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TRS Equat 89423 pair #381732824
details
property
value
status
complete
benchmark
AC18.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.55927109718 seconds
cpu usage
11.529185889
max memory
6.07264768E8
stage attributes
key
value
output-size
17838
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 153 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 41 ms] (4) ETRS (5) RRRPoloETRSProof [EQUIVALENT, 25 ms] (6) ETRS (7) RRRPoloETRSProof [EQUIVALENT, 1119 ms] (8) ETRS (9) EquationalDependencyPairsProof [EQUIVALENT, 125 ms] (10) EDP (11) EUsableRulesReductionPairsProof [EQUIVALENT, 33 ms] (12) EDP (13) ERuleRemovalProof [EQUIVALENT, 20 ms] (14) EDP (15) EDPPoloProof [EQUIVALENT, 18 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: 0(S) -> S plus(S, x) -> x plus(0(x), 0(y)) -> 0(plus(x, y)) plus(0(x), 1(y)) -> 1(plus(x, y)) plus(0(x), j(y)) -> j(plus(x, y)) plus(1(x), 1(y)) -> j(plus(1(S), plus(x, y))) plus(j(x), j(y)) -> 1(plus(j(S), plus(x, y))) plus(1(x), j(y)) -> 0(plus(x, y)) opp(S) -> S opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) minus(x, y) -> plus(opp(y), x) times(S, x) -> S times(0(x), y) -> 0(times(x, y)) times(1(x), y) -> plus(0(times(x, y)), y) times(j(x), y) -> minus(0(times(x, y)), 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(S, x) -> x plus(0(x), 0(y)) -> 0(plus(x, y)) plus(0(x), 1(y)) -> 1(plus(x, y)) plus(0(x), j(y)) -> j(plus(x, y)) plus(1(x), 1(y)) -> j(plus(1(S), plus(x, y))) plus(j(x), j(y)) -> 1(plus(j(S), plus(x, y))) plus(1(x), j(y)) -> 0(plus(x, y)) opp(S) -> S opp(0(x)) -> 0(opp(x)) opp(1(x)) -> j(opp(x)) opp(j(x)) -> 1(opp(x)) minus(x, y) -> plus(opp(y), x) times(S, x) -> S times(0(x), y) -> 0(times(x, y)) times(1(x), y) -> plus(0(times(x, y)), y) times(j(x), y) -> minus(0(times(x, y)), 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:
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