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TRS Stand 20472 pair #381715270
details
property
value
status
complete
benchmark
Ex5_DLMMU04_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n010.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
2.45275402069 seconds
cpu usage
2.444484383
max memory
4.012032E7
stage attributes
key
value
output-size
63688
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 incr : [o] --> o mark : [o] --> o nil : [] --> o oddNs : [] --> o ok : [o] --> o pair : [o * o] --> o pairNs : [] --> o proper : [o] --> o repItems : [o] --> o s : [o] --> o tail : [o] --> o take : [o * o] --> o top : [o] --> o zip : [o * o] --> o active(pairNs) => mark(cons(0, incr(oddNs))) active(oddNs) => mark(incr(pairNs)) active(incr(cons(X, Y))) => mark(cons(s(X), incr(Y))) active(take(0, X)) => mark(nil) active(take(s(X), cons(Y, Z))) => mark(cons(Y, take(X, Z))) active(zip(nil, X)) => mark(nil) active(zip(X, nil)) => mark(nil) active(zip(cons(X, Y), cons(Z, U))) => mark(cons(pair(X, Z), zip(Y, U))) active(tail(cons(X, Y))) => mark(Y) active(repItems(nil)) => mark(nil) active(repItems(cons(X, Y))) => mark(cons(X, cons(X, repItems(Y)))) active(cons(X, Y)) => cons(active(X), Y) active(incr(X)) => incr(active(X)) active(s(X)) => s(active(X)) active(take(X, Y)) => take(active(X), Y) active(take(X, Y)) => take(X, active(Y)) active(zip(X, Y)) => zip(active(X), Y) active(zip(X, Y)) => zip(X, active(Y)) active(pair(X, Y)) => pair(active(X), Y) active(pair(X, Y)) => pair(X, active(Y)) active(tail(X)) => tail(active(X)) active(repItems(X)) => repItems(active(X)) cons(mark(X), Y) => mark(cons(X, Y)) incr(mark(X)) => mark(incr(X)) s(mark(X)) => mark(s(X)) take(mark(X), Y) => mark(take(X, Y)) take(X, mark(Y)) => mark(take(X, Y)) zip(mark(X), Y) => mark(zip(X, Y)) zip(X, mark(Y)) => mark(zip(X, Y)) pair(mark(X), Y) => mark(pair(X, Y)) pair(X, mark(Y)) => mark(pair(X, Y)) tail(mark(X)) => mark(tail(X)) repItems(mark(X)) => mark(repItems(X)) proper(pairNs) => ok(pairNs) proper(cons(X, Y)) => cons(proper(X), proper(Y)) proper(0) => ok(0) proper(incr(X)) => incr(proper(X)) proper(oddNs) => ok(oddNs) proper(s(X)) => s(proper(X)) proper(take(X, Y)) => take(proper(X), proper(Y)) proper(nil) => ok(nil) proper(zip(X, Y)) => zip(proper(X), proper(Y)) proper(pair(X, Y)) => pair(proper(X), proper(Y)) proper(tail(X)) => tail(proper(X)) proper(repItems(X)) => repItems(proper(X)) cons(ok(X), ok(Y)) => ok(cons(X, Y)) incr(ok(X)) => ok(incr(X)) s(ok(X)) => ok(s(X)) take(ok(X), ok(Y)) => ok(take(X, Y)) zip(ok(X), ok(Y)) => ok(zip(X, Y)) pair(ok(X), ok(Y)) => ok(pair(X, Y)) tail(ok(X)) => ok(tail(X)) repItems(ok(X)) => ok(repItems(X)) top(mark(X)) => top(proper(X)) top(ok(X)) => top(active(X)) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): active(pairNs) >? mark(cons(0, incr(oddNs))) active(oddNs) >? mark(incr(pairNs)) active(incr(cons(X, Y))) >? mark(cons(s(X), incr(Y))) active(take(0, X)) >? mark(nil) active(take(s(X), cons(Y, Z))) >? mark(cons(Y, take(X, Z))) active(zip(nil, X)) >? mark(nil) active(zip(X, nil)) >? mark(nil) active(zip(cons(X, Y), cons(Z, U))) >? mark(cons(pair(X, Z), zip(Y, U))) active(tail(cons(X, Y))) >? mark(Y) active(repItems(nil)) >? mark(nil) active(repItems(cons(X, Y))) >? mark(cons(X, cons(X, repItems(Y))))
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