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TRS Stand 20472 pair #381716630
details
property
value
status
complete
benchmark
Ex14_AEGL02_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.453635931015 seconds
cpu usage
0.330485799
max memory
9711616.0
stage attributes
key
value
output-size
21298
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o active : [o] --> o cons : [o * o] --> o from : [o] --> o length : [o] --> o length1 : [o] --> o mark : [o] --> o nil : [] --> o s : [o] --> o active(from(X)) => mark(cons(X, from(s(X)))) active(length(nil)) => mark(0) active(length(cons(X, Y))) => mark(s(length1(Y))) active(length1(X)) => mark(length(X)) mark(from(X)) => active(from(mark(X))) mark(cons(X, Y)) => active(cons(mark(X), Y)) mark(s(X)) => active(s(mark(X))) mark(length(X)) => active(length(X)) mark(nil) => active(nil) mark(0) => active(0) mark(length1(X)) => active(length1(X)) from(mark(X)) => from(X) from(active(X)) => from(X) cons(mark(X), Y) => cons(X, Y) cons(X, mark(Y)) => cons(X, Y) cons(active(X), Y) => cons(X, Y) cons(X, active(Y)) => cons(X, Y) s(mark(X)) => s(X) s(active(X)) => s(X) length(mark(X)) => length(X) length(active(X)) => length(X) length1(mark(X)) => length1(X) length1(active(X)) => length1(X) We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]). We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] active#(from(X)) =#> mark#(cons(X, from(s(X)))) 1] active#(from(X)) =#> cons#(X, from(s(X))) 2] active#(from(X)) =#> from#(s(X)) 3] active#(from(X)) =#> s#(X) 4] active#(length(nil)) =#> mark#(0) 5] active#(length(cons(X, Y))) =#> mark#(s(length1(Y))) 6] active#(length(cons(X, Y))) =#> s#(length1(Y)) 7] active#(length(cons(X, Y))) =#> length1#(Y) 8] active#(length1(X)) =#> mark#(length(X)) 9] active#(length1(X)) =#> length#(X) 10] mark#(from(X)) =#> active#(from(mark(X))) 11] mark#(from(X)) =#> from#(mark(X)) 12] mark#(from(X)) =#> mark#(X) 13] mark#(cons(X, Y)) =#> active#(cons(mark(X), Y)) 14] mark#(cons(X, Y)) =#> cons#(mark(X), Y) 15] mark#(cons(X, Y)) =#> mark#(X) 16] mark#(s(X)) =#> active#(s(mark(X))) 17] mark#(s(X)) =#> s#(mark(X)) 18] mark#(s(X)) =#> mark#(X) 19] mark#(length(X)) =#> active#(length(X)) 20] mark#(length(X)) =#> length#(X) 21] mark#(nil) =#> active#(nil) 22] mark#(0) =#> active#(0) 23] mark#(length1(X)) =#> active#(length1(X)) 24] mark#(length1(X)) =#> length1#(X) 25] from#(mark(X)) =#> from#(X) 26] from#(active(X)) =#> from#(X) 27] cons#(mark(X), Y) =#> cons#(X, Y) 28] cons#(X, mark(Y)) =#> cons#(X, Y) 29] cons#(active(X), Y) =#> cons#(X, Y) 30] cons#(X, active(Y)) =#> cons#(X, Y) 31] s#(mark(X)) =#> s#(X) 32] s#(active(X)) =#> s#(X) 33] length#(mark(X)) =#> length#(X) 34] length#(active(X)) =#> length#(X) 35] length1#(mark(X)) =#> length1#(X) 36] length1#(active(X)) =#> length1#(X) Rules R_0: active(from(X)) => mark(cons(X, from(s(X)))) active(length(nil)) => mark(0) active(length(cons(X, Y))) => mark(s(length1(Y))) active(length1(X)) => mark(length(X)) mark(from(X)) => active(from(mark(X))) mark(cons(X, Y)) => active(cons(mark(X), Y)) mark(s(X)) => active(s(mark(X))) mark(length(X)) => active(length(X)) mark(nil) => active(nil)
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