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TRS Equat 89423 pair #381732732
details
property
value
status
complete
benchmark
AC51.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n092.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.89557600021 seconds
cpu usage
3.76934782
max memory
1.9318784E8
stage attributes
key
value
output-size
3031
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 141 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 9 ms] (4) ETRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: plus(0, y) -> y plus(s(x), 0) -> s(x) plus(s(x), s(y)) -> s(plus(s(x), plus(y, 0))) 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: plus(0, y) -> y plus(s(x), 0) -> s(x) plus(s(x), s(y)) -> s(plus(s(x), plus(y, 0))) 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(s(x), s(y)) -> s(plus(s(x), plus(y, 0))) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(plus(x_1, x_2)) = x_1 + x_1*x_2 + x_2 POL(s(x_1)) = 1 + x_1 ---------------------------------------- (2) Obligation: Equational rewrite system: The TRS R consists of the following rules: plus(0, y) -> y plus(s(x), 0) -> s(x) 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(0, y) -> y plus(s(x), 0) -> s(x) 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(0, y) -> y
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