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TRS Stand 20472 pair #381715575
details
property
value
status
complete
benchmark
Ex23_Luc06_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n014.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.186131000519 seconds
cpu usage
0.181110078
max memory
4603904.0
stage attributes
key
value
output-size
6438
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. a : [] --> o active : [o] --> o c : [o] --> o f : [o] --> o g : [o] --> o mark : [o] --> o active(f(f(a))) => mark(c(f(g(f(a))))) mark(f(X)) => active(f(mark(X))) mark(a) => active(a) mark(c(X)) => active(c(X)) mark(g(X)) => active(g(mark(X))) f(mark(X)) => f(X) f(active(X)) => f(X) c(mark(X)) => c(X) c(active(X)) => c(X) g(mark(X)) => g(X) g(active(X)) => g(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#(f(f(a))) =#> mark#(c(f(g(f(a))))) 1] active#(f(f(a))) =#> c#(f(g(f(a)))) 2] active#(f(f(a))) =#> f#(g(f(a))) 3] active#(f(f(a))) =#> g#(f(a)) 4] active#(f(f(a))) =#> f#(a) 5] mark#(f(X)) =#> active#(f(mark(X))) 6] mark#(f(X)) =#> f#(mark(X)) 7] mark#(f(X)) =#> mark#(X) 8] mark#(a) =#> active#(a) 9] mark#(c(X)) =#> active#(c(X)) 10] mark#(c(X)) =#> c#(X) 11] mark#(g(X)) =#> active#(g(mark(X))) 12] mark#(g(X)) =#> g#(mark(X)) 13] mark#(g(X)) =#> mark#(X) 14] f#(mark(X)) =#> f#(X) 15] f#(active(X)) =#> f#(X) 16] c#(mark(X)) =#> c#(X) 17] c#(active(X)) =#> c#(X) 18] g#(mark(X)) =#> g#(X) 19] g#(active(X)) =#> g#(X) Rules R_0: active(f(f(a))) => mark(c(f(g(f(a))))) mark(f(X)) => active(f(mark(X))) mark(a) => active(a) mark(c(X)) => active(c(X)) mark(g(X)) => active(g(mark(X))) f(mark(X)) => f(X) f(active(X)) => f(X) c(mark(X)) => c(X) c(active(X)) => c(X) g(mark(X)) => g(X) g(active(X)) => g(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 : 9, 10 * 1 : * 2 : * 3 : * 4 : * 5 : 0, 1, 2, 3, 4 * 6 : 14, 15 * 7 : 5, 6, 7, 8, 9, 10, 11, 12, 13 * 8 : * 9 : * 10 : 16, 17 * 11 : * 12 : 18, 19 * 13 : 5, 6, 7, 8, 9, 10, 11, 12, 13 * 14 : 14, 15 * 15 : 14, 15 * 16 : 16, 17 * 17 : 16, 17 * 18 : 18, 19 * 19 : 18, 19 This graph has the following strongly connected components:
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