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TRS Equational pair #516978212
details
property
value
status
complete
benchmark
AC22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
4.52364993095 seconds
cpu usage
10.930354189
max memory
6.81127936E8
stage attributes
key
value
output-size
18057
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 263 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 36 ms] (4) ETRS (5) RRRPoloETRSProof [EQUIVALENT, 20 ms] (6) ETRS (7) EquationalDependencyPairsProof [EQUIVALENT, 51 ms] (8) EDP (9) EUsableRulesReductionPairsProof [EQUIVALENT, 50 ms] (10) EDP (11) ERuleRemovalProof [EQUIVALENT, 36 ms] (12) EDP (13) EDPPoloProof [EQUIVALENT, 3 ms] (14) EDP (15) PisEmptyProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: zero(0) -> 0 plus(x, 0) -> x plus(zero(x), zero(y)) -> zero(plus(x, y)) plus(zero(x), un(y)) -> un(plus(x, y)) plus(zero(x), j(y)) -> j(plus(x, y)) plus(un(x), j(y)) -> zero(plus(x, y)) plus(un(x), un(y)) -> j(plus(x, plus(y, un(0)))) plus(j(x), j(y)) -> un(plus(x, plus(y, j(0)))) minus(x, y) -> plus(x, neg(y)) neg(0) -> 0 neg(zero(x)) -> zero(neg(x)) neg(un(x)) -> j(neg(x)) neg(j(x)) -> un(neg(x)) times(x, 0) -> 0 times(x, times(0, z)) -> times(0, 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) times(x, j(y)) -> plus(zero(times(x, y)), neg(x)) times(x, times(j(y), z)) -> times(plus(zero(times(x, y)), neg(x)), 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(0) -> 0 plus(x, 0) -> x plus(zero(x), zero(y)) -> zero(plus(x, y)) plus(zero(x), un(y)) -> un(plus(x, y)) plus(zero(x), j(y)) -> j(plus(x, y)) plus(un(x), j(y)) -> zero(plus(x, y)) plus(un(x), un(y)) -> j(plus(x, plus(y, un(0)))) plus(j(x), j(y)) -> un(plus(x, plus(y, j(0)))) minus(x, y) -> plus(x, neg(y)) neg(0) -> 0 neg(zero(x)) -> zero(neg(x)) neg(un(x)) -> j(neg(x)) neg(j(x)) -> un(neg(x)) times(x, 0) -> 0 times(x, times(0, z)) -> times(0, 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) times(x, j(y)) -> plus(zero(times(x, y)), neg(x)) times(x, times(j(y), z)) -> times(plus(zero(times(x, y)), neg(x)), z) The set E consists of the following equations: plus(x, y) == plus(y, x)
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