details

property	value
status	complete
benchmark	AC49.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.65728 seconds
cpu usage	6.901
user time	6.64999
system time	0.251013
max virtual memory	1.8343376E7
max residence set size	452472.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 344 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 160 ms] (4) ETRS (5) RRRPoloETRSProof [EQUIVALENT, 238 ms] (6) ETRS (7) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (8) EDP (9) EDependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) ---------------------------------------- (1) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: app(cons(x, l), k) -> cons(x, app(l, k)) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(app(x_1, x_2)) = 2*x_1 + 2*x_1*x_2 + x_2 POL(cons(x_1, x_2)) = 1 + x_1 + x_1*x_2 + 2*x_2 POL(nil) = 0 POL(plus(x_1, x_2)) = 2 + 2*x_1 + x_1*x_2 + 2*x_2 POL(s(x_1)) = 3 + 2*x_1 POL(sum(x_1)) = x_1 ---------------------------------------- (2) Obligation: Equational rewrite system: The TRS R consists of the following rules: app(nil, k) -> k app(l, nil) -> l sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) popout

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all output return to TRS Equational