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TRS Stand 20472 pair #381711547
details
property
value
status
complete
benchmark
divhard.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.375393152237 seconds
cpu usage
0.36538087
max memory
1.8653184E7
stage attributes
key
value
output-size
2047
starexec-result
MAYBE
output
/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o div : [o * o] --> o false : [] --> o ge : [o * o] --> o gt : [o * o] --> o if : [o * o * o] --> o if1 : [o * o * o] --> o if2 : [o * o * o] --> o minus : [o * o] --> o p : [o] --> o s : [o] --> o true : [] --> o minus(X, Y) => if(gt(X, Y), X, Y) if(true, X, Y) => s(minus(p(X), Y)) if(false, X, Y) => 0 p(0) => 0 p(s(X)) => X ge(X, 0) => true ge(0, s(X)) => false ge(s(X), s(Y)) => ge(X, Y) gt(0, X) => false gt(s(X), 0) => true gt(s(X), s(Y)) => gt(X, Y) div(X, Y) => if1(ge(X, Y), X, Y) if1(true, X, Y) => if2(gt(Y, 0), X, Y) if1(false, X, Y) => 0 if2(true, X, Y) => s(div(minus(X, Y), Y)) if2(false, X, Y) => 0 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 : [] --> qe div : [qe * qe] --> qe false : [] --> rd ge : [qe * qe] --> rd gt : [qe * qe] --> rd if : [rd * qe * qe] --> qe if1 : [rd * qe * qe] --> qe if2 : [rd * qe * qe] --> qe minus : [qe * qe] --> qe p : [qe] --> qe s : [qe] --> qe true : [] --> rd +++ 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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