details

property	value
status	complete
benchmark	AC50.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n005.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	10.8382189274 seconds
cpu usage	9.673523877
max memory	6.71080448E8

stage attributes

key	value
output-size	4680
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 1127 ms] (2) ETRS (3) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (4) EDP (5) EDependencyGraphProof [EQUIVALENT, 0 ms] (6) 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))))) sum(cons(0, cons(plus(x, y), l))) -> pred(sum(cons(s(x), cons(y, l)))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) pred(cons(s(x), nil)) -> cons(x, nil) 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))))) sum(cons(0, cons(plus(x, y), l))) -> pred(sum(cons(s(x), cons(y, l)))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) pred(cons(s(x), nil)) -> cons(x, nil) 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(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) sum(cons(0, cons(plus(x, y), l))) -> pred(sum(cons(s(x), cons(y, l)))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) pred(cons(s(x), nil)) -> cons(x, nil) Used ordering: Polynomial interpretation [POLO]: POL(0) = 2 POL(app(x_1, x_2)) = 1 + 3*x_1 + 2*x_1*x_2 + x_2 POL(cons(x_1, x_2)) = 3 + 2*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(pred(x_1)) = 1 + x_1 POL(s(x_1)) = 3 + x_1 POL(sum(x_1)) = x_1 ---------------------------------------- (2) Obligation: Equational rewrite system: The TRS R consists of the following rules: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Equational