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TRS Stand 20472 pair #381716380
details
property
value
status
complete
benchmark
Ex2_Luc03b_FR.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
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.45194196701 seconds
cpu usage
0.448577656
max memory
1.3242368E7
stage attributes
key
value
output-size
25434
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 activate : [o] --> o add : [o * o] --> o cons : [o * o] --> o from : [o] --> o fst : [o * o] --> o len : [o] --> o n!6220!6220add : [o * o] --> o n!6220!6220from : [o] --> o n!6220!6220fst : [o * o] --> o n!6220!6220len : [o] --> o n!6220!6220s : [o] --> o nil : [] --> o s : [o] --> o fst(0, X) => nil fst(s(X), cons(Y, Z)) => cons(Y, n!6220!6220fst(activate(X), activate(Z))) from(X) => cons(X, n!6220!6220from(n!6220!6220s(X))) add(0, X) => X add(s(X), Y) => s(n!6220!6220add(activate(X), Y)) len(nil) => 0 len(cons(X, Y)) => s(n!6220!6220len(activate(Y))) fst(X, Y) => n!6220!6220fst(X, Y) from(X) => n!6220!6220from(X) s(X) => n!6220!6220s(X) add(X, Y) => n!6220!6220add(X, Y) len(X) => n!6220!6220len(X) activate(n!6220!6220fst(X, Y)) => fst(activate(X), activate(Y)) activate(n!6220!6220from(X)) => from(activate(X)) activate(n!6220!6220s(X)) => s(X) activate(n!6220!6220add(X, Y)) => add(activate(X), activate(Y)) activate(n!6220!6220len(X)) => len(activate(X)) activate(X) => 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] fst#(s(X), cons(Y, Z)) =#> activate#(X) 1] fst#(s(X), cons(Y, Z)) =#> activate#(Z) 2] add#(s(X), Y) =#> s#(n!6220!6220add(activate(X), Y)) 3] add#(s(X), Y) =#> activate#(X) 4] len#(cons(X, Y)) =#> s#(n!6220!6220len(activate(Y))) 5] len#(cons(X, Y)) =#> activate#(Y) 6] activate#(n!6220!6220fst(X, Y)) =#> fst#(activate(X), activate(Y)) 7] activate#(n!6220!6220fst(X, Y)) =#> activate#(X) 8] activate#(n!6220!6220fst(X, Y)) =#> activate#(Y) 9] activate#(n!6220!6220from(X)) =#> from#(activate(X)) 10] activate#(n!6220!6220from(X)) =#> activate#(X) 11] activate#(n!6220!6220s(X)) =#> s#(X) 12] activate#(n!6220!6220add(X, Y)) =#> add#(activate(X), activate(Y)) 13] activate#(n!6220!6220add(X, Y)) =#> activate#(X) 14] activate#(n!6220!6220add(X, Y)) =#> activate#(Y) 15] activate#(n!6220!6220len(X)) =#> len#(activate(X)) 16] activate#(n!6220!6220len(X)) =#> activate#(X) Rules R_0: fst(0, X) => nil fst(s(X), cons(Y, Z)) => cons(Y, n!6220!6220fst(activate(X), activate(Z))) from(X) => cons(X, n!6220!6220from(n!6220!6220s(X))) add(0, X) => X add(s(X), Y) => s(n!6220!6220add(activate(X), Y)) len(nil) => 0 len(cons(X, Y)) => s(n!6220!6220len(activate(Y))) fst(X, Y) => n!6220!6220fst(X, Y) from(X) => n!6220!6220from(X) s(X) => n!6220!6220s(X) add(X, Y) => n!6220!6220add(X, Y) len(X) => n!6220!6220len(X) activate(n!6220!6220fst(X, Y)) => fst(activate(X), activate(Y)) activate(n!6220!6220from(X)) => from(activate(X)) activate(n!6220!6220s(X)) => s(X) activate(n!6220!6220add(X, Y)) => add(activate(X), activate(Y)) activate(n!6220!6220len(X)) => len(activate(X)) activate(X) => X Thus, the original system is terminating if (P_0, R_0, minimal, formative) is finite. We consider the dependency pair problem (P_0, R_0, minimal, formative). We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows: * 0 : 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 * 1 : 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 * 2 : * 3 : 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
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