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TRS Stand 20472 pair #381715960
details
property
value
status
complete
benchmark
MYNAT_nokinds_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n191.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
2.99237084389 seconds
cpu usage
2.868583152
max memory
3.8510592E7
stage attributes
key
value
output-size
64516
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 U11 : [o * o] --> o U21 : [o * o * o] --> o U31 : [o] --> o U41 : [o * o * o] --> o active : [o] --> o and : [o * o] --> o isNat : [o] --> o mark : [o] --> o plus : [o * o] --> o s : [o] --> o tt : [] --> o x : [o * o] --> o active(U11(tt, X)) => mark(X) active(U21(tt, X, Y)) => mark(s(plus(Y, X))) active(U31(tt)) => mark(0) active(U41(tt, X, Y)) => mark(plus(x(Y, X), Y)) active(and(tt, X)) => mark(X) active(isNat(0)) => mark(tt) active(isNat(plus(X, Y))) => mark(and(isNat(X), isNat(Y))) active(isNat(s(X))) => mark(isNat(X)) active(isNat(x(X, Y))) => mark(and(isNat(X), isNat(Y))) active(plus(X, 0)) => mark(U11(isNat(X), X)) active(plus(X, s(Y))) => mark(U21(and(isNat(Y), isNat(X)), Y, X)) active(x(X, 0)) => mark(U31(isNat(X))) active(x(X, s(Y))) => mark(U41(and(isNat(Y), isNat(X)), Y, X)) mark(U11(X, Y)) => active(U11(mark(X), Y)) mark(tt) => active(tt) mark(U21(X, Y, Z)) => active(U21(mark(X), Y, Z)) mark(s(X)) => active(s(mark(X))) mark(plus(X, Y)) => active(plus(mark(X), mark(Y))) mark(U31(X)) => active(U31(mark(X))) mark(0) => active(0) mark(U41(X, Y, Z)) => active(U41(mark(X), Y, Z)) mark(x(X, Y)) => active(x(mark(X), mark(Y))) mark(and(X, Y)) => active(and(mark(X), Y)) mark(isNat(X)) => active(isNat(X)) U11(mark(X), Y) => U11(X, Y) U11(X, mark(Y)) => U11(X, Y) U11(active(X), Y) => U11(X, Y) U11(X, active(Y)) => U11(X, Y) U21(mark(X), Y, Z) => U21(X, Y, Z) U21(X, mark(Y), Z) => U21(X, Y, Z) U21(X, Y, mark(Z)) => U21(X, Y, Z) U21(active(X), Y, Z) => U21(X, Y, Z) U21(X, active(Y), Z) => U21(X, Y, Z) U21(X, Y, active(Z)) => U21(X, Y, Z) s(mark(X)) => s(X) s(active(X)) => s(X) plus(mark(X), Y) => plus(X, Y) plus(X, mark(Y)) => plus(X, Y) plus(active(X), Y) => plus(X, Y) plus(X, active(Y)) => plus(X, Y) U31(mark(X)) => U31(X) U31(active(X)) => U31(X) U41(mark(X), Y, Z) => U41(X, Y, Z) U41(X, mark(Y), Z) => U41(X, Y, Z) U41(X, Y, mark(Z)) => U41(X, Y, Z) U41(active(X), Y, Z) => U41(X, Y, Z) U41(X, active(Y), Z) => U41(X, Y, Z) U41(X, Y, active(Z)) => U41(X, Y, Z) x(mark(X), Y) => x(X, Y) x(X, mark(Y)) => x(X, Y) x(active(X), Y) => x(X, Y) x(X, active(Y)) => x(X, Y) and(mark(X), Y) => and(X, Y) and(X, mark(Y)) => and(X, Y) and(active(X), Y) => and(X, Y) and(X, active(Y)) => and(X, Y) isNat(mark(X)) => isNat(X) isNat(active(X)) => isNat(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(U11(tt, X)) >? mark(X) active(U21(tt, X, Y)) >? mark(s(plus(Y, X))) active(U31(tt)) >? mark(0) active(U41(tt, X, Y)) >? mark(plus(x(Y, X), Y)) active(and(tt, X)) >? mark(X) active(isNat(0)) >? mark(tt) active(isNat(plus(X, Y))) >? mark(and(isNat(X), isNat(Y))) active(isNat(s(X))) >? mark(isNat(X)) active(isNat(x(X, Y))) >? mark(and(isNat(X), isNat(Y))) active(plus(X, 0)) >? mark(U11(isNat(X), X)) active(plus(X, s(Y))) >? mark(U21(and(isNat(Y), isNat(X)), Y, X)) active(x(X, 0)) >? mark(U31(isNat(X)))
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