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TRS Stand 20472 pair #381715615
details
property
value
status
complete
benchmark
Ex9_BLR02_C.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)
0.833158016205 seconds
cpu usage
0.820576483
max memory
2.4424448E7
stage attributes
key
value
output-size
31146
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 filter : [o * o * o] --> o mark : [o] --> o nats : [o] --> o ok : [o] --> o proper : [o] --> o s : [o] --> o sieve : [o] --> o top : [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))))) active(filter(X, Y, Z)) => filter(active(X), Y, Z) active(filter(X, Y, Z)) => filter(X, active(Y), Z) active(filter(X, Y, Z)) => filter(X, Y, active(Z)) active(cons(X, Y)) => cons(active(X), Y) active(s(X)) => s(active(X)) active(sieve(X)) => sieve(active(X)) active(nats(X)) => nats(active(X)) filter(mark(X), Y, Z) => mark(filter(X, Y, Z)) filter(X, mark(Y), Z) => mark(filter(X, Y, Z)) filter(X, Y, mark(Z)) => mark(filter(X, Y, Z)) cons(mark(X), Y) => mark(cons(X, Y)) s(mark(X)) => mark(s(X)) sieve(mark(X)) => mark(sieve(X)) nats(mark(X)) => mark(nats(X)) proper(filter(X, Y, Z)) => filter(proper(X), proper(Y), proper(Z)) proper(cons(X, Y)) => cons(proper(X), proper(Y)) proper(0) => ok(0) proper(s(X)) => s(proper(X)) proper(sieve(X)) => sieve(proper(X)) proper(nats(X)) => nats(proper(X)) proper(zprimes) => ok(zprimes) filter(ok(X), ok(Y), ok(Z)) => ok(filter(X, Y, Z)) cons(ok(X), ok(Y)) => ok(cons(X, Y)) s(ok(X)) => ok(s(X)) sieve(ok(X)) => ok(sieve(X)) nats(ok(X)) => ok(nats(X)) top(mark(X)) => top(proper(X)) top(ok(X)) => top(active(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)) =#> cons#(0, filter(Y, Z, Z)) 1] active#(filter(cons(X, Y), 0, Z)) =#> filter#(Y, Z, Z) 2] active#(filter(cons(X, Y), s(Z), U)) =#> cons#(X, filter(Y, Z, U)) 3] active#(filter(cons(X, Y), s(Z), U)) =#> filter#(Y, Z, U) 4] active#(sieve(cons(0, X))) =#> cons#(0, sieve(X)) 5] active#(sieve(cons(0, X))) =#> sieve#(X) 6] active#(sieve(cons(s(X), Y))) =#> cons#(s(X), sieve(filter(Y, X, X))) 7] active#(sieve(cons(s(X), Y))) =#> s#(X) 8] active#(sieve(cons(s(X), Y))) =#> sieve#(filter(Y, X, X)) 9] active#(sieve(cons(s(X), Y))) =#> filter#(Y, X, X) 10] active#(nats(X)) =#> cons#(X, nats(s(X))) 11] active#(nats(X)) =#> nats#(s(X)) 12] active#(nats(X)) =#> s#(X) 13] active#(zprimes) =#> sieve#(nats(s(s(0)))) 14] active#(zprimes) =#> nats#(s(s(0))) 15] active#(zprimes) =#> s#(s(0)) 16] active#(zprimes) =#> s#(0) 17] active#(filter(X, Y, Z)) =#> filter#(active(X), Y, Z) 18] active#(filter(X, Y, Z)) =#> active#(X) 19] active#(filter(X, Y, Z)) =#> filter#(X, active(Y), Z) 20] active#(filter(X, Y, Z)) =#> active#(Y) 21] active#(filter(X, Y, Z)) =#> filter#(X, Y, active(Z)) 22] active#(filter(X, Y, Z)) =#> active#(Z) 23] active#(cons(X, Y)) =#> cons#(active(X), Y) 24] active#(cons(X, Y)) =#> active#(X) 25] active#(s(X)) =#> s#(active(X)) 26] active#(s(X)) =#> active#(X) 27] active#(sieve(X)) =#> sieve#(active(X)) 28] active#(sieve(X)) =#> active#(X) 29] active#(nats(X)) =#> nats#(active(X)) 30] active#(nats(X)) =#> active#(X) 31] filter#(mark(X), Y, Z) =#> filter#(X, Y, Z) 32] filter#(X, mark(Y), Z) =#> filter#(X, Y, Z) 33] filter#(X, Y, mark(Z)) =#> filter#(X, Y, Z) 34] cons#(mark(X), Y) =#> cons#(X, Y)
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