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TRS Equat 89423 pair #381732738
details
property
value
status
complete
benchmark
AC53.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n104.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.00638794899 seconds
cpu usage
4.813785076
max memory
2.64933376E8
stage attributes
key
value
output-size
5978
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof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) EDP (5) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (6) EDP (7) EDPProblemToQDPProblemProof [EQUIVALENT, 0 ms] (8) QDP (9) MNOCProof [EQUIVALENT, 1 ms] (10) QDP (11) MRRProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: p(s(x)) -> x fac(0) -> s(0) fac(s(x)) -> times(s(x), fac(p(s(x)))) The set E consists of the following equations: times(x, y) == times(y, x) 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: FAC(s(x)) -> FAC(p(s(x))) FAC(s(x)) -> P(s(x)) The TRS R consists of the following rules: p(s(x)) -> x fac(0) -> s(0) fac(s(x)) -> times(s(x), fac(p(s(x)))) The set E consists of the following equations: times(x, y) == times(y, x) times(times(x, y), z) == times(x, times(y, z)) E# is empty. We have to consider all minimal (P,E#,R,E)-chains ---------------------------------------- (2) Obligation: The TRS P consists of the following rules: FAC(s(x)) -> FAC(p(s(x))) FAC(s(x)) -> P(s(x)) The TRS R consists of the following rules: p(s(x)) -> x fac(0) -> s(0) fac(s(x)) -> times(s(x), fac(p(s(x)))) The set E consists of the following equations: times(x, y) == times(y, x) times(times(x, y), z) == times(x, times(y, z)) E# is empty. We have to consider all minimal (P,E#,R,E)-chains ---------------------------------------- (3) EDependencyGraphProof (EQUIVALENT) The approximation of the Equational Dependency Graph [DA_STEIN] contains 1 SCC with 1 less node. ---------------------------------------- (4) Obligation:
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