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TRS Stand 20472 pair #381715140
details
property
value
status
complete
benchmark
Ex1_GL02a_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.396685123444 seconds
cpu usage
0.380206593
max memory
1.4286848E7
stage attributes
key
value
output-size
20871
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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 eq : [o * o] --> o false : [] --> o inf : [o] --> o length : [o] --> o mark : [o] --> o nil : [] --> o s : [o] --> o take : [o * o] --> o true : [] --> o active(eq(0, 0)) => mark(true) active(eq(s(X), s(Y))) => mark(eq(X, Y)) active(eq(X, Y)) => mark(false) active(inf(X)) => mark(cons(X, inf(s(X)))) active(take(0, X)) => mark(nil) active(take(s(X), cons(Y, Z))) => mark(cons(Y, take(X, Z))) active(length(nil)) => mark(0) active(length(cons(X, Y))) => mark(s(length(Y))) mark(eq(X, Y)) => active(eq(X, Y)) mark(0) => active(0) mark(true) => active(true) mark(s(X)) => active(s(X)) mark(false) => active(false) mark(inf(X)) => active(inf(mark(X))) mark(cons(X, Y)) => active(cons(X, Y)) mark(take(X, Y)) => active(take(mark(X), mark(Y))) mark(nil) => active(nil) mark(length(X)) => active(length(mark(X))) eq(mark(X), Y) => eq(X, Y) eq(X, mark(Y)) => eq(X, Y) eq(active(X), Y) => eq(X, Y) eq(X, active(Y)) => eq(X, Y) s(mark(X)) => s(X) s(active(X)) => s(X) inf(mark(X)) => inf(X) inf(active(X)) => inf(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) take(mark(X), Y) => take(X, Y) take(X, mark(Y)) => take(X, Y) take(active(X), Y) => take(X, Y) take(X, active(Y)) => take(X, Y) length(mark(X)) => length(X) length(active(X)) => length(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#(eq(0, 0)) =#> mark#(true) 1] active#(eq(s(X), s(Y))) =#> mark#(eq(X, Y)) 2] active#(eq(s(X), s(Y))) =#> eq#(X, Y) 3] active#(eq(X, Y)) =#> mark#(false) 4] active#(inf(X)) =#> mark#(cons(X, inf(s(X)))) 5] active#(inf(X)) =#> cons#(X, inf(s(X))) 6] active#(inf(X)) =#> inf#(s(X)) 7] active#(inf(X)) =#> s#(X) 8] active#(take(0, X)) =#> mark#(nil) 9] active#(take(s(X), cons(Y, Z))) =#> mark#(cons(Y, take(X, Z))) 10] active#(take(s(X), cons(Y, Z))) =#> cons#(Y, take(X, Z)) 11] active#(take(s(X), cons(Y, Z))) =#> take#(X, Z) 12] active#(length(nil)) =#> mark#(0) 13] active#(length(cons(X, Y))) =#> mark#(s(length(Y))) 14] active#(length(cons(X, Y))) =#> s#(length(Y)) 15] active#(length(cons(X, Y))) =#> length#(Y) 16] mark#(eq(X, Y)) =#> active#(eq(X, Y)) 17] mark#(eq(X, Y)) =#> eq#(X, Y) 18] mark#(0) =#> active#(0) 19] mark#(true) =#> active#(true) 20] mark#(s(X)) =#> active#(s(X)) 21] mark#(s(X)) =#> s#(X) 22] mark#(false) =#> active#(false) 23] mark#(inf(X)) =#> active#(inf(mark(X))) 24] mark#(inf(X)) =#> inf#(mark(X)) 25] mark#(inf(X)) =#> mark#(X) 26] mark#(cons(X, Y)) =#> active#(cons(X, Y)) 27] mark#(cons(X, Y)) =#> cons#(X, Y) 28] mark#(take(X, Y)) =#> active#(take(mark(X), mark(Y))) 29] mark#(take(X, Y)) =#> take#(mark(X), mark(Y)) 30] mark#(take(X, Y)) =#> mark#(X) 31] mark#(take(X, Y)) =#> mark#(Y) 32] mark#(nil) =#> active#(nil)
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