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TRS Equational pair #487523307
details
property
value
status
complete
benchmark
AC43.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
Mixed_C
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.04089903831 seconds
cpu usage
4.483422369
max memory
2.502656E8
stage attributes
key
value
output-size
13408
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) EDP (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 6 ms] (9) EDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) EDP (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (14) EDP (15) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES (19) EDP (20) EDPPoloProof [EQUIVALENT, 0 ms] (21) EDP (22) EDependencyGraphProof [EQUIVALENT, 0 ms] (23) TRUE ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) gcd(0, y) -> y gcd(s(x), 0) -> s(x) gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) The set E consists of the following equations: gcd(x, y) == gcd(y, x) ---------------------------------------- (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: LE(s(x), s(y)) -> LE(x, y) MINUS(s(x), s(y)) -> MINUS(x, y) GCD(s(x), s(y)) -> IF_GCD(le(y, x), s(x), s(y)) GCD(s(x), s(y)) -> LE(y, x) IF_GCD(true, s(x), s(y)) -> GCD(minus(x, y), s(y)) IF_GCD(true, s(x), s(y)) -> MINUS(x, y) IF_GCD(false, s(x), s(y)) -> GCD(minus(y, x), s(x)) IF_GCD(false, s(x), s(y)) -> MINUS(y, x) The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) gcd(0, y) -> y gcd(s(x), 0) -> s(x) gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) The set E consists of the following equations: gcd(x, y) == gcd(y, x) The set E# consists of the following equations: GCD(x, y) == GCD(y, x) We have to consider all minimal (P,E#,R,E)-chains
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