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TRS Equat 89423 pair #381732664
details
property
value
status
complete
benchmark
AC45.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Mixed_C
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.13241100311 seconds
cpu usage
4.529445563
max memory
2.22052352E8
stage attributes
key
value
output-size
12870
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) EDP (6) EUsableRulesReductionPairsProof [EQUIVALENT, 8 ms] (7) EDP (8) PisEmptyProof [EQUIVALENT, 0 ms] (9) YES (10) EDP (11) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (12) EDP (13) EDPPoloProof [EQUIVALENT, 13 ms] (14) EDP (15) PisEmptyProof [EQUIVALENT, 0 ms] (16) YES (17) EDP (18) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (19) EDP (20) EDPPoloProof [EQUIVALENT, 13 ms] (21) EDP (22) PisEmptyProof [EQUIVALENT, 0 ms] (23) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) rm(n, nil) -> nil rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) if_rm(true, n, add(m, x)) -> rm(n, x) if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) purge(nil) -> nil purge(add(n, x)) -> add(n, purge(rm(n, x))) The set E consists of the following equations: eq(x, y) == eq(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: EQ(s(x), s(y)) -> EQ(x, y) RM(n, add(m, x)) -> IF_RM(eq(n, m), n, add(m, x)) RM(n, add(m, x)) -> EQ(n, m) IF_RM(true, n, add(m, x)) -> RM(n, x) IF_RM(false, n, add(m, x)) -> RM(n, x) PURGE(add(n, x)) -> PURGE(rm(n, x)) PURGE(add(n, x)) -> RM(n, x) The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) rm(n, nil) -> nil rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) if_rm(true, n, add(m, x)) -> rm(n, x) if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) purge(nil) -> nil purge(add(n, x)) -> add(n, purge(rm(n, x))) The set E consists of the following equations: eq(x, y) == eq(y, x) The set E# consists of the following equations: EQ(x, y) == EQ(y, x) We have to consider all minimal (P,E#,R,E)-chains ----------------------------------------
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