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TRS Equational pair #487523100
details
property
value
status
complete
benchmark
AC17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.53893303871 seconds
cpu usage
5.753103532
max memory
3.29162752E8
stage attributes
key
value
output-size
5317
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 159 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 243 ms] (4) ETRS (5) RRRPoloETRSProof [EQUIVALENT, 182 ms] (6) ETRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: 0(S) -> S plus(x, S) -> x plus(0(x), 0(y)) -> 0(plus(x, y)) plus(0(x), 1(y)) -> 1(plus(x, y)) plus(1(x), 1(y)) -> 0(1(plus(plus(x, y), S))) times(x, S) -> S times(x, 0(y)) -> 0(times(x, y)) times(x, 1(y)) -> plus(x, 0(times(x, y))) The set E consists of the following equations: plus(x, y) == plus(y, x) times(x, y) == times(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) times(times(x, y), z) == times(x, times(y, z)) ---------------------------------------- (1) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: 0(S) -> S plus(x, S) -> x plus(0(x), 0(y)) -> 0(plus(x, y)) plus(0(x), 1(y)) -> 1(plus(x, y)) plus(1(x), 1(y)) -> 0(1(plus(plus(x, y), S))) times(x, S) -> S times(x, 0(y)) -> 0(times(x, y)) times(x, 1(y)) -> plus(x, 0(times(x, y))) The set E consists of the following equations: plus(x, y) == plus(y, x) times(x, y) == times(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) times(times(x, y), z) == times(x, times(y, z)) The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: 0(S) -> S plus(0(x), 0(y)) -> 0(plus(x, y)) plus(0(x), 1(y)) -> 1(plus(x, y)) times(x, S) -> S times(x, 0(y)) -> 0(times(x, y)) times(x, 1(y)) -> plus(x, 0(times(x, y))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2 + x_1 POL(1(x_1)) = 2 + x_1 POL(S) = 0 POL(plus(x_1, x_2)) = x_1 + x_2 POL(times(x_1, x_2)) = 3 + 3*x_1 + 2*x_1*x_2 + 3*x_2 ---------------------------------------- (2) Obligation: Equational rewrite system: The TRS R consists of the following rules: plus(x, S) -> x plus(1(x), 1(y)) -> 0(1(plus(plus(x, y), S)))
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