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TRS Stand 20472 pair #381716970
details
property
value
status
complete
benchmark
Ex9_BLR02_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n003.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
1.41192507744 seconds
cpu usage
1.395635534
max memory
3.1629312E7
stage attributes
key
value
output-size
45891
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 filter : [o * o * o] --> o mark : [o] --> o nats : [o] --> o s : [o] --> o sieve : [o] --> o zprimes : [] --> o active(filter(cons(X, Y), 0, Z)) => mark(cons(0, filter(Y, Z, Z))) active(filter(cons(X, Y), s(Z), U)) => mark(cons(X, filter(Y, Z, U))) active(sieve(cons(0, X))) => mark(cons(0, sieve(X))) active(sieve(cons(s(X), Y))) => mark(cons(s(X), sieve(filter(Y, X, X)))) active(nats(X)) => mark(cons(X, nats(s(X)))) active(zprimes) => mark(sieve(nats(s(s(0))))) mark(filter(X, Y, Z)) => active(filter(mark(X), mark(Y), mark(Z))) mark(cons(X, Y)) => active(cons(mark(X), Y)) mark(0) => active(0) mark(s(X)) => active(s(mark(X))) mark(sieve(X)) => active(sieve(mark(X))) mark(nats(X)) => active(nats(mark(X))) mark(zprimes) => active(zprimes) filter(mark(X), Y, Z) => filter(X, Y, Z) filter(X, mark(Y), Z) => filter(X, Y, Z) filter(X, Y, mark(Z)) => filter(X, Y, Z) filter(active(X), Y, Z) => filter(X, Y, Z) filter(X, active(Y), Z) => filter(X, Y, Z) filter(X, Y, active(Z)) => filter(X, Y, Z) 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) sieve(mark(X)) => sieve(X) sieve(active(X)) => sieve(X) nats(mark(X)) => nats(X) nats(active(X)) => nats(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#(filter(cons(X, Y), 0, Z)) =#> mark#(cons(0, filter(Y, Z, Z))) 1] active#(filter(cons(X, Y), 0, Z)) =#> cons#(0, filter(Y, Z, Z)) 2] active#(filter(cons(X, Y), 0, Z)) =#> filter#(Y, Z, Z) 3] active#(filter(cons(X, Y), s(Z), U)) =#> mark#(cons(X, filter(Y, Z, U))) 4] active#(filter(cons(X, Y), s(Z), U)) =#> cons#(X, filter(Y, Z, U)) 5] active#(filter(cons(X, Y), s(Z), U)) =#> filter#(Y, Z, U) 6] active#(sieve(cons(0, X))) =#> mark#(cons(0, sieve(X))) 7] active#(sieve(cons(0, X))) =#> cons#(0, sieve(X)) 8] active#(sieve(cons(0, X))) =#> sieve#(X) 9] active#(sieve(cons(s(X), Y))) =#> mark#(cons(s(X), sieve(filter(Y, X, X)))) 10] active#(sieve(cons(s(X), Y))) =#> cons#(s(X), sieve(filter(Y, X, X))) 11] active#(sieve(cons(s(X), Y))) =#> s#(X) 12] active#(sieve(cons(s(X), Y))) =#> sieve#(filter(Y, X, X)) 13] active#(sieve(cons(s(X), Y))) =#> filter#(Y, X, X) 14] active#(nats(X)) =#> mark#(cons(X, nats(s(X)))) 15] active#(nats(X)) =#> cons#(X, nats(s(X))) 16] active#(nats(X)) =#> nats#(s(X)) 17] active#(nats(X)) =#> s#(X) 18] active#(zprimes) =#> mark#(sieve(nats(s(s(0))))) 19] active#(zprimes) =#> sieve#(nats(s(s(0)))) 20] active#(zprimes) =#> nats#(s(s(0))) 21] active#(zprimes) =#> s#(s(0)) 22] active#(zprimes) =#> s#(0) 23] mark#(filter(X, Y, Z)) =#> active#(filter(mark(X), mark(Y), mark(Z))) 24] mark#(filter(X, Y, Z)) =#> filter#(mark(X), mark(Y), mark(Z)) 25] mark#(filter(X, Y, Z)) =#> mark#(X) 26] mark#(filter(X, Y, Z)) =#> mark#(Y) 27] mark#(filter(X, Y, Z)) =#> mark#(Z) 28] mark#(cons(X, Y)) =#> active#(cons(mark(X), Y)) 29] mark#(cons(X, Y)) =#> cons#(mark(X), Y) 30] mark#(cons(X, Y)) =#> mark#(X) 31] mark#(0) =#> active#(0) 32] mark#(s(X)) =#> active#(s(mark(X))) 33] mark#(s(X)) =#> s#(mark(X)) 34] mark#(s(X)) =#> mark#(X) 35] mark#(sieve(X)) =#> active#(sieve(mark(X))) 36] mark#(sieve(X)) =#> sieve#(mark(X)) 37] mark#(sieve(X)) =#> mark#(X) 38] mark#(nats(X)) =#> active#(nats(mark(X))) 39] mark#(nats(X)) =#> nats#(mark(X)) 40] mark#(nats(X)) =#> mark#(X) 41] mark#(zprimes) =#> active#(zprimes) 42] filter#(mark(X), Y, Z) =#> filter#(X, Y, Z)
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