property
value
status
complete
benchmark
YWHM14_2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.34060382843 seconds
cpu usage
5.872385189
max memory
4.73219072E8
stage attributes
key
value
output-size
2981
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 193 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 37 ms] (4) ETRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: f(plus(a, a)) -> plus(f(a), f(a)) plus(f(a), f(a)) -> plus(a, f(f(a))) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) ---------------------------------------- (1) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: f(plus(a, a)) -> plus(f(a), f(a)) plus(f(a), f(a)) -> plus(a, f(f(a))) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: f(plus(a, a)) -> plus(f(a), f(a)) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(f(x_1)) = 3*x_1 POL(plus(x_1, x_2)) = 3 + x_1 + x_2 ---------------------------------------- (2) Obligation: Equational rewrite system: The TRS R consists of the following rules: plus(f(a), f(a)) -> plus(a, f(f(a))) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) ---------------------------------------- (3) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: plus(f(a), f(a)) -> plus(a, f(f(a))) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: plus(f(a), f(a)) -> plus(a, f(f(a))) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0
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