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	n141.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.12123 seconds
cpu usage	4.50701
user time	4.31936
system time	0.187652
max virtual memory	1.8343376E7
max residence set size	257732.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof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) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (7) EDP (8) PisEmptyProof [EQUIVALENT, 0 ms] (9) YES (10) EDP (11) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (12) EDP (13) EDPPoloProof [EQUIVALENT, 0 ms] (14) EDP (15) PisEmptyProof [EQUIVALENT, 0 ms] (16) YES (17) EDP (18) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (19) EDP (20) EDPPoloProof [EQUIVALENT, 0 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 ---------------------------------------- (2) Obligation: The TRS P consists of the following rules: EQ(s(x), s(y)) -> EQ(x, y) popout

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job log

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actions

all output return to TRS Equational