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TRS Equational pair #487092689
details
property
value
status
complete
benchmark
AC23.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)
2.00935 seconds
cpu usage
3.91826
user time
3.77208
system time
0.146184
max virtual memory
1.8343376E7
max residence set size
233056.0
stage attributes
key
value
starexec-result
YES
output
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 157 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 24 ms] (4) ETRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: zero(S) -> S plus(x, S) -> x plus(zero(x), zero(y)) -> zero(plus(x, y)) plus(zero(x), un(y)) -> un(plus(x, y)) plus(un(x), un(y)) -> zero(plus(x, plus(y, un(S)))) times(x, S) -> S times(x, times(S, z)) -> times(S, z) times(x, zero(y)) -> zero(times(x, y)) times(x, times(zero(y), z)) -> times(zero(times(x, y)), z) times(x, un(y)) -> plus(x, zero(times(x, y))) times(x, times(un(y), z)) -> times(plus(x, zero(times(x, y))), z) 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: zero(S) -> S plus(x, S) -> x plus(zero(x), zero(y)) -> zero(plus(x, y)) plus(zero(x), un(y)) -> un(plus(x, y)) plus(un(x), un(y)) -> zero(plus(x, plus(y, un(S)))) times(x, S) -> S times(x, times(S, z)) -> times(S, z) times(x, zero(y)) -> zero(times(x, y)) times(x, times(zero(y), z)) -> times(zero(times(x, y)), z) times(x, un(y)) -> plus(x, zero(times(x, y))) times(x, times(un(y), z)) -> times(plus(x, zero(times(x, y))), z) 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: plus(un(x), un(y)) -> zero(plus(x, plus(y, un(S)))) times(x, un(y)) -> plus(x, zero(times(x, y))) times(x, times(un(y), z)) -> times(plus(x, zero(times(x, y))), z) Used ordering: Polynomial interpretation [POLO]: POL(S) = 0 POL(plus(x_1, x_2)) = x_1 + x_2 POL(times(x_1, x_2)) = x_1 + x_1*x_2 + x_2 POL(un(x_1)) = 2 + x_1 POL(zero(x_1)) = x_1 ---------------------------------------- (2) Obligation: Equational rewrite system: The TRS R consists of the following rules: zero(S) -> S plus(x, S) -> x plus(zero(x), zero(y)) -> zero(plus(x, y)) plus(zero(x), un(y)) -> un(plus(x, y)) times(x, S) -> S times(x, times(S, z)) -> times(S, z) times(x, zero(y)) -> zero(times(x, y)) times(x, times(zero(y), z)) -> times(zero(times(x, y)), z)
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