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TRS Stand 20472 pair #381710896
details
property
value
status
complete
benchmark
gcd2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n104.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.734001159668 seconds
cpu usage
0.722342849
max memory
2.2421504E7
stage attributes
key
value
output-size
2128
starexec-result
MAYBE
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o false : [] --> o gcd : [o * o] --> o ge : [o * o] --> o gt : [o * o] --> o if : [o * o * o] --> o if1 : [o * o * o] --> o if2 : [o * o * o] --> o if3 : [o * o * o] --> o minus : [o * o] --> o s : [o] --> o true : [] --> o minus(s(X), Y) => if(gt(s(X), Y), X, Y) if(true, X, Y) => s(minus(X, Y)) if(false, X, Y) => 0 gcd(X, Y) => if1(ge(X, Y), X, Y) if1(true, X, Y) => if2(gt(Y, 0), X, Y) if1(false, X, Y) => if3(gt(X, 0), X, Y) if2(true, X, Y) => gcd(minus(X, Y), Y) if2(false, X, Y) => X if3(true, X, Y) => gcd(X, minus(Y, X)) if3(false, X, Y) => Y gt(0, X) => false gt(s(X), 0) => true gt(s(X), s(Y)) => gt(X, Y) ge(X, 0) => true ge(0, s(X)) => false ge(s(X), s(Y)) => ge(X, Y) As the system is orthogonal, it is terminating if it is innermost terminating by [Gra95]. Then, by [FuhGieParSchSwi11], it suffices to prove (innermost) termination of the typed system, with sort annotations chosen to respect the rules, as follows: 0 : [] --> ze false : [] --> df gcd : [ze * ze] --> ze ge : [ze * ze] --> df gt : [ze * ze] --> df if : [df * ze * ze] --> ze if1 : [df * ze * ze] --> ze if2 : [df * ze * ze] --> ze if3 : [df * ze * ze] --> ze minus : [ze * ze] --> ze s : [ze] --> ze true : [] --> df +++ Citations +++ [FuhGieParSchSwi11] C. Fuhs, J. Giesl, M. Parting, P. Schneider-Kamp, and S. Swiderski. Proving Termination by Dependency Pairs and Inductive Theorem Proving. In volume 47(2) of Journal of Automated Reasoning. 133--160, 2011. [Gra95] B. Gramlich. Abstract Relations Between Restricted Termination and Confluence Properties of Rewrite Systems. In volume 24(1-2) of Fundamentae Informaticae. 3--23, 1995.
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