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TRS Equational pair #487523109
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
n146.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.87155103683 seconds
cpu usage
7.066140913
max memory
4.60713984E8
stage attributes
key
value
output-size
4686
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 796 ms] (2) ETRS (3) EquationalDependencyPairsProof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:
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