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TRS Equational pair #516978263
details
property
value
status
complete
benchmark
AC52.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n067.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.97483587265 seconds
cpu usage
8.071854844
max memory
5.63146752E8
stage attributes
key
value
output-size
8704
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 56 ms] (2) EDP (3) EDPPoloProof [EQUIVALENT, 81 ms] (4) EDP (5) EDPPoloProof [EQUIVALENT, 17 ms] (6) EDP (7) PisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: times(plus(x, y), z) -> plus(times(x, z), times(y, z)) times(z, plus(x, f(y))) -> times(g(z, y), plus(x, a)) 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) EquationalDependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem: The TRS P consists of the following rules: TIMES(plus(x, y), z) -> TIMES(x, z) TIMES(plus(x, y), z) -> TIMES(y, z) TIMES(z, plus(x, f(y))) -> TIMES(g(z, y), plus(x, a)) TIMES(times(plus(x, y), z), ext) -> TIMES(plus(times(x, z), times(y, z)), ext) TIMES(times(plus(x, y), z), ext) -> TIMES(x, z) TIMES(times(plus(x, y), z), ext) -> TIMES(y, z) TIMES(times(z, plus(x, f(y))), ext) -> TIMES(times(g(z, y), plus(x, a)), ext) TIMES(times(z, plus(x, f(y))), ext) -> TIMES(g(z, y), plus(x, a)) The TRS R consists of the following rules: times(plus(x, y), z) -> plus(times(x, z), times(y, z)) times(z, plus(x, f(y))) -> times(g(z, y), plus(x, a)) times(times(plus(x, y), z), ext) -> times(plus(times(x, z), times(y, z)), ext) times(times(z, plus(x, f(y))), ext) -> times(times(g(z, y), plus(x, a)), ext) 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 set E# consists of the following equations: TIMES(x, y) == TIMES(y, x) TIMES(times(x, y), z) == TIMES(x, times(y, z)) We have to consider all minimal (P,E#,R,E)-chains ---------------------------------------- (2) Obligation: The TRS P consists of the following rules: TIMES(plus(x, y), z) -> TIMES(x, z) TIMES(plus(x, y), z) -> TIMES(y, z) TIMES(z, plus(x, f(y))) -> TIMES(g(z, y), plus(x, a)) TIMES(times(plus(x, y), z), ext) -> TIMES(plus(times(x, z), times(y, z)), ext) TIMES(times(plus(x, y), z), ext) -> TIMES(x, z) TIMES(times(plus(x, y), z), ext) -> TIMES(y, z) TIMES(times(z, plus(x, f(y))), ext) -> TIMES(times(g(z, y), plus(x, a)), ext) TIMES(times(z, plus(x, f(y))), ext) -> TIMES(g(z, y), plus(x, a)) The TRS R consists of the following rules: times(plus(x, y), z) -> plus(times(x, z), times(y, z)) times(z, plus(x, f(y))) -> times(g(z, y), plus(x, a)) times(times(plus(x, y), z), ext) -> times(plus(times(x, z), times(y, z)), ext) times(times(z, plus(x, f(y))), ext) -> times(times(g(z, y), plus(x, a)), ext)
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